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.

September Humble Bundle

The September Humble Monthly prepurchase games have been announced and they've added a new twist in this month. I'm not really sure why exactly, but they're giving you the choice between three games or a single game that was in a previous Humble Monthly. I'm guessing maybe the distributors for Rise of the Tomb Raider wanted to be featured again but Humble really didn't want to give away the same game to someone who's been a subscriber of their system forever. At any rate, you can get that single game ($70) or you can get Sniper Elite 4 ($67, but currently on sale on Steam for $10), Tales of Berseria ($65), and Staxel ($22). I've decided I intend to stream Humble Monthly games on the weekend going forward to shake things up from always playing Blood Bowl and decided to go with the three game option primarily because my sister keeps trying to get me to play a Tales game.

The three games are a sniper shooter game, a jRPG, and a farming simulator. A good variety that probably hits a lot of games with at least one of the games and seems like it should really hit me with two of them. I remain bad at aiming but jRPGs are ostensibly my favourite game genre and I really like Stardew Valley. I say ostensibly because I was thinking about it earlier and haven't actually played a new jRPG since probably Final Fantasy XIII in 2009 and I didn't even finish that one. So, well, I have high hopes but maybe my mental image of the genres I like doesn't line up with who I am today? Hard to say.

I'm going to stream Tales of Berseria tomorrow and see how it goes!

World of Warcraft: Expansion Additions

There's a new World of Warcraft expansion coming out in two weeks and I thought I'd take a look and see what stuff they're adding in this time around. This was probably a mistake because it turns out it sounds pretty sweet and now I'm probably going to end up wanting to play it again. They're adding two new game modes that sound pretty fun and they added one in the last expansion that I didn't really play that they're continuing on that really seemed up my alley. Thematically it sounds like this expansion is trying to return to making the Alliance and the Horde be fighting each other again instead of teaming up to fight the big bad. I don't much care about this one way or the other, but it does mean the mechanics are more PvP focused.

The first new mode is a Warcraft II mode to take over control of a zone from the other faction. Oddly it isn't PvP at all; it seems they actively want the zone to flip back and forth and if it was PvP then on most servers it wouldn't flip at all. Instead it's like a 20 person PvE fight where you build resource gathering buildings and barracks and stuff and then lead dudes into battle. It sounds neat, but probably not something you're going to want to do a ton of. You could just go play WCIII (which got a patch recently to revive that game) instead. But it should be fun.

The second new mode is a 3v3 race to score the most points by doing WoW type things. Kill monsters, do quests, open treasures, etc. The map is covered by a fog of war so you need to explore around and adapt your plan based on what actually spawned in this particular instance. There are a bunch of different islands to create ground rules but the location of things is procedurally generated so you need to adapt on the fly. Blizzard claims to have designed good bots to play the other 3 person team for the easier difficulty levels but the hardest mode requires you to have a premade group of 3 and pits you against another 3 person team. Spread out and get treasures? Gank squad to kill the other team? Someone with stealth and a lot of CC? Healers? Lots of options and it should be fun. Small scale skirmishes are the sort of PvP I can get behind, so hopefully this mode is done well.

The last mode, which existed already, is mythic+ dungeons. It's a system that's been evolving for a while, and has stolen some things from Path of Exile, and seems to be in a pretty good spot now. The basic idea is you do a hard 5 man dungeon with a time limit. Finish under the time limit and you get an item to let you run another harder 5 man dungeon. Beat that one in time and you get an even harder one. As you get harder and harder ones you start getting affixes on the dungeons that change the way things work. More enemy damage, less healing, weird dots... All sorts of options, and they're adding new ones. The loot is good and I think people pushing the really high mythic+s is a fairly competitive thing so I'd like to get in on the ground floor for it this expansion and see what I can do. It takes 4 other people and I don't know people who play anymore, but I imagine my old guild will at least have a few people interested at the start. I'm pretty sure Death Knights rate to be really good tanks for mythic dungeons at any rate, so I have a niche to fill! And who knows, maybe streaming mythic dungeons is a thing people are interested in watching?

August Humble Monthly Bundle

Humble Monthly is a subscription service run by the Humble Bundle people where they sell you a fixed bunch of games for a low price. The bundles tend to be 'worth' about $200 and it costs $12 per month but they are using a non-discounted MSRP to determine that value and you don't get to pick the games you get so chances are you're going to get some games you're simply not interested in due to genres or whatnot.

The trick they use to get people to sign up is they announce some of the key games for the next month shortly into the current month. Typically this will be three games, but when they get a particularly big game they have it as the only headliner. Civilization VI and Destiny 2 are examples of those sorts of games from previous months.

My brother got me a year long subscription for Christmas last year and it's been pretty sweet thus far. I spend too much time playing a lot of individual games (like Blood Bowl in recent times) to play all of them but I have played some of them, that I never would have played on my own, which were great. Quantum Break was a movie/FPS hybrid that I would have never considered getting on my own but it was very cool.

I have recently signed up to be a Humble Partner. Basically this means I advertise for them and if people buy things through my link I get a cut. I did a little bit of this for the game Cultist Simulator which I was given a copy of to stream and generate hype for them prior to release, but I could and should do more.

I think what I should start doing is streaming the preview games for the Humble Monthly with my chat bot periodically spamming the link. Humble really wants their partners to sell the Monthly bundle in that I actually get most of the payment for someone who signs up for the first time. It will also give me a little structure for playing different games, which is always a good thing for me.

The advance games for August were just announced and they are A Hat in Time, The Escapists 2, and Conan Exiles. A cute platformer, a cool looking prison break simulator, and some sort of open world crafting game. The first two were both on my wishlist from browsing through various Steam sales, the third I'd marked uninterested. But it's one of the top sellers of the year, and has a $50 base price, so I'm going to give it a try. Letting people know they can get it (and some other stuff) for $12 could be a useful thing!

Path of Exile: Ultimate Party Buffs?

Path of Exile is a game that can be played in a group of up to 6 players and has a massive number of different options for how one character can do things to help the other characters in their party. Group buffs, enemy debuffs, specialized roles... The world is your grouping oyster!

And yet right now I feel like I get very little benefit from playing with my friends right now. We've all built characters in order to be able to successfully play alone which means they're all self sufficient. They haven't really put any effort into buffing a group (since it tends to be more expensive skill point wise to buff a group than to just find something to buff yourself) and the efforts put into debuffing the enemies will often come into conflict with each other (curses overwriting each other, elemental equilibriuming away an ally's damage, knockbacks, non-magic finders killing things).

So we started mulling over the idea of creating characters actively designed to work well together. If a character is built knowing they're going to get buffs from friends then they can make tradeoffs as they build their character. For example, if I know someone is going to make some really good curses to put on the enemy then I know I don't have to put any skill points into making my curses better. I don't have to waste skill gems on a curse setup. If I know someone is going to focus on doing a lot of damage then I don't have to worry about taking any damage nodes in the tree at all! Everyone can focus on being tough and doing a couple of good things for the group and actually play together without feeling bad about it.

I'm a little hyped, but now I want to make sure I pick up all the ways to help that I can! So I wanted to go through the list of skills and uniques and stuff to see what the different ways of helping out would be. It's important to not try to take too many helping things and end up squishy but it's entirely possible there are some fairly trivial buffs that people could pick up as long as they know about them. So I want to have a list of broad 'roles' and then a list of extra add-ons that could be picked up.

Roles:
- AoE damage dealer
- single target damage dealer (for bosses)
- aurabot(s)
- multi-curser
- magic finder
- super tank

Specifics:
- elemental equilibrium (would need to coordinate to use the right element)
- conduit to share power, frenzy, and/or endurance charges
- consecrated ground
- no stun after blocking from Guardian
- speed buff after warcry from Guardian
- armour, energy shield, physical reduction, life regen from Guardian auras
- attack/cast speed, damage, resists from Necro auras
- maim
- blind
- culling strike (@20% from Slayer)
- taunts (double reduction from Champion)
- damage and move speed from Champion
- bleeds buff Bloodlust support gem
- knockback (reverse with unique gloves?)
- stuns/freezes
- hinder
- warcries?
- corpse consumption?
- vaal auras
- frost bomb (cold resist reduction)
- spirited response jewel (rallying cry -> mana regen for party)
- the vigil jewel (vigilant strike fortifies the party)
- dying breath weapon (curse, aura, damage amp) {animate guardian?}
- shaper's seed amulet (health/mana regen aura)
- leer cast hat (damage amp) {animate guardian?}


Enemy damage increases
- Inquisitor (nearby 16% elemental damage)
- Champion (taunted 20% damage)
- intimidate (Champion)
- Warchief (near totem 16% phys/fire damage)
- maim support gem (10-14% physical damage)
- shocks!
- wither (140% chaos damage)

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.

Twitch Subscriptions for Affiliates

On Wednesday of this week Twitch rolled out the third stage of their program for getting more income streams for small streamers. The first was the bit system, the second was the game selling system (but the games I play aren't part of that scheme so I haven't really looked into it), and the third is opening up the subscription service, which is arguably the most important option of them all.

Subscriptions allow someone to pay $5, $10, or $25 each month in order to get a few bonuses for chatting on Twitch. Twitch takes a pretty big chunk of that (I had one person sub to me yesterday and my dashboard says I made $1.74, so I guess Twitch takes $3.25, but it could be that Twitch Prime subs are worth less? I don't know!) but it's still a way to set up ostensibly recurring income. Donations (direct through Paypal or via the bit system) are super nice and all but they're very erratic. Someone who is looking to be able to pay rent off of streaming is going to appreciate the consistency of subscription revenue.

There's also the weirdness around Amazon Prime which automatically comes with Twitch Prime which lets the person subscribe for free to one streamer. So it's like your Amazon Prime subscription actually comes with a $1.74 rebate, you just have to have the rebate mailed to someone else. Someone else like me!

As for what the person gets, they get a few things that have never seemed terribly interesting to me but there are a lot of people who get really into them. The first is you get an icon beside your name when chatting in that stream's chat that shows you're a subscriber. Partners can customize that icon and can have different ones for different numbers of consecutive months subscribed; affiliates just get a default star. But it's a way to show in chat that you're someone ponying up to support the streamer, and some people like that, so that's cool. The other thing they get is access to a chat emoticon designed explicitly for the stream. They can use it in any stream chat anywhere on Twitch so if you make a really cool emote then it becomes a form of advertising for your channel. (I've never watched AdmiralBahroo stream, for example, but he has some really sweet emotes that people use in my chat all the time.)

Partners get lots of emotes based on how many subscribers they have. Affiliates get exactly 3. One for each tier of subscription. (But if you have enough subscribers to be eligible for tons of emotes I'm pretty sure you can become a partner too so it's not that big a restriction.)

I didn't do a good job of planning ahead (they did say this was coming in the near future) so I don't even have any emote ideas let alone anything made. You can make changes, though it'll take a couple weeks to get things in or changed, so I really need to keep in mind that it doesn't need to be perfect. Getting something decent implemented quickly is more important than getting the optimal thing done in a year.

So I need to come up with some ideas, and then I need to get 28x28, 56x56, and 112x112 PNGs for those ideas.

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.