'Free to play' games have evolved over time to have more and more obscure monetization schemes. Humans are bad at making many decisions on a row and the developers have figured this out, so they tend to make things take more effort to figure out. The less clear it is what you're doing, the more likely you are to make a purchase that you wouldn't actually make with a clear head and perfect information.
You'll never find an actual price tag on a thing you want to buy. In League of Legends, for example, the new champion costs 7800 blue essence or 975 riot points. What does that even mean? Blue essence you get over time for playing the game, riot points you can buy with cash. 490 points for $5, with 'bonuses' if you buy in bulk. So Senna is priced at $9.95, but you can't spend exactly that amount. In this case the next highest amount you can actually spend is $10, so really close, but often that is not the case. They make you buy extra points and then you're committed to the platform by having more currency to spend later. But not too much more! You'll need to top up if you want to buy something else. The idea is you spend more now, so if you don't come back they get more than they would have with an actual price. And if you do come back you're hooked and more likely to spend more. And by having to look at all this math your brain gets a little overwhelmed, and if you have money to spare it's easy to just spend rather than work it out. They've also worked anchoring in there by giving you a base price for points but then giving you even more if you buy in bulk. Lots of marketing trickery going on.
MTG Arena has lots of this happening. Not necessarily maliciously evil, but it's certainly using things that worked in the past for other people and those things work by taking advantage of people. MTG Arena also seems to have extra systems making it more convoluted but I suspect this was more no one had an actual vision for how to do things so more people tacked things on that they thought was needed. It certainly has kept me from really figuring out what I should be doing to build a collection properly. But I've qualified for some sort of tournament so I need to play a wider variety of decks. So I need more cards. So I need to work this all out.
MTG Arena doesn't use a disenchanting system like Hearthstone does, so you never need to make a decision about keeping cards you've opened. You always keep them, you can't destroy them, and if you get more than the max amount you get a very minor boost elsewhere in your collection. I think this is an actively good decision. I've hated that I've had to blow up Hearthstone cards to build decks in the past because it actively hurts my collection to make short term progress and that's a bad feeling no matter which side you're on.
There are a bunch of different currencies going on. You've got gold, which you earn by doing daily quests and as tournament prizes. You've got gems, which you buy with money and earn as tournament prizes. You've got XP, which you earn by doing daily quests. You've got wildcards, which you earn by opening packs. You've got packs, which you can buy with gold, or gems, or cash, or earn as prizes, or earn from XP. And you have the individual cards that you can get by drafting, or playing sealed, or opening packs, or doing dailies, or as prizes, or from earning XP. They all switch back and forth in different ratios depending on different tournament formats!
But for now, all I really care about is getting more cards. How do I make best use of the different currencies in order to get more cards? Gold and gems are the two hard ones to look at, so I'll do the rest first and hope that makes it easier to look at those.
XP - There's a cap on how much XP you can earn and not really anything to spend it on. You can get at most 750 XP per day (first 10 wins and the daily quest) and every 1000 XP gets you a level on their mastery system. You do also get 3750 XP per week (first 15 wins) for a max of 9000 XP per week. There are 110 levels with rewards and 112 days in the season for a max of 144k xp. So you do have some extra to spare, but you really need to go hard to get all the rewards. (For every 1000 XP above the cap you get an extra uncommon for whatever that is worth.) You need to spend gems to get access to all the rewards, with the following being available.
everyone - 42 packs
old players - 6 packs, 10 uncommons
3400 gems - 20 packs, 2000 gems, 10k gold, 10 mythics, 3 rares
wildcards - These are how you actually make specific cards that you want. There are wildcards for each of the different types of cards (common, uncommon, rare, mythic) and nothing to do with them except trade them for cards. You earn more wildcards in one of three ways. You can open them in packs as a replacement for an actual card (1:3 packs for commons, 1:5 for uncommon, 1:24 for rare/mythic). For every 6 packs you open you get an uncommon wildcard and a rare wildcard. (Every 5 rare wildcards in this way are mythic instead.) And you can get wildcards out of 'the vault' which turns extra commons and uncommons into 3 uncommon, 2 rare, and 1 mythic wildcard. It takes 1000 extra commons to get this reward, with extra uncommons counting as 3 commons. You get these extras by opening packs and doing drafts/sealed events.
packs - Opening a pack gets you 5 commons, 2 uncommons, and a rare. (1 in 8 rares will be mythics instead) Getting your 5th copy of a common or uncommon gets you vault progress. A 5th copy of a rare gets converted into a different rare from the same set. If you own every rare you get 20 gems. Same with mythics except you get 40 gems when full. You also get 1/6th of an uncommon wildcard and 4/30ths of a rare wildcard and 1/30th of a mythic wildcard each time you open a pack.
individual card rewards - Daily reward uncommons have a 9/80 chance to become a rare and a 1/80 chance to become a mythic. If you already have 4 of the assigned card you get vault progress, 20 gems, or 40 gems.
gold - 1000 gold gets you a pack
gems - 200 gems gets you a pack
Ranked draft events cost 750 gems or 5000 gold. You draft 3 packs and keep the cards, with 5+ copies replaced by vault progress or 20/40 gems. You do not get wildcards from the packs. You do not get wildcard progress for opening packs. You do get 14 cards per pack instead of 8. You also earn prizes based on how well you do in the event, which are packs and gems. If you have a 30% win rate then you rate to get 1.23 packs and 153 gems. A 50% win rate is worth 1.33 packs and 347 gems. A 70% win rate is worth 1.62 packs and 672 gems.
Traditional draft costs 1500 gems with the same cards drafted. It's best of 3 instead of best of 1, and the prizes are spikier. A 30% match win rate is worth 1.85 packs and 244 gems. 50% gets you 4.4 packs and 1350 gems. 70% match win rate is 6.9 packs and 2361 gems.
Sealed aren't up right now, but the info for the last sealed shows it was 2000 gems to join and you got the cards from 6 packs. You don't get to rare draft them. You always won 3 packs and then scaling gems based on your wins. 30%-524, 50%-1002, 70%-1672
Standard events cost 95 gems or 500 gold. The rewards are gold and three uncommon cards. The cards have upgrade chances based on how many wins you get. The gold return is 230 for 30%, 410 for 50%, and 715 for 70%. As for card upgrades, you have a 7% chance of an upgrade with 4 or fewer wins,. A guaranteed upgrade (and 6% more) at 5 wins. And another guaranteed upgrade (and 5% more) at 6 or 7 wins.
Traditional standard is 190 gems or 1000 gold, with a best of 3 format. Prizes again are 3 uncommons and some gold. Gold returns are again spikier, with only 415 for 30%, 1470 for 50%, and 2396 for 70%. The card upgrades are better here, but not twice as good so you definitely lose out here compared to the best of 1 event.
Ok, so, let's assume I'll hit the 70% win rates for everything except ranked draft, where 50% is more reasonable. (The problem with ranked draft is it pairs by rating, not by record in the draft, so I expect to only play good players the whole time. The other events aren't on the ranking system so I expect to get a decent mix of everyone interested in playing events. Constructed I'd need an actual good deck to hit that, unfortunately, but let's pretend we get one.) For building a collection the main thing that matters is rares. Rare wildcards, in fact, since there are a lot of junk rares out there, but any rare is decent. For now I'm going to assert I get enough mythics, uncommons, and commons. I'm going to count a random rare as half as good as a rare wild card. Well, mythic wildcards I'll count as rare wildcards even though they're worse because if they're worth nothing I won't have enough and it makes things a little easier for my spreadsheet.
An opened pack is worth .7385 rares. Constructed uncommon rewards are actually worth .64 rares if you win 70% of the time. The best of 3 constructed uncommons are worth 1.16 rares. A limited pack is worth .557 rares, but you do get some selection in a draft and can choose to rare draft the shock lands and not the garbage rares. And if you do end up with most of the rares you can get small gem rebates.
So a ranked draft is 5000 gold or 750 gems for 2.65 rares and 347 gems. This is a better use of gems than buying packs (you spend the gems that would buy 2 packs to get 2.65 rares). It's actually a bad use of gold compared to buying packs.
A traditional draft is 1500 gems for 6.77 rares and 2361 gems. If you could actually win 70% of your matches this would be an absurd rate of return. I feel like this can't actually be a fair potential win rate. Looking at a 50% win rate is 4.94 rares and 1350 gems which is still really, really good.
Sealed is 5.56 rares and 1672 of your 2000 gems back. Or 1002 of your 2000 gems back at 50% win rate. So just worse than the traditional draft, but also probably an easier place to get a high win rate.
Standard events are both essentially infinite ways to grind up small amounts of value. They don't actually make wildcards is the big problem, so while you can still use the random rares they both seem good. They do also let you build up gold to spend on something else. That something else could be packs, but probably it should be drafts so that you can launder the gold into gems in order to do more drafts.
It's really not much clearer now than it was before, but I think what I've learned going forward is that sealed events are actually a pretty good deal. They only show up right after a set is released so saving up some gems to do some for the next set makes sense. Beyond that if you have a good constructed deck you should grind cards in constructed tournaments. Drafting should be used to convert gold into gems, and then the gems should be spent drafting or sealeding.
New cards likely get banned tomorrow, so it seems like I need to see what happens there, then build a new deck and play tournaments for uncommon upgrades. I should also spend most of my uncommon wild cards to make it more likely I get vault progress out of drafting.
Showing posts with label Crunching The Numbers. Show all posts
Showing posts with label Crunching The Numbers. Show all posts
Sunday, November 17, 2019
Saturday, November 24, 2018
Blood Bowl: Fireball The Orcs!
I played a game of Blood Bowl yesterday as Lizards against an Orc team that set itself up on the opening kick-off with 8 orcs in a little box in the backfield. Getting 8 coin flips to get a mighty blow hit on an orc seemed too good to pass up, so I threw my wizard at him. It ended up knocking 3 guys over and removing none of them, and ultimately the game ended up as a draw where he barely scored and I likely win the game 87% of the time if I'd kept the wizard for the lightning bolt on the ball carrier. It got me thinking about if I got played on the kickoff... Did I get unlucky to not hurt anyone or are orcs just tough enough that it was strong play from him to bait me into using the fireball.
I decided to do a spreadsheet to figure out the numbers and then discovered Excel just straight up has a function that does it for me. Hello BINOMDIST, thank you very much. Here are the odds against any number of 9AV targets (columns) of getting any number of KO+ removals (rows).
So I was 55% to remove 0 orcs when I shot a fireball at 8 of them. Maybe this play would make sense if I was desperate to get lucky, but I didn't need that at all. I'm convinced the attrition fireball was a mistake, and I definitely got baited.
On the other hand, if 7AV elves were to make the same offer we'd get the following:
Now we're 75% to get rid of at least one and have pretty good chances of removing multiples. They're also better at recovering from the lightning bolt, so if an elf team were to give me that opportunity I would jump all over it.
I decided to do a spreadsheet to figure out the numbers and then discovered Excel just straight up has a function that does it for me. Hello BINOMDIST, thank you very much. Here are the odds against any number of 9AV targets (columns) of getting any number of KO+ removals (rows).
So I was 55% to remove 0 orcs when I shot a fireball at 8 of them. Maybe this play would make sense if I was desperate to get lucky, but I didn't need that at all. I'm convinced the attrition fireball was a mistake, and I definitely got baited.
On the other hand, if 7AV elves were to make the same offer we'd get the following:
Now we're 75% to get rid of at least one and have pretty good chances of removing multiples. They're also better at recovering from the lightning bolt, so if an elf team were to give me that opportunity I would jump all over it.
Tuesday, August 22, 2017
Path of Exile: Perma-Freeze Bosses
I have been playing a lot of Path of Exile lately. My current character is running the freezing pulse skill gem because they added a unique jewel that buffs it and I had fun with it years ago. The goal of the build is to do a bunch of cold damage and inflict the 'freeze' debuff on all of the enemies. This means they can't take actions, which means they can't do damage, which means I get to be invincible! Mwahaha!
The theory turns out to be better than the practice, however. I can absolutely crush trash monsters but I've been having trouble with bosses. I've been trying to straddle a line of being able to still deal with bosses that aren't frozen so I've ended up with a mishmash of a build where I have some survivability and some freezability but not really enough of either. I will be getting more of both with more levels (both in terms of getting more passive points in the tree and in terms of leveling up my skill gems) but I'm starting to feel like I need to really go all in on one or the other. Running a bunch of curses and instant leech and the like is fine if enemies aren't frozen but if they are then it's not really doing anything for me and maybe I'll be better off without 4 item slots dedicated to doing all my cursing.
Alternatively maybe I'm better off doing all the cursing and leeching without worrying about freezing at all. If I'm building up to being able to leech tank bosses I can do the same for all the trash too and I'd be better off without all the freeze related points in the tree. At that point I may even be better off just using a different spell entirely!
So I think the way to proceed is to work out what I could do to go all in on freezing. See if I think that'd be good enough to freeze some bosses. If so, great! If not, well, probably start a new dude.
Ok, so, freezing... What are the specific mechanics behind freezing enemies? For our purposes only cold damage can freeze and a hit of cold damage will freeze if two conditions are met:
- The hit is a crit OR an inate 'chance to freeze' roll succeeds.
- The hit does enough damage to freeze the enemy for .3 seconds, which at base means doing 5% of the enemy's max health in cold damage.
The first condition is relatively easy to meet. In my current setup I have a 19% chance to crit, 20% chance to freeze, 20% chance to freeze a chilled enemy, 13% chance to freeze a frostbiten enemy, and somewhere from 0-25% chance to freeze based on distance from my character. So while not every hit will meet this check a significant number of them will. If bosses were getting frozen some but not all of the time I would worry more about working on this condition, but they aren't, so I won't.
The second condition is the one I'm getting stuck on. Having to hit a boss for 5% of their health in order to freeze them actually seems a little silly. If I only need to hit them 20 times in order to kill them I don't think I care that they're not frozen. I can kite and/or use flasks for the 7 seconds it'll take to burn them down! Fortunately damage isn't the only way to work on this condition. You can also work to extend the duration of your freezes so that smaller amounts of damage are good enough to hit the .3 second threshold. If you had 100% freeze duration you'd only need to hit them for 2.5% of their max health. 400% freeze duration would mean you only need to hit them for 1% of their max health. I'm not quite sure that would be good enough, and I really doubt I could get that much freeze duration anyway, but I might as well look into it.
Currently I have 60% increased freeze duration, which is every freeze duration node in the tree. There is one 10% ailment duration node which probably also applies, but I don't have. Other potential sources of freeze duration would be:
- jewels which can add up to 16% freeze duration each
- 20%+ freeze duration from quality on a frostbite gem (and maybe more if my curse nodes impact the quality boost)
- elemental proliferation support gem would be up to ~29% freeze duration (and 20% chance to freeze)
- The Halcyon unique amulet has 30% freeze duration (and 10% chance to freeze, and potentially 80% cold damage)
- Southbound unique gloves have 25% freeze duration
- Rashkaldor's Patience unique amulet had 20% elemental ailment duration
And that is all. The last two unique items don't feel very good while The Halcyon runs over 150 chaos to buy. I do have that much, and I suspect I can flip the amulet back if I don't like it, so possibly that is what I need to do if I'm going forward. I can probably grab jewel sockets to get 3 of those jewels, and I can easily get a quality frostbite gem. I currently need my amulet for life and resists, so switching to The Halcyon hurts my health to the point where I probably need to give up on the Kitava's Thirst 4-curse plan. I also _might_ be able to stretch my tree to get that last 10% ailment node at the assassin start location.
All told I can probably get my freeze duration up to 164% without elemental proliferation and 203% with it. That's almost twice what I'm currently sitting at (303 compared to 160) which almost certainly gets me a little closer to freezing some bosses. That's enough that it's probably worth working on...
On top of that, I can also work on doing more cold damage. With all the freeze duration I can manage I only need to do enough damage to hit for 1.7% of the enemy's max health. I'm still not sure if that is good enough... That's 60 hits to kill them, and I attack almost 3 times per second, so it's probably trivializing a fight that would be lasting 25 seconds otherwise? That's actually a lot of dodging... I don't think I can facetank a lot of these fights for 25 seconds with my current setup, so it is probably worth trying. But let's max out our damage too...
Initially my thinking was that if I'm doing a perma-freeze plan I don't want to be relying on the swings involved in crits. So I've taken the node that makes me do 40% more damage if I've crit in the last 8 seconds. This is way better for consistent damage and it saves me taking crit nodes but it's entirely possible I could be freezing some of the time with crits instead of the current none of the time. At this point I'm really committed to this line I think (I'd want a different bandit reward and probably an entirely different class for critting) but maybe I want to create a different character to do crit freezing pulse...
Anyway, with crits totally abstracted away there are really 4 ways to boost the damage of my spell. I can increase the base cold damage of the spell with flat damage (including leveling the gem itself), I can add to the 'increased damage' multiplier in a variety of ways, I can get extra 'more damage' multipliers, and I can lower the enemy cold resistance.
There are so many ways to change all of those things so I went and built a spreadsheet. It was a little surprising to me in some ways, in particular that a level 4 empower gem isn't really worth using. I suspect that's because of how much flat damage I'm adding to the spell via herald of ice? It means there isn't a red gem worth using which makes me sad... I'm going to have to spend a bunch of chromatics to change my 6 link away from BBGGGR into BBBGGG. (I only have a level 2 empower gem anyway...)
At any rate, here's the support gem ordering for different criteria:
30 cold resist (standard boss), freeze duration - controlled destruction > hypothermia > ice bite > slower projectiles > empower (4) > cold penetration > unbounded ailments > added cold damage > pierce > efficacy > empower (3) > elemental proliferation > iron will > empower (2) > faster projectiles > faster casting > spell echo
30 cold resist (standard boss), DPS - spell echo > controlled destruction > ice bite > hypothermia > faster casting > slower projectiles > empower (4) > cold penetration > added cold damage > pierce > efficacy > empower (3) > iron will > faster projectiles > empower (2) > elemental proliferation = unbounded ailments
85 cold resist (cold boss), freeze duration - controlled destruction > hypothermia > cold penetration > ice bite > slower projectiles > empower (4) > unbounded ailments > added cold damage > pierce > efficacy > empower (3) > elemental proliferation > iron will > empower (2) > faster projectiles > faster casting > spell echo
85 cold resist (cold boss), DPS - spell echo > controlled destruction > ice bite > hypothermia > cold penetration > faster casting > slower projectiles > empower (4) > added cold damage > pierce > efficacy > empower (3) > iron will > faster projectiles > empower (2) > elemental proliferation = unbounded ailments
Basically it seems I have enough spell penetration that unless a boss is overcapped it barely isn't worth using the cold pen gem. This is only true if frost bomb is up, and that's not a given.
The spreadsheet wants me to use slower projectiles, but the spreadsheet don't understand that freezing pulse loses damage the longer it travels so slower projectiles has an invisible less damage multiplier in it. This depends on how close I get to the enemies, and it really hurts my trash clear because the size of my attack is based on how fast it travels. Similarly the faster projectiles damage is better than it seems here (but it still seems quite bad).
Spell echo is the best for doing damage, but it's actively bad at freezing a boss. This means I may want to carry one around to swap in on bosses I can't freeze? I suspect I'd rather have faster casting instead for mobility reasons if I can't freeze the boss? Hard to say.
Ice bite looks good, but that's because it's a way to get frenzy charges. If I can get the charges up then it is worth using. If I can't then it's trash. You get them for killing frozen enemies, which will happen all the time on trash and on boss fights with tons of adds but never on a standalone boss.
I think what I'm ultimately going to want to run is controlled destruction, hypothermia, ice bite, cold penetration, and faster casting. It feels like a good setup for trash with a reasonable shot at freezing most bosses. I can swap in a slower projectiles for the ice bite when I can't keep up the frenzy charges and just get right up in the single boss' face. Either way I do want my colours to be BBBGGG so I should get on that.
The theory turns out to be better than the practice, however. I can absolutely crush trash monsters but I've been having trouble with bosses. I've been trying to straddle a line of being able to still deal with bosses that aren't frozen so I've ended up with a mishmash of a build where I have some survivability and some freezability but not really enough of either. I will be getting more of both with more levels (both in terms of getting more passive points in the tree and in terms of leveling up my skill gems) but I'm starting to feel like I need to really go all in on one or the other. Running a bunch of curses and instant leech and the like is fine if enemies aren't frozen but if they are then it's not really doing anything for me and maybe I'll be better off without 4 item slots dedicated to doing all my cursing.
Alternatively maybe I'm better off doing all the cursing and leeching without worrying about freezing at all. If I'm building up to being able to leech tank bosses I can do the same for all the trash too and I'd be better off without all the freeze related points in the tree. At that point I may even be better off just using a different spell entirely!
So I think the way to proceed is to work out what I could do to go all in on freezing. See if I think that'd be good enough to freeze some bosses. If so, great! If not, well, probably start a new dude.
Ok, so, freezing... What are the specific mechanics behind freezing enemies? For our purposes only cold damage can freeze and a hit of cold damage will freeze if two conditions are met:
- The hit is a crit OR an inate 'chance to freeze' roll succeeds.
- The hit does enough damage to freeze the enemy for .3 seconds, which at base means doing 5% of the enemy's max health in cold damage.
The first condition is relatively easy to meet. In my current setup I have a 19% chance to crit, 20% chance to freeze, 20% chance to freeze a chilled enemy, 13% chance to freeze a frostbiten enemy, and somewhere from 0-25% chance to freeze based on distance from my character. So while not every hit will meet this check a significant number of them will. If bosses were getting frozen some but not all of the time I would worry more about working on this condition, but they aren't, so I won't.
The second condition is the one I'm getting stuck on. Having to hit a boss for 5% of their health in order to freeze them actually seems a little silly. If I only need to hit them 20 times in order to kill them I don't think I care that they're not frozen. I can kite and/or use flasks for the 7 seconds it'll take to burn them down! Fortunately damage isn't the only way to work on this condition. You can also work to extend the duration of your freezes so that smaller amounts of damage are good enough to hit the .3 second threshold. If you had 100% freeze duration you'd only need to hit them for 2.5% of their max health. 400% freeze duration would mean you only need to hit them for 1% of their max health. I'm not quite sure that would be good enough, and I really doubt I could get that much freeze duration anyway, but I might as well look into it.
Currently I have 60% increased freeze duration, which is every freeze duration node in the tree. There is one 10% ailment duration node which probably also applies, but I don't have. Other potential sources of freeze duration would be:
- jewels which can add up to 16% freeze duration each
- 20%+ freeze duration from quality on a frostbite gem (and maybe more if my curse nodes impact the quality boost)
- elemental proliferation support gem would be up to ~29% freeze duration (and 20% chance to freeze)
- The Halcyon unique amulet has 30% freeze duration (and 10% chance to freeze, and potentially 80% cold damage)
- Southbound unique gloves have 25% freeze duration
- Rashkaldor's Patience unique amulet had 20% elemental ailment duration
And that is all. The last two unique items don't feel very good while The Halcyon runs over 150 chaos to buy. I do have that much, and I suspect I can flip the amulet back if I don't like it, so possibly that is what I need to do if I'm going forward. I can probably grab jewel sockets to get 3 of those jewels, and I can easily get a quality frostbite gem. I currently need my amulet for life and resists, so switching to The Halcyon hurts my health to the point where I probably need to give up on the Kitava's Thirst 4-curse plan. I also _might_ be able to stretch my tree to get that last 10% ailment node at the assassin start location.
All told I can probably get my freeze duration up to 164% without elemental proliferation and 203% with it. That's almost twice what I'm currently sitting at (303 compared to 160) which almost certainly gets me a little closer to freezing some bosses. That's enough that it's probably worth working on...
On top of that, I can also work on doing more cold damage. With all the freeze duration I can manage I only need to do enough damage to hit for 1.7% of the enemy's max health. I'm still not sure if that is good enough... That's 60 hits to kill them, and I attack almost 3 times per second, so it's probably trivializing a fight that would be lasting 25 seconds otherwise? That's actually a lot of dodging... I don't think I can facetank a lot of these fights for 25 seconds with my current setup, so it is probably worth trying. But let's max out our damage too...
Initially my thinking was that if I'm doing a perma-freeze plan I don't want to be relying on the swings involved in crits. So I've taken the node that makes me do 40% more damage if I've crit in the last 8 seconds. This is way better for consistent damage and it saves me taking crit nodes but it's entirely possible I could be freezing some of the time with crits instead of the current none of the time. At this point I'm really committed to this line I think (I'd want a different bandit reward and probably an entirely different class for critting) but maybe I want to create a different character to do crit freezing pulse...
Anyway, with crits totally abstracted away there are really 4 ways to boost the damage of my spell. I can increase the base cold damage of the spell with flat damage (including leveling the gem itself), I can add to the 'increased damage' multiplier in a variety of ways, I can get extra 'more damage' multipliers, and I can lower the enemy cold resistance.
There are so many ways to change all of those things so I went and built a spreadsheet. It was a little surprising to me in some ways, in particular that a level 4 empower gem isn't really worth using. I suspect that's because of how much flat damage I'm adding to the spell via herald of ice? It means there isn't a red gem worth using which makes me sad... I'm going to have to spend a bunch of chromatics to change my 6 link away from BBGGGR into BBBGGG. (I only have a level 2 empower gem anyway...)
At any rate, here's the support gem ordering for different criteria:
30 cold resist (standard boss), freeze duration - controlled destruction > hypothermia > ice bite > slower projectiles > empower (4) > cold penetration > unbounded ailments > added cold damage > pierce > efficacy > empower (3) > elemental proliferation > iron will > empower (2) > faster projectiles > faster casting > spell echo
30 cold resist (standard boss), DPS - spell echo > controlled destruction > ice bite > hypothermia > faster casting > slower projectiles > empower (4) > cold penetration > added cold damage > pierce > efficacy > empower (3) > iron will > faster projectiles > empower (2) > elemental proliferation = unbounded ailments
85 cold resist (cold boss), freeze duration - controlled destruction > hypothermia > cold penetration > ice bite > slower projectiles > empower (4) > unbounded ailments > added cold damage > pierce > efficacy > empower (3) > elemental proliferation > iron will > empower (2) > faster projectiles > faster casting > spell echo
85 cold resist (cold boss), DPS - spell echo > controlled destruction > ice bite > hypothermia > cold penetration > faster casting > slower projectiles > empower (4) > added cold damage > pierce > efficacy > empower (3) > iron will > faster projectiles > empower (2) > elemental proliferation = unbounded ailments
Basically it seems I have enough spell penetration that unless a boss is overcapped it barely isn't worth using the cold pen gem. This is only true if frost bomb is up, and that's not a given.
The spreadsheet wants me to use slower projectiles, but the spreadsheet don't understand that freezing pulse loses damage the longer it travels so slower projectiles has an invisible less damage multiplier in it. This depends on how close I get to the enemies, and it really hurts my trash clear because the size of my attack is based on how fast it travels. Similarly the faster projectiles damage is better than it seems here (but it still seems quite bad).
Spell echo is the best for doing damage, but it's actively bad at freezing a boss. This means I may want to carry one around to swap in on bosses I can't freeze? I suspect I'd rather have faster casting instead for mobility reasons if I can't freeze the boss? Hard to say.
Ice bite looks good, but that's because it's a way to get frenzy charges. If I can get the charges up then it is worth using. If I can't then it's trash. You get them for killing frozen enemies, which will happen all the time on trash and on boss fights with tons of adds but never on a standalone boss.
I think what I'm ultimately going to want to run is controlled destruction, hypothermia, ice bite, cold penetration, and faster casting. It feels like a good setup for trash with a reasonable shot at freezing most bosses. I can swap in a slower projectiles for the ice bite when I can't keep up the frenzy charges and just get right up in the single boss' face. Either way I do want my colours to be BBBGGG so I should get on that.
Thursday, June 22, 2017
WBC: Expected Laurel Case Studies
During this week's Agricola stream we had a bit of a side discussion going about laurels at WBC based off of my last post. Of particular concern was that I may not be properly considering the time invested in making it to the semis which dovetailed into the idea that even if we can use the butt-hour formula (which determines prize levels) to approximate available laurels that it may not hold across different tournament formats. By this I mean that maybe a single elimination tournament is just more efficient than a heats into semifinal tournament. Or, as Randy suspected, the opposite may be true. Twilight Struggle was the game that was brought up as a particular example. My gut feeling is that Twilight Struggle is an excellent game to play, if you are good at it, because it is a skill intensive game with a ton of laurels on the line. Randy thought that the amount of time you need to invest in a day long tournament (it's 5 3-hour rounds all in one day with a final afterwards) would be a huge problem.
I suspect it would probably be a problem because losing an entire day probably kills off a bunch of other tournaments. But my gut feeling is that that's only a problem for someone who plays other games and would be looking to add another and not something intrinsic to the single elimination format. So it's probably a terrible game for Randy or I to pick up in a quest for Consul, but that someone could build a Consul plan around it. But I don't want to just go on gut feelings, I want to crunch some numbers!
Another game that came up was Advanced Civ. It was brought up as being way too much time for the potential payout and my response was that it was likely true, but only because the formula caps at 6 and that Advanced Civ was probably worth about a 10 because of how many hours get invested and therefore it's a bad play because of formula inefficiency. So I wanted to check into that... Turns out I definitely have egg on my face here because it only has a 5 prize level! Having to sink 16 or 24 hours into a game is a really big investment, especially compared to Stone Age only needing 10 hours. But actually, maybe your odds of earning laurels could be a lot higher? (Keven Youells has earned laurels in it for 14 straight years...)
So I want to crunch some numbers for a few games to see how things line up with a couple assumptions. After that I'll decide if I care enough to go through all of the games or maybe if I'll learn some shortcuts that can be used to make assumptions about the rest of the games? Who knows!
Twilight Struggle
This game is run swiss style, but they play until they have 2 undefeated people and then only those two play in the finals. So it's basically single elimination when it comes to 1st or 2nd, but for 3rd-6th you can keep playing after a loss. I'm going to assume you enjoy the game enough to keep playing with a single loss but will drop out with 2 losses. (Actually, the say they use strength of schedule to determine 3rd-6th, so probably I should assume a loss in one of the first 2 rounds is a drop.) The last couple years have seen attendance swing up barely above the magical 64 number so I'm actually surprised they've been able to finish in only 6 rounds. From the recap they had only 3 undefeated players after 4 rounds last year which really doesn't make sense. That implies only 48 people were really playing but they had 70 sign up. There were also only 2 draws in the whole event, so it isn't like that was eliminating people either. So there must have been quite a few people who showed up, won a round, and dropped. So I'm going to assume there are only 48 people in the tournament even if 70 show up, which will inflate the laurel numbers a little because in reality you could be the person who loses to someone who drops.
(Alternatively it could have gone 70->35->17->8->3 if one of the draws was between undefeated people in round 3. I'm not sure which is more likely to be honest. I should hedge a little and assume more like 54 people show up.)
Here are your potential outcomes, assuming a 50% chance to win each game.
50% - drop after 3 hours (0-1)
25% - drop after 6 hours (1-1)
6.25% - drop after 12 hours (2-2)
6.25% - drop after 15 hours (3-2)
3.125% - make finals
9.375% - make top 7
Twilight Struggle has 5 prizes, so you're looking at...
50% - 3 hours for 0 laurels
25% - 6 hours for 0 laurels
6.25% - 12 hours for 0 laurels
6.25% - 15 hours for 0 laurels
1.5625% - 18 hours for 50 laurels
1.5625% - 18 hours for 30 laurels
1.3393% - 15 hours for 20 laurels1.3393% - 15 hours for 15 laurels
1.3393% - 15 hours for 10 laurels
1.3393% - 15 hours for 5 laurels
1.3393% - 15 hours for 0 laurels
For a total EV of 2.1875 laurels earned for 6.65625 hours invested. Or .32 laurels per hour.
Your odds of winning are not going to be 50%, though. This is where a little bit of art needs to seep into our science. If we're looking at someone who is actively good at the game what are there odds of winning a game? Those odds would need to get worse as you got later in the tournament as the worse players would get removed from the pool. Looking at the laurel list the top player has a massive 443 laurels with second place having 161. There are many people with a significant number of laurels which makes me think this is a very high skill game. I think I want to start our mythical great player off with a 90% chance of winning in round 1 and linearly trend that down to 60% in the finals. That changes the above numbers to:
10% - 3 hours for 0 laurels
14.4% - 6 hours for 0 laurels
4.66% - 12 hours for 0 laurels
9.69% - 15 hours for 0 laurels
16.8% - 18 hours for 50 laurels
11.2% - 18 hours for 30 laurels
6.65% - 15 hours for 20 laurels6.65% - 15 hours for 15 laurels
6.65% - 15 hours for 10 laurels
6.65% - 15 hours for 5 laurels
6.65% - 15 hours for 0 laurels
For a total EV of 15.09 laurels earned for 13.2 hours invested. Or 1.14 laurels per hour. Better, but that actually doesn't feel very good...
Advanced Civilization
This game plays two heats and then advances the top 8 players to a final. Each game is 8 hours in length and you can't leave partway through. They get around 40 players total, so if every player played in both heats you'd be looking at somewhere between 10 and 12 winners. I don't know how likely that is to happen. The recap for last year says they only had 9 people play in both heats, with 28 people in the first heat and 16 in the second heat. So they only had 6 games total, with one guy winning in both heats. Two of the winners didn't even show up for the finals, so they advanced 5 people who hadn't won a game. By the sounds of it, showing up for the finals after playing a decent game advanced you. But two years ago they had 8 games in the 2 heats with one double winner with all winners showing up and a very tight battle for closest 2nd...
To be safe, I think we need to assert that you need a win or a very close second to advance. If that isn't true, and it turns out to be a 'soft' game, then enough of us will show up to make it become true for future years. It seems like games in the heats are often 7 players, but they could be anywhere from 6 to 8.
This means that it's likely that the breakdown for this game is going to be:
1/7 - 8 hours to make finals
6/49 - 16 hours to make finals
36*2/49/8 - 16 hours to advance as a close second (assuming you play both heats and that 2 of 8 2nd placers advance)
55% - 16 hours for 0 laurels
Then once you're in the finals you need to commit another 8 hours for a 1 in 8 chance at each possible result. It's a 5 prize event, so 50-30-20-15-10-5-0-0. The math churns out to be 7.29 laurels for 18.4 hours, or .395 laurels per hour. Better than Twilight Struggle when the games are coin flips!
But Advanced Civ games are _not_ coin flips. There is definitely some randomness, but since there's a guy who laureled 14 years in a row I think it's pretty safe to say that someone who is really good at the game is going to be really good at the game. But how good is really good? Are they going to be 50% to win a heat against 6 other players? More than that? What about their finals odds?
I think I want to give the good player 50% to win a heat, 25% to come a close second. Finals odds I want to be 20-20-20-20-5-5-5-5. Advanced Civ is a game that ends at quasi-random times, especially in a final where people can be playing for best position as opposed to a heat where I wouldn't anticipate a lot of playing for 3rd or 4th.
This puts the EV at 22.2 laurels in 19.5 hours for an overall laurels per hour of 1.14. I swear I didn't cook these numbers... They really do round to the same as Twilight Struggle.
Thurn & Taxis
This game is run with 3 heats of 2 hours each. Winning a heat is good enough to advance to the quarterfinals but if you do particularly well you can earn a bye into the semis. This leads to two different possible plans... You can try to win a single heat and then sit the rest out or you can play every heat in an attempt to earn that bye. If Thurn is the game you care about you definitely want to try to earn that bye but if you're trying to maximize total laurels it likely depends what you could be doing with those time slots.
Last year had 36 people play in 3 heats, 51 people play in 2 heats, and 61 people play in a single heat. That means something like 70 games were played. I believe 4 people got byes to the semis which means 2 wins is not good enough for a bye. I don't know how to track things forward to future years, but I suspect a decent assumption would be that 3 wins is worth a bye to the semis and everyone else has to play the quarters. So my player is going to play at least two heats but only commit to playing the third heat if they have 0 or 2 wins.
1/64 - spend 6 hours to make semis (WWW)
3/64 - spend 6 hours to make quarters (WWL)
3/16 - spend 4 hours to make quarters (WL)
3/16 - spend 4 hours to make quarters (LW)
9/64 - spend 6 hours to make quarters (LLW)
27/64 - spend 6 hours to cry (LLL)
From there it's a bunch of number crunching because of the different number of hours that can be spent on each branch, but my spreadsheet spits out that you expect to earn 1.27 laurels after spending 6.77 hours, for .188 laurels per hour. Which makes T&T a worse use of time than the previous two games when every game is a coin flip! I suspect the reason for this is that no-skill semis are actually a real bad use of time and no-skill quarters are even worse. 94% of people not earning any laurels at all is pretty rough! I guess that's the downside to 150ish player fields compared to 40 player fields!
Anyway, how good can you be at T&T? This is a harder one for me to estimate because I simply don't grok the game at all. It has had repeat winners, I recognize the names of the winners as all being quite good at games, and the laurel list has some big numbers on top so there's definitely skill there. The TrueSkill list on Yucata makes me think it's more random than Stone Age, but still has a pretty high skill component. So I'm going to say our good player wins 45% of heats, 40% of QFs, 35% of SFs, and 30% of Fs.
Swapping in those win rates to my spreadsheet spits out 5.07 laurels in 8.27 hours, for .613 laurels per hour. Much worse than either of the last two games! Is that my being unfair to skill factors in the games, or is it just that the big Euro heat game is not a very good play for laurels? (Heats do get punished by the WBC butt-hour formula, for what it's worth.)
Innovation
Innovation is a super short single elimination tournament. Heats are scheduled for an hour but it's pretty likely 4 rounds will get compressed into 3 hours. I think I need to keep assuming every round is a full hour though, because sometimes slow people play... At any rate, I'll be considering it to be a mulligan + 6 rounds, with everyone who makes it to the 4th round getting laurels. (The game historically has had 6 people make it that far.) I'm also going to assert that if you win the mulligan you don't show for round 1, but if you lose it then you do.
In coinflip land, this means:
1/4 - out after 2 hours (LL)
1/4 - out after 2 hours (W-L)
1/8 - out after 3 hours (LWL)
1/8 - out after 3 hours (W-WL)
1/16 - out after 4 hours (LWWL)
3/16 - top 6
From there it actually gets a little tricky because of issues with byes/eliminators and that potential extra hour from the mulligan and round 1. Eugh. I'm going to assume the eliminator always loses, which is not true historically so maybe you should bump the numbers up a bit. With that assumption, off to the spreadsheet... (Oh, and Innovation is a trial, so it's only worth 20 laurels for 1st place.)
It pans out to earning 1.5 laurels for an investment of 2.95 hours. This means .508 laurels per hour which is our best coinflip rate so far! I suspect this is because not enough people play so first place shouldn't be worth 20 in a perfect world. So the people who do play get extra value for doing so?
How about a skill factor? Well, one person (Pounder) has made the finals in each of the last 4 years. We've played quite a few times for fun over the years and he routinely smashes me. I beat him once that I can remember (in the finals in 2015, hah!) but other than that I'm not sure I've ever beaten him. There are 7 rounds, so we need 7 win percentages. Round 1 should be the highest number since all the mulligan winners are taking that round off. I feel like I want the finals odds for our great player to be 60, so we'll use a similar scaling backwards thing that we did in Twilight Struggle? With the mulligan round being the same as round 2? So 84%-90%-84%-78%-72%-66%-60%.
Doing that gives us 7.13 laurels in 4.39 hours, or 1.63 laurels per hour. Unsurprisingly the highest coinflip game thus far is also the highest skilled game thus far. Is it fair to say Innovation is as skill intensive as Twilight Struggle?
Vegas Showdown
I want to do at least one more Euro, so let's do one that I think is more random than T&T or Stone Age. The reason I think Vegas Showdown is more random is that you have to pick a strategy pretty early on in the game but the winning strategy can't be known without knowing the order of the card deck. There are certainly still edges that good players will eke out over the course of the game, Showdown isn't on the level of Can't Stop or anything, but I think even the best players are going to win less frequently at this than at some other Euros. (It probably doesn't help that the elimination games are 5 player games.)
There are 3 heats of Vegas Showdown cutting 25 players to the semifinals. The last 2 years have each had 39 games played across the heats so there are likely to be a couple people with a win who don't make the semis. Last year had 7 double winners, leaving 25 more single winners, so 7 winners didn't advance. As such I think you definitely need to play at least 2 heats, and should probably play the third unless you already have at least a first and a second. Heats tend to be 4 player games and this is a 4 prize event.
It ends up being one heck of a spreadsheet, but it churns out 1.89 laurels in 6.21 hours or .303 laurels per hour. Which puts it ahead of Thurn, but behind all of the other games looked at thus far. It feels like games where you need to do better than win a heat to advance are bad deals.
We need to pick some skill numbers for Showdown. I think it'll be fair to pick numbers a little lower than Thurn because Showdown feels more random to me. I'm thinking a 40% chance to win a heat, 30% chance to come second in a heat, 30% chance to win a semi and finals odds of 25%-25%-20%-15%-15% for the different places.
Plugging those numbers in gives us 4.84 laurels in 6.87 hours, or .705 laurels per hour. That doesn't change where it lands relative to the other games.
I am getting very tired, and it turns out to be a fair amount of effort to do individual games. I'm more than happy to discuss methodologies if people disagree with these numbers, but I don't feel like my mind has been changed by looking at these games. Needing to do better than a win in a heat feels really bad to me now. You're getting dinged in the butt-hour formula for having heats but you don't get to save any time by taking heats off. Trials do feel good though, since they're probably heavily overvalued by being worth 20 laurels for a win.
I suspect it would probably be a problem because losing an entire day probably kills off a bunch of other tournaments. But my gut feeling is that that's only a problem for someone who plays other games and would be looking to add another and not something intrinsic to the single elimination format. So it's probably a terrible game for Randy or I to pick up in a quest for Consul, but that someone could build a Consul plan around it. But I don't want to just go on gut feelings, I want to crunch some numbers!
Another game that came up was Advanced Civ. It was brought up as being way too much time for the potential payout and my response was that it was likely true, but only because the formula caps at 6 and that Advanced Civ was probably worth about a 10 because of how many hours get invested and therefore it's a bad play because of formula inefficiency. So I wanted to check into that... Turns out I definitely have egg on my face here because it only has a 5 prize level! Having to sink 16 or 24 hours into a game is a really big investment, especially compared to Stone Age only needing 10 hours. But actually, maybe your odds of earning laurels could be a lot higher? (Keven Youells has earned laurels in it for 14 straight years...)
So I want to crunch some numbers for a few games to see how things line up with a couple assumptions. After that I'll decide if I care enough to go through all of the games or maybe if I'll learn some shortcuts that can be used to make assumptions about the rest of the games? Who knows!
Twilight Struggle
This game is run swiss style, but they play until they have 2 undefeated people and then only those two play in the finals. So it's basically single elimination when it comes to 1st or 2nd, but for 3rd-6th you can keep playing after a loss. I'm going to assume you enjoy the game enough to keep playing with a single loss but will drop out with 2 losses. (Actually, the say they use strength of schedule to determine 3rd-6th, so probably I should assume a loss in one of the first 2 rounds is a drop.) The last couple years have seen attendance swing up barely above the magical 64 number so I'm actually surprised they've been able to finish in only 6 rounds. From the recap they had only 3 undefeated players after 4 rounds last year which really doesn't make sense. That implies only 48 people were really playing but they had 70 sign up. There were also only 2 draws in the whole event, so it isn't like that was eliminating people either. So there must have been quite a few people who showed up, won a round, and dropped. So I'm going to assume there are only 48 people in the tournament even if 70 show up, which will inflate the laurel numbers a little because in reality you could be the person who loses to someone who drops.
(Alternatively it could have gone 70->35->17->8->3 if one of the draws was between undefeated people in round 3. I'm not sure which is more likely to be honest. I should hedge a little and assume more like 54 people show up.)
Here are your potential outcomes, assuming a 50% chance to win each game.
50% - drop after 3 hours (0-1)
25% - drop after 6 hours (1-1)
6.25% - drop after 12 hours (2-2)
6.25% - drop after 15 hours (3-2)
3.125% - make finals
9.375% - make top 7
Twilight Struggle has 5 prizes, so you're looking at...
50% - 3 hours for 0 laurels
25% - 6 hours for 0 laurels
6.25% - 12 hours for 0 laurels
6.25% - 15 hours for 0 laurels
1.5625% - 18 hours for 50 laurels
1.5625% - 18 hours for 30 laurels
1.3393% - 15 hours for 20 laurels1.3393% - 15 hours for 15 laurels
1.3393% - 15 hours for 10 laurels
1.3393% - 15 hours for 5 laurels
1.3393% - 15 hours for 0 laurels
For a total EV of 2.1875 laurels earned for 6.65625 hours invested. Or .32 laurels per hour.
Your odds of winning are not going to be 50%, though. This is where a little bit of art needs to seep into our science. If we're looking at someone who is actively good at the game what are there odds of winning a game? Those odds would need to get worse as you got later in the tournament as the worse players would get removed from the pool. Looking at the laurel list the top player has a massive 443 laurels with second place having 161. There are many people with a significant number of laurels which makes me think this is a very high skill game. I think I want to start our mythical great player off with a 90% chance of winning in round 1 and linearly trend that down to 60% in the finals. That changes the above numbers to:
10% - 3 hours for 0 laurels
14.4% - 6 hours for 0 laurels
4.66% - 12 hours for 0 laurels
9.69% - 15 hours for 0 laurels
16.8% - 18 hours for 50 laurels
11.2% - 18 hours for 30 laurels
6.65% - 15 hours for 20 laurels6.65% - 15 hours for 15 laurels
6.65% - 15 hours for 10 laurels
6.65% - 15 hours for 5 laurels
6.65% - 15 hours for 0 laurels
For a total EV of 15.09 laurels earned for 13.2 hours invested. Or 1.14 laurels per hour. Better, but that actually doesn't feel very good...
Advanced Civilization
This game plays two heats and then advances the top 8 players to a final. Each game is 8 hours in length and you can't leave partway through. They get around 40 players total, so if every player played in both heats you'd be looking at somewhere between 10 and 12 winners. I don't know how likely that is to happen. The recap for last year says they only had 9 people play in both heats, with 28 people in the first heat and 16 in the second heat. So they only had 6 games total, with one guy winning in both heats. Two of the winners didn't even show up for the finals, so they advanced 5 people who hadn't won a game. By the sounds of it, showing up for the finals after playing a decent game advanced you. But two years ago they had 8 games in the 2 heats with one double winner with all winners showing up and a very tight battle for closest 2nd...
To be safe, I think we need to assert that you need a win or a very close second to advance. If that isn't true, and it turns out to be a 'soft' game, then enough of us will show up to make it become true for future years. It seems like games in the heats are often 7 players, but they could be anywhere from 6 to 8.
This means that it's likely that the breakdown for this game is going to be:
1/7 - 8 hours to make finals
6/49 - 16 hours to make finals
36*2/49/8 - 16 hours to advance as a close second (assuming you play both heats and that 2 of 8 2nd placers advance)
55% - 16 hours for 0 laurels
Then once you're in the finals you need to commit another 8 hours for a 1 in 8 chance at each possible result. It's a 5 prize event, so 50-30-20-15-10-5-0-0. The math churns out to be 7.29 laurels for 18.4 hours, or .395 laurels per hour. Better than Twilight Struggle when the games are coin flips!
But Advanced Civ games are _not_ coin flips. There is definitely some randomness, but since there's a guy who laureled 14 years in a row I think it's pretty safe to say that someone who is really good at the game is going to be really good at the game. But how good is really good? Are they going to be 50% to win a heat against 6 other players? More than that? What about their finals odds?
I think I want to give the good player 50% to win a heat, 25% to come a close second. Finals odds I want to be 20-20-20-20-5-5-5-5. Advanced Civ is a game that ends at quasi-random times, especially in a final where people can be playing for best position as opposed to a heat where I wouldn't anticipate a lot of playing for 3rd or 4th.
This puts the EV at 22.2 laurels in 19.5 hours for an overall laurels per hour of 1.14. I swear I didn't cook these numbers... They really do round to the same as Twilight Struggle.
Thurn & Taxis
This game is run with 3 heats of 2 hours each. Winning a heat is good enough to advance to the quarterfinals but if you do particularly well you can earn a bye into the semis. This leads to two different possible plans... You can try to win a single heat and then sit the rest out or you can play every heat in an attempt to earn that bye. If Thurn is the game you care about you definitely want to try to earn that bye but if you're trying to maximize total laurels it likely depends what you could be doing with those time slots.
Last year had 36 people play in 3 heats, 51 people play in 2 heats, and 61 people play in a single heat. That means something like 70 games were played. I believe 4 people got byes to the semis which means 2 wins is not good enough for a bye. I don't know how to track things forward to future years, but I suspect a decent assumption would be that 3 wins is worth a bye to the semis and everyone else has to play the quarters. So my player is going to play at least two heats but only commit to playing the third heat if they have 0 or 2 wins.
1/64 - spend 6 hours to make semis (WWW)
3/64 - spend 6 hours to make quarters (WWL)
3/16 - spend 4 hours to make quarters (WL)
3/16 - spend 4 hours to make quarters (LW)
9/64 - spend 6 hours to make quarters (LLW)
27/64 - spend 6 hours to cry (LLL)
From there it's a bunch of number crunching because of the different number of hours that can be spent on each branch, but my spreadsheet spits out that you expect to earn 1.27 laurels after spending 6.77 hours, for .188 laurels per hour. Which makes T&T a worse use of time than the previous two games when every game is a coin flip! I suspect the reason for this is that no-skill semis are actually a real bad use of time and no-skill quarters are even worse. 94% of people not earning any laurels at all is pretty rough! I guess that's the downside to 150ish player fields compared to 40 player fields!
Anyway, how good can you be at T&T? This is a harder one for me to estimate because I simply don't grok the game at all. It has had repeat winners, I recognize the names of the winners as all being quite good at games, and the laurel list has some big numbers on top so there's definitely skill there. The TrueSkill list on Yucata makes me think it's more random than Stone Age, but still has a pretty high skill component. So I'm going to say our good player wins 45% of heats, 40% of QFs, 35% of SFs, and 30% of Fs.
Swapping in those win rates to my spreadsheet spits out 5.07 laurels in 8.27 hours, for .613 laurels per hour. Much worse than either of the last two games! Is that my being unfair to skill factors in the games, or is it just that the big Euro heat game is not a very good play for laurels? (Heats do get punished by the WBC butt-hour formula, for what it's worth.)
Innovation
Innovation is a super short single elimination tournament. Heats are scheduled for an hour but it's pretty likely 4 rounds will get compressed into 3 hours. I think I need to keep assuming every round is a full hour though, because sometimes slow people play... At any rate, I'll be considering it to be a mulligan + 6 rounds, with everyone who makes it to the 4th round getting laurels. (The game historically has had 6 people make it that far.) I'm also going to assert that if you win the mulligan you don't show for round 1, but if you lose it then you do.
In coinflip land, this means:
1/4 - out after 2 hours (LL)
1/4 - out after 2 hours (W-L)
1/8 - out after 3 hours (LWL)
1/8 - out after 3 hours (W-WL)
1/16 - out after 4 hours (LWWL)
3/16 - top 6
From there it actually gets a little tricky because of issues with byes/eliminators and that potential extra hour from the mulligan and round 1. Eugh. I'm going to assume the eliminator always loses, which is not true historically so maybe you should bump the numbers up a bit. With that assumption, off to the spreadsheet... (Oh, and Innovation is a trial, so it's only worth 20 laurels for 1st place.)
It pans out to earning 1.5 laurels for an investment of 2.95 hours. This means .508 laurels per hour which is our best coinflip rate so far! I suspect this is because not enough people play so first place shouldn't be worth 20 in a perfect world. So the people who do play get extra value for doing so?
How about a skill factor? Well, one person (Pounder) has made the finals in each of the last 4 years. We've played quite a few times for fun over the years and he routinely smashes me. I beat him once that I can remember (in the finals in 2015, hah!) but other than that I'm not sure I've ever beaten him. There are 7 rounds, so we need 7 win percentages. Round 1 should be the highest number since all the mulligan winners are taking that round off. I feel like I want the finals odds for our great player to be 60, so we'll use a similar scaling backwards thing that we did in Twilight Struggle? With the mulligan round being the same as round 2? So 84%-90%-84%-78%-72%-66%-60%.
Doing that gives us 7.13 laurels in 4.39 hours, or 1.63 laurels per hour. Unsurprisingly the highest coinflip game thus far is also the highest skilled game thus far. Is it fair to say Innovation is as skill intensive as Twilight Struggle?
Vegas Showdown
I want to do at least one more Euro, so let's do one that I think is more random than T&T or Stone Age. The reason I think Vegas Showdown is more random is that you have to pick a strategy pretty early on in the game but the winning strategy can't be known without knowing the order of the card deck. There are certainly still edges that good players will eke out over the course of the game, Showdown isn't on the level of Can't Stop or anything, but I think even the best players are going to win less frequently at this than at some other Euros. (It probably doesn't help that the elimination games are 5 player games.)
There are 3 heats of Vegas Showdown cutting 25 players to the semifinals. The last 2 years have each had 39 games played across the heats so there are likely to be a couple people with a win who don't make the semis. Last year had 7 double winners, leaving 25 more single winners, so 7 winners didn't advance. As such I think you definitely need to play at least 2 heats, and should probably play the third unless you already have at least a first and a second. Heats tend to be 4 player games and this is a 4 prize event.
It ends up being one heck of a spreadsheet, but it churns out 1.89 laurels in 6.21 hours or .303 laurels per hour. Which puts it ahead of Thurn, but behind all of the other games looked at thus far. It feels like games where you need to do better than win a heat to advance are bad deals.
We need to pick some skill numbers for Showdown. I think it'll be fair to pick numbers a little lower than Thurn because Showdown feels more random to me. I'm thinking a 40% chance to win a heat, 30% chance to come second in a heat, 30% chance to win a semi and finals odds of 25%-25%-20%-15%-15% for the different places.
Plugging those numbers in gives us 4.84 laurels in 6.87 hours, or .705 laurels per hour. That doesn't change where it lands relative to the other games.
I am getting very tired, and it turns out to be a fair amount of effort to do individual games. I'm more than happy to discuss methodologies if people disagree with these numbers, but I don't feel like my mind has been changed by looking at these games. Needing to do better than a win in a heat feels really bad to me now. You're getting dinged in the butt-hour formula for having heats but you don't get to save any time by taking heats off. Trials do feel good though, since they're probably heavily overvalued by being worth 20 laurels for a win.
Monday, May 01, 2017
Blood Bowl: How Bad is Stab?
A couple weeks ago I played against a Dark Elf opponent that was running two assassins on a relatively unleveled team. This means they chose to take the assassin over other positionals, which means they must have valued them pretty highly. Twitch chat was not very charitable to the skill level of my opponent, and the assassins actually accomplished basically nothing. They spent a lot of time intentionally standing beside my guys and then getting hit for it with their 7 armour, but that held up just fine.
It got me wondering... Should I have been able to just get free SPP for killing them? Should he have been able to hurt any of my guys first? Is conventional wisdom about how bad they are correct or should I be trying them out? Setting up with 2 of them on the line, making stabs, and then blocking away anyone who didn't get stabbed feels at least worth investigating. (My opponent tried this, but I was playing necro and the players he was stabbing had 9 armour and stand firm so blocking them away couldn't happen.) What are the odds here?
The first table is for stab against the 3 likely armour values the target is apt to have. The next one is the odds for a 2 die block with block against someone without block. The next one is the odds for a 2 die block without block against someone with block. The last one is the odds for a 2 die block without block against someone with both block and dodge.
The first thing to point out is that there is no downside to the stab. Throwing a block without block has an 11 percent chance of knocking yourself down. You can reroll it, of course, but burning up rerolls on opening line blocks feels really bad. Especially when the upside of throwing the block is only a 4% chance of removal!
Then there's the fact that even if you give up a 2 die block back after failing a stab they are only 13% to remove you back. If you're stabbing a 7 AV person that means the stabber has the advantage. Otherwise you're less likely to hurt them as you are to be hurt back, so you really need the followup block from a friend trying for a push to free you up. Hitting a flesh golem with an assassin is not a good play.
That all said... A 13% chance to be removed back is actually a really big deal. And that's assuming they don't have mighty blow, which, now that we mention it...
Now we're up to a 23% chance of being removed! Those are the sorts of numbers I'm talking about. Mighty blow really lets you murder the 7 AV dudes with no skills. No wonder my rats keep dying...
The next thing I notice is just how hard it is to hurt someone with block and dodge with a regular hit. Even with 7 armour you're only getting removed on 5% of hits. 5% of regular hits, anyway. Throw on tackle and mighty blow and things get a lot scarier. But it's not like a Dark Elf team is going to have many (or any) players with those skills. If we're trying to kill a gutter runner or a skink or something then maybe the assassin is the way to go. 17% instead of 5% is a pretty big change!
My feeling now after looking at things a little is that blitzing anyone except for a low armour dodgy dude is a mistake with an assassin. This means they have to start in contact on the start of your turn to get a hit off, which is very dangerous for a 7 armour dude with no defensive skills. Using them against enemies on the line feels pretty good though. Take a free armour roll, then hit them with a regular block to push them away (or knock them down) afterwards. If you knock them down beside the assassin then next turn they have to dodge away or give you another stab...
It also feels like they just aren't likely enough to knock anyone down to justify using them on the ball carrier if you have an actual ball removal player. Tackle, wrestle, strip ball... These are all better tools than the assassin. But those all require a lot of levels; the assassin comes straight out of the box with stab.
Another downside is the stab doesn't earn any experience, so the assassin is a removal tool that doesn't level through removals! Can you feed them touchdowns to level them up? All the players on a Dark Elf team want to level up through touchdowns, can you justify feeding the spp onto the assassin?
And really, that's what it comes down to... Assassins are expensive players on a team full of expensive players. They're pretty much the squishiest player in the game, too, since they have only 7 AV and no defensive skills. Even goblins, which have stunty, start with dodge, so they're harder to hurt. Harder to hurt for everyone but an assassin, anyway!
So I feel like I'd maybe want an assassin (or two!) against some specific teams but very much not against others.
Good: Skaven, High Elf, Brettonian, Wood Elf, Lizardman, Norse, Khemri
Ok: Human, Dark Elf, Undead, Chaos Dwarves
Bad: Orc, Dwarf, Chaos, Necromantic, Nurgle
Hmm... Looking at it there are actually 7 of 16 teams where I'd probably want an assassin and only really 5 where they'd be a real detriment. Of course on the champion ladder it turns out that the bottom group there contains a lot of the most played teams. Orcs are #1 by a large margin, with Chaos and Chaos Dwarves as the next two. Those 5 bad teams represent 40% of all games played and that really makes me question wanting to play assassins on the ladder.
But in a league? That's more tempting. Especially if the league enforces some kind of race parity like the NWFL league I played on FumBBL did.
Of course you could just be looking at having your expensive defenseless 7 AV player die in the first game...
It got me wondering... Should I have been able to just get free SPP for killing them? Should he have been able to hurt any of my guys first? Is conventional wisdom about how bad they are correct or should I be trying them out? Setting up with 2 of them on the line, making stabs, and then blocking away anyone who didn't get stabbed feels at least worth investigating. (My opponent tried this, but I was playing necro and the players he was stabbing had 9 armour and stand firm so blocking them away couldn't happen.) What are the odds here?
| Nothing | Stun | KO | Cas | |
| 7 AV | 58% | 24% | 10% | 7% |
| 8 AV | 72% | 16% | 7% | 5% |
| 9 AV | 83% | 10% | 4% | 3% |
| TO | Push | Down | Stun | KO | Cas | |
| 7 AV | 3% | 22% | 44% | 18% | 8% | 5% |
| 8 AV | 3% | 22% | 54% | 12% | 5% | 3% |
| 9 AV | 3% | 22% | 63% | 7% | 3% | 2% |
| TO | Push | Down | Stun | KO | Cas | |
| 7 AV | 11% | 33% | 32% | 14% | 6% | 4% |
| 8 AV | 11% | 33% | 40% | 9% | 4% | 3% |
| 9 AV | 11% | 33% | 46% | 5% | 2% | 2% |
| TO | Push | Down | Stun | KO | Cas | |
| 7 AV | 11% | 58% | 18% | 7% | 3% | 2% |
| 8 AV | 11% | 58% | 22% | 5% | 2% | 1% |
| 9 AV | 11% | 58% | 25% | 3% | 1% | 1% |
The first table is for stab against the 3 likely armour values the target is apt to have. The next one is the odds for a 2 die block with block against someone without block. The next one is the odds for a 2 die block without block against someone with block. The last one is the odds for a 2 die block without block against someone with both block and dodge.
The first thing to point out is that there is no downside to the stab. Throwing a block without block has an 11 percent chance of knocking yourself down. You can reroll it, of course, but burning up rerolls on opening line blocks feels really bad. Especially when the upside of throwing the block is only a 4% chance of removal!
Then there's the fact that even if you give up a 2 die block back after failing a stab they are only 13% to remove you back. If you're stabbing a 7 AV person that means the stabber has the advantage. Otherwise you're less likely to hurt them as you are to be hurt back, so you really need the followup block from a friend trying for a push to free you up. Hitting a flesh golem with an assassin is not a good play.
That all said... A 13% chance to be removed back is actually a really big deal. And that's assuming they don't have mighty blow, which, now that we mention it...
| TO | Push | Down | Stun | KO | Cas | |
| 7 AV | 3% | 22% | 31% | 20% | 13% | 11% |
| 8 AV | 3% | 22% | 44% | 15% | 9% | 8% |
| 9 AV | 3% | 22% | 54% | 10% | 6% | 5% |
Now we're up to a 23% chance of being removed! Those are the sorts of numbers I'm talking about. Mighty blow really lets you murder the 7 AV dudes with no skills. No wonder my rats keep dying...
The next thing I notice is just how hard it is to hurt someone with block and dodge with a regular hit. Even with 7 armour you're only getting removed on 5% of hits. 5% of regular hits, anyway. Throw on tackle and mighty blow and things get a lot scarier. But it's not like a Dark Elf team is going to have many (or any) players with those skills. If we're trying to kill a gutter runner or a skink or something then maybe the assassin is the way to go. 17% instead of 5% is a pretty big change!
My feeling now after looking at things a little is that blitzing anyone except for a low armour dodgy dude is a mistake with an assassin. This means they have to start in contact on the start of your turn to get a hit off, which is very dangerous for a 7 armour dude with no defensive skills. Using them against enemies on the line feels pretty good though. Take a free armour roll, then hit them with a regular block to push them away (or knock them down) afterwards. If you knock them down beside the assassin then next turn they have to dodge away or give you another stab...
It also feels like they just aren't likely enough to knock anyone down to justify using them on the ball carrier if you have an actual ball removal player. Tackle, wrestle, strip ball... These are all better tools than the assassin. But those all require a lot of levels; the assassin comes straight out of the box with stab.
Another downside is the stab doesn't earn any experience, so the assassin is a removal tool that doesn't level through removals! Can you feed them touchdowns to level them up? All the players on a Dark Elf team want to level up through touchdowns, can you justify feeding the spp onto the assassin?
And really, that's what it comes down to... Assassins are expensive players on a team full of expensive players. They're pretty much the squishiest player in the game, too, since they have only 7 AV and no defensive skills. Even goblins, which have stunty, start with dodge, so they're harder to hurt. Harder to hurt for everyone but an assassin, anyway!
So I feel like I'd maybe want an assassin (or two!) against some specific teams but very much not against others.
Good: Skaven, High Elf, Brettonian, Wood Elf, Lizardman, Norse, Khemri
Ok: Human, Dark Elf, Undead, Chaos Dwarves
Bad: Orc, Dwarf, Chaos, Necromantic, Nurgle
Hmm... Looking at it there are actually 7 of 16 teams where I'd probably want an assassin and only really 5 where they'd be a real detriment. Of course on the champion ladder it turns out that the bottom group there contains a lot of the most played teams. Orcs are #1 by a large margin, with Chaos and Chaos Dwarves as the next two. Those 5 bad teams represent 40% of all games played and that really makes me question wanting to play assassins on the ladder.
But in a league? That's more tempting. Especially if the league enforces some kind of race parity like the NWFL league I played on FumBBL did.
Of course you could just be looking at having your expensive defenseless 7 AV player die in the first game...
Friday, September 02, 2016
Path of Exile: Fire and Ice
Many leagues ago Sceadeau and I created characters to level up together. He wanted to test out a unique jewel which increased fireball's radius by what sounded like a ludicrous amount. I wanted to test out using freezing pulse and projectile speed to permanently freeze bosses. Both ended up working out pretty well, and it was a lot of fun to play them.
Apparently there's a new Path of Exile league starting today, and Sceadeau sent me the following snipit from the patch notes.
Fireball: 50% more damage. Ice Spear: 70% more damage.
Ice spear is a different spell than glacial spike but it would probably work about the same in practice and 70% is a really big number. PoE has a history of overbuffing things when they buff them, so I wouldn't be surprised if both of these spells end up being really good. Also the game has a much higher power level now than it did back when we last did this, because of the whole ascendancy system.
So I think we're going to go back to Path of Exile for a while... I really like the game because it simply has so many different ways to play it. It often gets compared to Diablo III and I like PoE a lot more, especially when playing with other people, because the game feels so different when running with different builds.
Now there are two things to figure out... How exactly does ice spear work, and what ascendancy class do I want to use with it?
Ice spear is a spell with 2 stages. The first stage has 100% pierce chance, so it's useful for clearing out packs of dudes who are nearby. After it travels a set distance it switches to the second stage where it no longer pierces but has a 600% increased chance to crit. Considering the spell has a base crit chance of 7% this means the end portion will crit almost half the time without any other investment. Ice spear also has an increased modifier to chill duration, but not to freeze. So it probably isn't as good for perma-freezing things... Except crits also freeze, and this crits a lot, so maybe it still works. Chilling things is still good, especially if you have other abilities that get better on monsters that have an elemental debuff on them.
The first thing this brings to mind is the Inquisitor ascendancy for the Templar. One of the points in that tree is 100% increased crit chance against enemies with no elemental status ailment, and 45% to crit multiplier against enemies with an elemental status ailment. If Sceadeau hits the enemy first it'll have a fire debuff on it most likely, and enemies that I hit a second time will certainly have a debuff from the first hit. So that's already pretty strong. The big point behind that node says your crits ignore elemental resistances and your non-crits penetrate 10% elemental resistances...
Penetrating elemental resistance is a _huge_ deal. The best nodes in the tree for casters in my experience have always been the ones that penetrate resists. I've always supported my spells with resist penetration. So completely ignoring resistances sounds incredibly good. It would have the downside of not being able to use a good support gem or take some good nodes in the tree, but I can adapt to other things.
One other thing that immediately leaped to mind is the node elemental equilibrium. It makes it so enemies you hit get 25% resistance to your element and lose 50% resistance to the other elements. If I'm playing with Sceadeau, and he's casting fireballs, then this node would drastically amplify his damage while only hurting my damage some of the time. This feels really good, but would require putting a huge focus on extra crit chance. And I hate relying on feelings... Let's look at some math!
These numbers assume I crit 75% of the time for triple damage and that both Sceadeau and I would be running 34% penetration unless I'm an inquisitor in which case I have none and he still has 34%.
What we see here is that my picking up EE boosts Sceadeau's damage by anywhere between 37% and 85%. This is a more multiplier and is an incredibly big deal. Even with nothing special going on, EE would only cost me 19% to 30% of my damage, so overall as a team we'd be doing better if I took EE even with no mitigating circumstances. Inquisitor by itself actually hurts at low levels of mob resist because I won't have the penetration to drive the enemies into negative resists. I will have an extra support gem and other tree nodes, so that's going to be fine, and I'm pretty sure mobs with no resistances aren't going to be a concern one way or the other. Inquisitor is a 58% more damage buff at high levels of monster resist which is insane. Marauders have to take 10% extra damage to unlock their 40% more damage point! I just get it for free! Of course, it's only this high because my spell of choice has 42% extra crit chance on it, and this all assumes I'm cracking hard enemies with the sweet spot...
The best thing, though, is when I compare Inquisitor to Inquisitor with elemental equilibrium. I lose somewhere between 2 and 3% of my damage at low monster resist levels to give Sceadeau a huge boost. I think I'm pretty ok with that.
So assuming Sceadeau isn't also going Inquisitor I am definitely going to try it out, and will take EE to boost his damage by a ton.
Time to play around with the tree tool to see how much extra crit chance and multiplier I can actually pick up...
Apparently there's a new Path of Exile league starting today, and Sceadeau sent me the following snipit from the patch notes.
Fireball: 50% more damage. Ice Spear: 70% more damage.
Ice spear is a different spell than glacial spike but it would probably work about the same in practice and 70% is a really big number. PoE has a history of overbuffing things when they buff them, so I wouldn't be surprised if both of these spells end up being really good. Also the game has a much higher power level now than it did back when we last did this, because of the whole ascendancy system.
So I think we're going to go back to Path of Exile for a while... I really like the game because it simply has so many different ways to play it. It often gets compared to Diablo III and I like PoE a lot more, especially when playing with other people, because the game feels so different when running with different builds.
Now there are two things to figure out... How exactly does ice spear work, and what ascendancy class do I want to use with it?
Ice spear is a spell with 2 stages. The first stage has 100% pierce chance, so it's useful for clearing out packs of dudes who are nearby. After it travels a set distance it switches to the second stage where it no longer pierces but has a 600% increased chance to crit. Considering the spell has a base crit chance of 7% this means the end portion will crit almost half the time without any other investment. Ice spear also has an increased modifier to chill duration, but not to freeze. So it probably isn't as good for perma-freezing things... Except crits also freeze, and this crits a lot, so maybe it still works. Chilling things is still good, especially if you have other abilities that get better on monsters that have an elemental debuff on them.
The first thing this brings to mind is the Inquisitor ascendancy for the Templar. One of the points in that tree is 100% increased crit chance against enemies with no elemental status ailment, and 45% to crit multiplier against enemies with an elemental status ailment. If Sceadeau hits the enemy first it'll have a fire debuff on it most likely, and enemies that I hit a second time will certainly have a debuff from the first hit. So that's already pretty strong. The big point behind that node says your crits ignore elemental resistances and your non-crits penetrate 10% elemental resistances...
Penetrating elemental resistance is a _huge_ deal. The best nodes in the tree for casters in my experience have always been the ones that penetrate resists. I've always supported my spells with resist penetration. So completely ignoring resistances sounds incredibly good. It would have the downside of not being able to use a good support gem or take some good nodes in the tree, but I can adapt to other things.
One other thing that immediately leaped to mind is the node elemental equilibrium. It makes it so enemies you hit get 25% resistance to your element and lose 50% resistance to the other elements. If I'm playing with Sceadeau, and he's casting fireballs, then this node would drastically amplify his damage while only hurting my damage some of the time. This feels really good, but would require putting a huge focus on extra crit chance. And I hate relying on feelings... Let's look at some math!
These numbers assume I crit 75% of the time for triple damage and that both Sceadeau and I would be running 34% penetration unless I'm an inquisitor in which case I have none and he still has 34%.
| Mob Resist | Sceadeau EE gain | Inq gain | EE gain | EE gain w/ Inq |
| 0 | 37% | -25% | -19% | -2% |
| 25 | 46% | -10% | -23% | -3% |
| 50 | 60% | 14% | -30% | -3% |
| 75 | 85% | 58% | 0% | 0% |
| 100 | 42% | 58% | 0% | 0% |
What we see here is that my picking up EE boosts Sceadeau's damage by anywhere between 37% and 85%. This is a more multiplier and is an incredibly big deal. Even with nothing special going on, EE would only cost me 19% to 30% of my damage, so overall as a team we'd be doing better if I took EE even with no mitigating circumstances. Inquisitor by itself actually hurts at low levels of mob resist because I won't have the penetration to drive the enemies into negative resists. I will have an extra support gem and other tree nodes, so that's going to be fine, and I'm pretty sure mobs with no resistances aren't going to be a concern one way or the other. Inquisitor is a 58% more damage buff at high levels of monster resist which is insane. Marauders have to take 10% extra damage to unlock their 40% more damage point! I just get it for free! Of course, it's only this high because my spell of choice has 42% extra crit chance on it, and this all assumes I'm cracking hard enemies with the sweet spot...
The best thing, though, is when I compare Inquisitor to Inquisitor with elemental equilibrium. I lose somewhere between 2 and 3% of my damage at low monster resist levels to give Sceadeau a huge boost. I think I'm pretty ok with that.
So assuming Sceadeau isn't also going Inquisitor I am definitely going to try it out, and will take EE to boost his damage by a ton.
Time to play around with the tree tool to see how much extra crit chance and multiplier I can actually pick up...
Monday, August 15, 2016
Star Wars Rebellion: Opposing Odds
I have become slightly obsessed with a board game that Adam taught me before WBC this year: Star Wars Rebellion. It's an asymmetric card driven 2 player wargame with a great theme. The game starts a little before the original Star Wars trilogy and goes through all three movies. One player is the rebel alliance which is trying to convince the galaxy to go into full on rebellion. The other player is the empire which is trying to find the hidden rebel base and eliminate them.
Even though the mechanics are basically the same for each side they play very differently which makes the game particularly interesting for me. Ostensibly the game is about the empire trying to find the rebel base so you'd think the rebels would have a game based on staying hidden, but that's really not the case. The length of the game depends on how many objectives the rebels can manage to achieve so really the rebels are trying to score as many objective points as they can while hoping the game mechanics keep their base safe. But then the empire could focus on denying objective points and just assume they'll stumble into the base eventually... But that probably means giving up on outproducing the rebels militarily, so then the rebels could just try to earn extra time with military actions...
As an aside, each game round you get to take one action per leader and generally speaking each side has the same number of leaders, and that number increases as the game gets longer. So on the first turn each side takes 4 actions but by turn 5 each side is taking 8 actions. Often you can spend a leader to try to counter the opponent's action instead of taking one of your own, but that's guaranteeing you lose an action to just have a chance of costing them an action. So unless the action you're giving up isn't very important or the odds are very good it just doesn't feel very good to do it.
One thing I found while playing as the rebels was there were two actions I wanted to take every single turn if I could. I always wanted to make an alliance with a region (which lets you produce units and is a criteria of many missions) and I always wanted to do some spy work to manipulate the objective deck. This lets you draw two cards and put one on top and one on the bottom, which accomplishes two things... It lets you end up with objectives you're likely to succeed at based on the current game state by burying hard ones and it lets you draw cards from the bottom of the deck. (The deck is pseudorandom in the sense that there are 3 tiers of 5 cards each, and the lower tier cards are just better.) But even though those actions seemed critical to my game plan regardless of the game state, my opponent would almost never contest them. And then when I finally played a game as the empire I kept finding other things to do instead of contesting those actions, even though I know how valuable those actions are for the other side.
This leaves me with a bit of an issue. Are all my actions as the empire equally valuable? Is my evaluation of how useful those two actions are for the rebels off? Are the odds of succeeding at an opposition really bad? Unless one of those three things are true I really need to change my empire strategy to put a premium on opposing those two actions.
I think it's pretty clear the first statement is false. All empire actions are not equally valuable. Each card can only be played once per turn, and each fleet can only be moved once per turn. Different actions will change in value based on the game state, so I'm not saying different actions are strictly superior or anything. But I am saying that on a given turn you will have an action that is worth less than another.
How about the odds of opposing an action? The way that works is all missions have an associated stat and each player rolls a die for each point their leaders have in that stat. So Chewbacca is really good at opposing a punching mission (he has 3 points in punching) but really bad at everything else (he has 0 points in the others). A die is worth 0, 0, 1, 1, 1, or 2 successes. The player who took the action needs more successes in order to have the action happen. Note that this means the opposer wins ties, and with small numbers of dice and small values on those dice, ties will actually happen pretty often. Andrew was saying he thought that meant even numbers of dice would be 60-40 but my intuition has that as being too favorable for the initial actor. Which means opposing would really be something worth considering! But let's work out the actual odds for differing numbers of dice...
Even though the mechanics are basically the same for each side they play very differently which makes the game particularly interesting for me. Ostensibly the game is about the empire trying to find the rebel base so you'd think the rebels would have a game based on staying hidden, but that's really not the case. The length of the game depends on how many objectives the rebels can manage to achieve so really the rebels are trying to score as many objective points as they can while hoping the game mechanics keep their base safe. But then the empire could focus on denying objective points and just assume they'll stumble into the base eventually... But that probably means giving up on outproducing the rebels militarily, so then the rebels could just try to earn extra time with military actions...
As an aside, each game round you get to take one action per leader and generally speaking each side has the same number of leaders, and that number increases as the game gets longer. So on the first turn each side takes 4 actions but by turn 5 each side is taking 8 actions. Often you can spend a leader to try to counter the opponent's action instead of taking one of your own, but that's guaranteeing you lose an action to just have a chance of costing them an action. So unless the action you're giving up isn't very important or the odds are very good it just doesn't feel very good to do it.
One thing I found while playing as the rebels was there were two actions I wanted to take every single turn if I could. I always wanted to make an alliance with a region (which lets you produce units and is a criteria of many missions) and I always wanted to do some spy work to manipulate the objective deck. This lets you draw two cards and put one on top and one on the bottom, which accomplishes two things... It lets you end up with objectives you're likely to succeed at based on the current game state by burying hard ones and it lets you draw cards from the bottom of the deck. (The deck is pseudorandom in the sense that there are 3 tiers of 5 cards each, and the lower tier cards are just better.) But even though those actions seemed critical to my game plan regardless of the game state, my opponent would almost never contest them. And then when I finally played a game as the empire I kept finding other things to do instead of contesting those actions, even though I know how valuable those actions are for the other side.
This leaves me with a bit of an issue. Are all my actions as the empire equally valuable? Is my evaluation of how useful those two actions are for the rebels off? Are the odds of succeeding at an opposition really bad? Unless one of those three things are true I really need to change my empire strategy to put a premium on opposing those two actions.
I think it's pretty clear the first statement is false. All empire actions are not equally valuable. Each card can only be played once per turn, and each fleet can only be moved once per turn. Different actions will change in value based on the game state, so I'm not saying different actions are strictly superior or anything. But I am saying that on a given turn you will have an action that is worth less than another.
How about the odds of opposing an action? The way that works is all missions have an associated stat and each player rolls a die for each point their leaders have in that stat. So Chewbacca is really good at opposing a punching mission (he has 3 points in punching) but really bad at everything else (he has 0 points in the others). A die is worth 0, 0, 1, 1, 1, or 2 successes. The player who took the action needs more successes in order to have the action happen. Note that this means the opposer wins ties, and with small numbers of dice and small values on those dice, ties will actually happen pretty often. Andrew was saying he thought that meant even numbers of dice would be 60-40 but my intuition has that as being too favorable for the initial actor. Which means opposing would really be something worth considering! But let's work out the actual odds for differing numbers of dice...
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| 0 | 67% | 89% | 96% | 99% | 100% | 100% | 100% | 100% | 100% | 100% |
| 1 | 31% | 61% | 80% | 91% | 96% | 98% | 99% | 100% | 100% | 100% |
| 2 | 13% | 36% | 58% | 75% | 87% | 93% | 97% | 98% | 99% | 100% |
| 3 | 5% | 19% | 38% | 57% | 72% | 83% | 91% | 95% | 97% | 99% |
| 4 | 2% | 10% | 23% | 40% | 56% | 70% | 81% | 88% | 93% | 96% |
| 5 | 1% | 5% | 13% | 26% | 41% | 56% | 69% | 79% | 87% | 92% |
| 6 | 0% | 2% | 7% | 16% | 28% | 42% | 55% | 67% | 77% | 85% |
| 7 | 0% | 1% | 4% | 9% | 18% | 30% | 42% | 55% | 66% | 76% |
| 8 | 0% | 0% | 2% | 5% | 11% | 20% | 31% | 43% | 55% | 66% |
| 9 | 0% | 0% | 1% | 3% | 7% | 13% | 22% | 32% | 43% | 54% |
| 10 | 0% | 0% | 0% | 1% | 4% | 8% | 14% | 23% | 33% | 44% |
What we have here is a table with the number of dice being rolled by the initial actor across the top and the number of dice being rolled by the opposer down the left. Typically you'd be looking at numbers between 0 and 3 but occasionally there will be lots of leaders in one spot working on a single action (trying to turn Luke to the Dark Side, for example). It turns out Andrew's initial guess was actually pretty good, with a 60-40 split when you're rolling 4 against 4, but at lower numbers of dice it gets better for the opposer at even strength.
Throwing a leader in just to 'make them roll' (an unopposed action doesn't have to roll dice) feels like it doesn't make much sense at anything except maybe 1v0. In that 1v0 case you're basically getting a third of an action. Is your worst action that bad? I doubt it, but I guess it might be. But if you have a good leader back then going in 1v2 is 87% of an action. Is your worst action worth 87% of their action? Yeah, yeah, that seems pretty good. I like 1v3 and 2v3 also. So leaving a good symbol leader back feels like something I need to encorporate more into my game.
What about trying to capture a leader? The empire can lock a leader up with a card that requires only a single punch symbol to start up. Capturing a leader means they can't take actions again until they get saved and opens up some powerful torture related actions for the empire, so it's pretty powerful. It's non-trivial to rescue a leader, but even if the rebels have one of the 3 cards that do it and succeed in it on the next turn, you're looking at a 1v0 roll being 2/3rds of costing them 2 actions and 1/3rd of doing nothing. That's going to cost them more actions than the one you're spending, so a 1v0 roll actually feels pretty good. You don't want even dice numbers being rolled, but any positive number of dice is probably a good idea.
The last thing to consider is some of the cards get 2 guaranteed successes if the correct leader runs the action. How good is that in terms of the odds?
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| 0 | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% |
| 1 | 94% | 98% | 99% | 100% | 100% | 100% | 100% | 100% | 100% | 100% |
| 2 | 71% | 86% | 94% | 97% | 99% | 100% | 100% | 100% | 100% | 100% |
| 3 | 46% | 67% | 81% | 90% | 95% | 98% | 99% | 99% | 100% | 100% |
| 4 | 26% | 46% | 64% | 78% | 87% | 93% | 96% | 98% | 99% | 100% |
| 5 | 14% | 29% | 47% | 63% | 75% | 85% | 91% | 95% | 97% | 98% |
| 6 | 7% | 17% | 32% | 47% | 62% | 74% | 83% | 89% | 93% | 96% |
| 7 | 3% | 10% | 20% | 33% | 47% | 61% | 72% | 81% | 88% | 92% |
| 8 | 1% | 5% | 12% | 22% | 34% | 47% | 60% | 71% | 79% | 86% |
| 9 | 1% | 3% | 7% | 14% | 24% | 35% | 48% | 59% | 70% | 78% |
| 10 | 0% | 1% | 4% | 9% | 16% | 25% | 36% | 48% | 59% | 69% |
Opposing these cards is a lot worse. You need to roll 2 extra dice on opposition to barely get better than 50-50. Now, some of these character specific action cards are so powerful you may want to take your 31% chance at stopping them (10v10 with +2, like when the Emperor is trying to turn Luke to the Dark Side) but in general, getting 2 free successes is pretty absurd for the odds.
What does this all mean? I think I need to try opposing more actions!
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