When I was preparing to work on the Realm First: Illustrious Cooking achievement I found a formula to work out the odds of getting a skill-up depending on when a recipe turned yellow, when it turned grey, and current skill level. I didn't find any proof of this formula anywhere or anyone really giving any justification for it. I found it in a few spots and ran with it, but I needed far less than I thought I would to max cooking. Sky needed far fewer metagems than he thought he would to max jewelcrafting, too. Did we just get a little lucky or is the formula wrong?
I want to find out by testing the formula to see if it stands up for at least one recipe. The issue then becomes that I need a lot of repetition at the same skill level to have any confidence in estimating the true odds of a skill-up at that skill level. My first thought was to just unlearn cooking over and over since it has a recipe at skill 1 that uses only vendor materials. Unfortunately it turns out you can't unlearn secondary professions, so that won't work. I could delete the character every time but you need to be level 5 to learn cooking so I'd need to level the new character every time in addition to having to transfer funds to buy the cheap vendor mats. Alternatively I could run tailoring off linen cloth or engineering off rough stone if I could gather up enough stuff. Tailoring has the advantage that I could make actual greens to disenchant to mitigate some of the cost.
How much stuff is enough stuff? The answer to that question depends on how confident I want to be. If I was testing a single event (like a die or a coin) I'd probably want to be sure within half a percent 99% of the time. Now, n = Z^2/(4E^2) where Z is pulled from a table of values for normal distributions and E is the maximum error I'd accept so I'd need to flip that coin n = (2.5759)^2/(4*(.005)^2) = 66353. That's a very big number. There's an added wrinkle for me as well in that I'm not testing a single event, I'm testing like 60 of them. There's a different probability at every skill level, so I'm estimating the odds of 60 numbers, not 1 number. To maintain that level of confidence would require 133k linen cloth per skill level. Even worse, the first few yellow points will give me a skill-up right away so getting 66k trials on them requires powering the first 24 orange ticks almost that many times as well.
What I can do, though, is relax my confidence requirements. Bolt of Linen Cloth has 25 skills between yellow and grey, so I'm expecting a 4% drop between each skill level. So if I set my maximum error to 2% I should still see the gradation between different skill levels. With 25 numbers here I should see if the formula is way wrong or not as long as most of my estimates are good, so I don't need the 99% confidence either. 95.45% (two standard deviations) seems like it should be more than good enough. With those new numbers n = 2500. Ugh. Nevermind the fact I cant force the same number of trials for each skill level, plowing 5k linen into each of the 25 skill points is absurd. We're talking a third of the linen needed to open the gates of Ahn'Qiraj just to run this test. That's not going to happen.
What if I assume I want the last skill point to have the 2500 iterations? Then the first one only gets 100 iterations. That really hurts my confidence in the first few goes but does bring my needed linen down to 70k. Is this something I can do or should I just give up? I do also get to make something from the bolts, so I get to run half again as many trials on Brown Linen Pants. 70k seems semi-reasonable but not something I'm going to farm myself. I think I'll just start buying cheap linen on the AH for a while and see how many I end up with.
I can't start now anyway, as I need a way to collect the data. The easiest way to do this has to be writing a LUA mod to output information each time something is crafted. Does the language have access to the right information? Only one way to find out, and that's to actually learn to write a WoW mod.
Tuesday, January 11, 2011
Monday, January 10, 2011
Death Strike Base Hits
Sthenno posted a comment asking about how often Death Strike lands for just the base heal. I assumed 50% in my analysis on how good stamina and mastery were but that was mostly just a guess. I decided to parse through our last raid and break it down by fight to see how close that guess was. (It's important to do it by fight since Chimaeron was one of the fights we did that night and it is certainly not typical.)
There are 6 possible outcomes here. The first is terrible and likely indicates I hit the button at full without having taken much damage in the last 5 seconds. The second is semi-reasonable. It's a base heal with some overheal in it, but at least it wasn't a fully wasted button. It also doesn't happen much at all. The third category is very reasonable. I get a full base heal and shield out of it and it's probably better to get 25k now when I need the healing than to wait and risk death or wasting healer mana in the hopes of getting more. The 4th is a little weird and rarely happened except on trash. It indicates I'm taking a real beating but got healed to full by other sources. This shows bored healers or excessively hard hitting trash than anything on my end I think. The 5th is a lot like the 4th except I snuck in for some healing. The last, and thankfully biggest, category is when I snag all of a large heal. Chimaeron skews these numbers a little (and would be worse if not for a lot of weak Death Strikes during phase 3) but you can argue Maloriak skews the numbers in the other direction.
I find it interesting that trash provides the biggest non-Chimaeron Death Strikes and even then is very close. I guess trash just hits really hard compared to bosses who do more raid damage. Base heals actually only make up 40% of all my heals, and even that is stretching it since the overheal ones don't get any extra benefit from more stamina and the full overheals don't get anything from mastery either. Really it's more like a quarter of relevant Death Strikes are for the base amount. I think this is because my first look into things was on Argaloth and has skewed the way I look at things a little. Real bosses hit way harder than Argaloth. In the context of my last post this makes stamina worse but it makes mastery better.
All this makes me think I need to get or build a rune mod. I saw reference to one on EJ that showed your current Death Strike heal that I may download and check out.
| Fight | Overheal Base Heal | Partial Base Heal | Full Base Heal | Overheal Big Heal | Partial Big Heal | Full Big Heal | Total |
| Argaloth | 4 | 1 | 4 | 0 | 0 | 6 | 15 |
| Trash | 9 | 3 | 15 | 6 | 9 | 45 | 87 |
| Omnitron | 13 | 1 | 11 | 3 | 8 | 31 | 67 |
| Maloriak | 4 | 1 | 12 | 0 | 0 | 4 | 21 |
| Chimaeron | 7 | 0 | 15 | 1 | 2 | 57 | 82 |
| Atramedes | 1 | 1 | 2 | 0 | 1 | 0 | 5 |
| Total | 38 | 7 | 59 | 10 | 20 | 143 | 277 |
| Fight | Overheal Base Heal | Partial Base Heal | Full Base Heal | Overheal Big Heal | Partial Big Heal | Full Big Heal |
| Argaloth | 27% | 7% | 27% | 0% | 0% | 40% |
| Trash | 10% | 3% | 17% | 7% | 10% | 52% |
| Omnitron | 19% | 1% | 16% | 4% | 12% | 46% |
| Maloriak | 19% | 5% | 57% | 0% | 0% | 19% |
| Chimaeron | 9% | 0% | 18% | 1% | 2% | 70% |
| Atramedes | 20% | 20% | 40% | 0% | 20% | 0% |
| Total | 14% | 3% | 21% | 4% | 7% | 52% |
There are 6 possible outcomes here. The first is terrible and likely indicates I hit the button at full without having taken much damage in the last 5 seconds. The second is semi-reasonable. It's a base heal with some overheal in it, but at least it wasn't a fully wasted button. It also doesn't happen much at all. The third category is very reasonable. I get a full base heal and shield out of it and it's probably better to get 25k now when I need the healing than to wait and risk death or wasting healer mana in the hopes of getting more. The 4th is a little weird and rarely happened except on trash. It indicates I'm taking a real beating but got healed to full by other sources. This shows bored healers or excessively hard hitting trash than anything on my end I think. The 5th is a lot like the 4th except I snuck in for some healing. The last, and thankfully biggest, category is when I snag all of a large heal. Chimaeron skews these numbers a little (and would be worse if not for a lot of weak Death Strikes during phase 3) but you can argue Maloriak skews the numbers in the other direction.
I find it interesting that trash provides the biggest non-Chimaeron Death Strikes and even then is very close. I guess trash just hits really hard compared to bosses who do more raid damage. Base heals actually only make up 40% of all my heals, and even that is stretching it since the overheal ones don't get any extra benefit from more stamina and the full overheals don't get anything from mastery either. Really it's more like a quarter of relevant Death Strikes are for the base amount. I think this is because my first look into things was on Argaloth and has skewed the way I look at things a little. Real bosses hit way harder than Argaloth. In the context of my last post this makes stamina worse but it makes mastery better.
All this makes me think I need to get or build a rune mod. I saw reference to one on EJ that showed your current Death Strike heal that I may download and check out.
Sunday, January 09, 2011
Bridge Match 1 - Board 101
Board 101 – Dealer North – No Vul
My hand: ♠ A J 6 ♥ K 8 ♦ K T 9 4 3 2 ♣ K T
I open 1 diamond in 3rd seat. Partner responds 1 spade. I retreat to 2 diamonds which gets passed out. West leads the 2 of clubs.
I have 5 diamonds and 2 spades. The lead has given me a club trick. I can set up a heart trick for sure and have spade and diamond finesses for more tricks. If everything is on I could make 5 diamonds, which could be unfortunate. At any rate, the club. 2-4-A-T. J-K-3-5.
I might as well draw trump. 2-5-A-6. J-Q-K-8. T-7-6 of clubs-3 of hearts. East has played 7 points so far, West has played none. So I don't like my odds of the spade finesse working. Maybe they're 3-3 and I can set up the long spade. For that to work I need to duck a spade. Sure. 6-3-5-9. East returns a heart. J-8-A-4. 5-6-7-K. I have a heart set up and an entry to it, but nothing to pitch since I ducked the spade. Oh well. I'm up, making 4.
Professor Jack disagrees with ducking a spade. In retrospect it really was giving up since I had 6 tricks with 8 cards to go and no way to avoid the A of heart loser. He wants me to run trump, possibly to set up a squeeze or endplay of some sort.
On the replay the bidding is the same. The play starts the same but when declarer gets in he finesses diamonds right away. Low to the J, losing to the Q. He also finesses the spades, losing to that Q as well. He has his long spade set up, but he pitched it away earlier when he drew trump. So he still loses the A of hearts. Making 3.
Nick: 130
Jack: 110
IMPs: +1 (+4 total)
My hand: ♠ A J 6 ♥ K 8 ♦ K T 9 4 3 2 ♣ K T
I open 1 diamond in 3rd seat. Partner responds 1 spade. I retreat to 2 diamonds which gets passed out. West leads the 2 of clubs.
NORTH ♠ K 8 7 5 ♥ Q 6 4 ♦ A J ♣ 7 6 5 4 | ||
| EAST ♣ 2 | ||
| SOUTH ♠ A J 6 ♥ K 8 ♦ K T 9 4 3 2 ♣ K T |
| West | North | East | South |
| Pass | Pass | 1♦ | |
| Pass | 1♠ | Pass | 2♦ |
| Pass | Pass | Pass |
I have 5 diamonds and 2 spades. The lead has given me a club trick. I can set up a heart trick for sure and have spade and diamond finesses for more tricks. If everything is on I could make 5 diamonds, which could be unfortunate. At any rate, the club. 2-4-A-T. J-K-3-5.
I might as well draw trump. 2-5-A-6. J-Q-K-8. T-7-6 of clubs-3 of hearts. East has played 7 points so far, West has played none. So I don't like my odds of the spade finesse working. Maybe they're 3-3 and I can set up the long spade. For that to work I need to duck a spade. Sure. 6-3-5-9. East returns a heart. J-8-A-4. 5-6-7-K. I have a heart set up and an entry to it, but nothing to pitch since I ducked the spade. Oh well. I'm up, making 4.
| NORTH ♠ K 8 7 5 ♥ Q 6 4 ♦ A J ♣ 7 6 5 4 | ||
| WEST ♠ Q T 3 ♥ A 5 2 ♦ 8 7 5 ♣ Q 8 3 2 | EAST ♠ 9 4 2 ♥ J T 9 7 3 ♦ Q 6 ♣ A J 9 | |
| SOUTH ♠ A J 6 ♥ K 8 ♦ K T 9 4 3 2 ♣ K T |
Professor Jack disagrees with ducking a spade. In retrospect it really was giving up since I had 6 tricks with 8 cards to go and no way to avoid the A of heart loser. He wants me to run trump, possibly to set up a squeeze or endplay of some sort.
On the replay the bidding is the same. The play starts the same but when declarer gets in he finesses diamonds right away. Low to the J, losing to the Q. He also finesses the spades, losing to that Q as well. He has his long spade set up, but he pitched it away earlier when he drew trump. So he still loses the A of hearts. Making 3.
Nick: 130
Jack: 110
IMPs: +1 (+4 total)
Saturday, January 08, 2011
Detailed Tanking Stats
Once upon a time the only tanking stat that really matter was maximum health. Sure, armor was good and you wouldn't say no to avoidance and threat stats but when given a choice it was all stamina all the time. If you had a socket to stick a gem into you put stamina in there, no questions asked. Imagine my surprise then when I wanted to get a stamina gem cut yesterday and nobody had the pattern. Apparently the 'mana matters' world of Cataclysm has changed things enough that everyone wants other stats instead. I got someone to buy the pattern for me and cut my stamina gem regardless because I'm still a fan. But the question is, should I be a fan? My mastery scales with stamina and mastery is my favourite rating so it seems like if any tank wants stamina it should be me. But, should I like stamina?
Also, I recently put on the Darkmoon Faire tanking trinket, replacing my old normal Putricide armour trinket. Now, that trinket has more armour than the new round of armour trinkets does, so it's entirely possible it's just better than current trinkets. The question here then is how good is armour relative to stamina and dodge?
Well, as a tank, what am I trying to accomplish with my gear? There are 3 different things I could be trying to accomplish:
The second option was relevant WAY back in the MC days (I geared avoid back then and stacked defense to try to get uncrittable back before anyone else did and I remember some healers were able to keep me up by changing how they healed and others just threw all their mana away) but hasn't been relevant since. The claim now is it's relevant again. I'm honestly not convinced. Healers certainly complain about mana more now than they used to and in early heroics I spent most of my time at medium to low health. But now, in raids? I'm full most of the time and if I'm not full I feel like I'm in real danger of dying. In heroics I used to hit cooldowns to try to save healer mana because I didn't feel like I was going to get spiked out. In raids I definitely feel like there are lots of spots where I could die and that I need to save my cooldowns just to live. Healer mana may matter a lot more in terms of how they handle raid damage and such but it feels like as a tank I just get spammed up reasonably often.
The third option I like to quantify in terms of what happens on the way from full to dead. Last expansion in particular I likened my health to a trinary system. Either I was at full life, or I was almost dead, or I was dead. Some people took this to the extreme and cared solely about "Effective Health" which took armor and health into account and completely ignored avoidance entirely. I've been a bigger proponent of "Tank Points" which take a long term look at how much damage you expect to have to take in order to be killed. A dodged attack absorbs the full amount with TP and is worthless in EH. The reality is probably somewhere between the two extremes and I tried to account for that in TBC with my own TPish program by adding in a parameter for spell damage that couldn't be avoided with dodge or armour and just cared about health. (Resists too, if the fight had enough magic damage.)
Finding the balance between those three things is non-trivial. I've tended towards just caring about the third weighting and assuming everything will work out fine with the other two. I think that model was clearly right in the last expansion and that Blizzard is claiming to be trying to change things this time. I'm not convinced they've succeeded but I can certainly find a value for every stat according to each of the three valuation systems to assign a relative ordering based on what I seem to be falling behind on.
The incremental value of each stat depends on my current stats. This is true because some stats interact well with each other and because some stats provide diminishing returns. Some stats have caps; getting more hit than the cap is useless for any of the three options. I will be comparing the value of stats according to how much a rare gem of that type would grant. For armour I will work out the equivalent amount based on the 346 trinkets.
Also, I recently put on the Darkmoon Faire tanking trinket, replacing my old normal Putricide armour trinket. Now, that trinket has more armour than the new round of armour trinkets does, so it's entirely possible it's just better than current trinkets. The question here then is how good is armour relative to stamina and dodge?
Well, as a tank, what am I trying to accomplish with my gear? There are 3 different things I could be trying to accomplish:
- Inflict more damage to the enemies, increasing my threat and killing them faster.
- Save healer mana.
- Stay alive in dangerous situation.
The second option was relevant WAY back in the MC days (I geared avoid back then and stacked defense to try to get uncrittable back before anyone else did and I remember some healers were able to keep me up by changing how they healed and others just threw all their mana away) but hasn't been relevant since. The claim now is it's relevant again. I'm honestly not convinced. Healers certainly complain about mana more now than they used to and in early heroics I spent most of my time at medium to low health. But now, in raids? I'm full most of the time and if I'm not full I feel like I'm in real danger of dying. In heroics I used to hit cooldowns to try to save healer mana because I didn't feel like I was going to get spiked out. In raids I definitely feel like there are lots of spots where I could die and that I need to save my cooldowns just to live. Healer mana may matter a lot more in terms of how they handle raid damage and such but it feels like as a tank I just get spammed up reasonably often.
The third option I like to quantify in terms of what happens on the way from full to dead. Last expansion in particular I likened my health to a trinary system. Either I was at full life, or I was almost dead, or I was dead. Some people took this to the extreme and cared solely about "Effective Health" which took armor and health into account and completely ignored avoidance entirely. I've been a bigger proponent of "Tank Points" which take a long term look at how much damage you expect to have to take in order to be killed. A dodged attack absorbs the full amount with TP and is worthless in EH. The reality is probably somewhere between the two extremes and I tried to account for that in TBC with my own TPish program by adding in a parameter for spell damage that couldn't be avoided with dodge or armour and just cared about health. (Resists too, if the fight had enough magic damage.)
Finding the balance between those three things is non-trivial. I've tended towards just caring about the third weighting and assuming everything will work out fine with the other two. I think that model was clearly right in the last expansion and that Blizzard is claiming to be trying to change things this time. I'm not convinced they've succeeded but I can certainly find a value for every stat according to each of the three valuation systems to assign a relative ordering based on what I seem to be falling behind on.
The incremental value of each stat depends on my current stats. This is true because some stats interact well with each other and because some stats provide diminishing returns. Some stats have caps; getting more hit than the cap is useless for any of the three options. I will be comparing the value of stats according to how much a rare gem of that type would grant. For armour I will work out the equivalent amount based on the 346 trinkets.
Stamina
Increases my maximum health which increases my time to live between full and dead. Increases the amount healed by my base Death Strike which generates threat from healing, which puts up a shield which keeps me alive longer, and which saves healer mana by healing myself and preventing damage with the shield. It also increases the amount I get healed by Rune Tap which has similar implications for threat, mana, and survivability. I believe it also increases the base health of my blood worms which increases the amount they heal which could save the healers some mana. Increasing maximum health also increases attack power from Vengeance which increases threat.
60 stamina is worth 756 health. Assume half of my Death Strikes would benefit from a bigger base and that I use Death Strike every 12 seconds. Then every 24 seconds I gain 53 health and a shield for 59, which is about 4.667 healing per second and 2.208 threat per second. Say I Rune Tap once a minute, then it also adds an extra 7.56 healing and threat per second. Blood worms seem to get about 25% of my extra hp as hp themselves and heal for 5% of their hp per stack. They explode at around 7.25 stacks every 15 seconds, so this adds an AE heal of 4.568 healing per second per target. Vengeance caps at 10% of my max health, so assuming I maintain a full Vengeance stack (requires taking 18k/s incoming damage which is not a given) I'd also gain 75 AP. Working out what that is worth is more effort than I want to put in, so I turned to BloodSim and ran a sim with about my stats and then again with some extra AP. It claims 1 AP is 3 TPS for me, so the extra 75 AP would be 225 threat per second.
- 235 TPS, ~100 DPS
- Assuming worms hits 2 people and none of the healing I gain is ever wasted, 21 HPS.
- 12 ADPS, 756 max hp.
Armour
Flat reduction of all incoming physical damage that isn't avoided in some other way. By comparing ilvl 346 trinkets it looks like you now get 2.664 armour per stamina in stat points on an item. So, to fit my comparison, I need to account for 213 armour. My runeforge weapon enchant boosts this armour, so 222 is the real compare number. Compared to my current armour this will reduce all incoming physical damage by 0.333%. Assume I'm getting punched for 34k every 2 seconds and I'm flat out avoiding 31% of incoming attacks. As such, it would prevent 39 damage per second. Armour also adds attack power for DKs, so I'd gain 7.1 AP from the armour for about 21 TPS.
- 21 TPS, ~10 DPS
- 39 HPS
- 39 ADPS
Dodge Rating
Spiky reduction of incoming physical damage. With my current dodge rating and agility levels I'd gain .1813% dodge from 40 dodge rating. Again assuming an incoming swing of 34k every 2 seconds this would prevent 31 damage per second.
- No effect
- 31 HPS
- 31 ADPS
Parry Rating
Spiky reduction of incoming physical damage. With my current parry rating I'd gain .1742% parry from 40 parry rating. Again assuming an incoming swing of 34k every 2 seconds this would prevent 30 damage per second.
- No effect
- 30 HPS
- 30 ADPS
Mastery Rating
Makes my Blood Shield better. 40 mastery rating is .2231 mastery, which adds 1.7849% of my Death Strike heal into the Blood Shield. Assume I land a Death Strike every 12 seconds and that half of them are for base (same assumption as for Stamina above) and we'll give twice base for the other half. I believe I'm around 180k buffed hp right now, so the base Death Strike is 12600 and double is 25200. So 40 mastery gives me a shield of 337 every 12 seconds or 28 damage prevented per second.
- No effect
- 28 HPS
- 28 ADPS
Haste Rating
Improves rune regen rate which increases amount healed by Death Strike. It also increases my threat in pretty much all ways since it increases my melee swing timer and lets me pump through the same proportion of extra everything. I guess it doesn't improve my dots or reduce the cooldown on rune tap so it's not quite a straight proportional improvement but it should be close enough. 40 haste rating would add on an extra .3124% haste to my existing 20.39% haste. This would bring my rune cooldown from every 8.3063 seconds to every 8.2848 seconds. This is a .2595% increase to everything. A quick look at the Omnotron encounter shows I have about 7k DPS right now, so a .2595% increase to that is an extra 18DPS and around 36 TPS. As well that would increase my Death Strike healing/shield from the current 3323 HPS by the same ratio, or a gain of 8.6 HPS. This would help the threat as well by just the heal, or an extra 4 TPS.
- 40 TPS, 18 DPS
- 8.6 HPS
- 8.6 ADPS
Hit Rating
Makes my interrupting and debuffing more consistent on top of increasing threat. Since runes aren't spent if the ability misses and I'm not GCD capped it's hard to work out the actual gain from hit rating. Currently on a boss I miss 4.98% of the time with melee attacks and 13.46% of the time with spells. 40 hit rating improves the melee hit chance by .33% and the spell hit by .39%. These are bigger numbers than the haste ones so theoretically if my resources were spent hit would be better than haste for everything. But they aren't. Missing a death strike is bad if I get pushed from a big death strike to a base death strike from the delay (or if I die from the delay) but really hit just isn't great. I do want to cap it out if possible to make sure my interrupts hit, though.
- Unclear
- Unclear
- Unclear
Expertise Rating
Right now I'm exactly at the point where dodges are gone. 40 expertise rating would decrease dodge/parry each by .33% (same as melee hit) and doesn't help spells at all. So up to the dodge cap it's twice as good on melee and worthless on spells as hit it. After the dodge cap it's just worse than hit. And it isn't needed for interrupting spells or applying debuffs, so it's not very good at all. I wanted to get up to the cap to help Death Strikes be more consistent, and I'm there, so I really don't think I want to work on removing more parries.
- Unclear
- Unclear
- Unclear
Crit Rating
Increases threat and has no impact on surviving at all. (Death Strike heals can't crit.) I appear to crit right now on 2% of my abilities (7% on some of the abilities that are glyphed to crit more). 40 crit rating would give me an extra .2231% crit. Averaging things out a bit and assuming about 4% of my stuff crits now I'd be going from 1.04 to 1.042231 or an increase of .2145%. This would be about 15 DPS and 30 TPS.
- 30 TPS, 15 DPS
- No effect
- No effect
Agility
Part dodge rating, part crit rating. 40 agility gets improved by mark, so it's really 42 agility. 1 agility is worth .4103 dodge rating (.4308 post mark) and .7357 crit rating (.7724 post mark).
- 23 TPS, 12 DPS
- 13 HPS
- 13 ADPS
Strength
25% of strength goes to parry rating. Also, strength is worth 2 AP each. Strength gets buffed by mark and Abomination's Might so 40 strength is really 42.84.
- 257 TPS, 129 DPS
- 8 HPS
- 8 ADPS
Every fight is different, of course, and the relative ranking of mastery to dodge depends a lot on the fight. One with spiky spell damage and reasonable melee damage favours mastery heavily. One with brutal melee swings (like Chimaeron) favours dodge rating with mastery being completely useless. I can also get better with my Death Strike timings which makes mastery, stamina, and haste better compared to armour and dodge. Stamina is oddly my second best threat stat (makes me wonder about the Vengeance capping assumption) and is a pretty good avoid stat too, plus it adds to max hp. I definitely feel like at the present time I should keep stacking stamina.
But what about Unidentified Organ? How good is 1890 armour and 240 stamina compared to 193 dodge, 128 mastery, and a cooldown use or 482 stamina and a cooldown use?
Organ - 1126 TPS, 489 DPS, 430 HPS, 394 ADPS, 3024 max hp
Darkmoon - 239 HPS, 239 ADPS, last stand use
Vial - 1887 TPS, 803 DPS, 169 HPS, 96 ADPS, 6073 max hp, dodge use
It feels like I should probably use Vial and Organ, sadly. If I had a heroic Organ it would be even better.
Friday, January 07, 2011
Bridge Match 1 - Board 100
Board 100 – Dealer West – All Vul
My hand: ♠ A Q T 9 8 6 ♥ T 4 ♦ K 5 2 ♣ A 8
West opens 1 heart and East raises to 2. I bid 2 spades. West bids 3 hearts and East goes to 4 with partner staying silent the whole time. I'm probably down 3 doubled if I bid again which is worse than their game, so I pass. Partner leads the 5 of spades.
5-2-A-J. Declarer likely has the K of spades so I can give partner a ruff. 6-K-5 of hearts-3. I hope partner realizes my lowest spade means I have a club entry. Instead he cashes the A of hearts. A-3-4-2. Now partner shifts to a club. 3-4-A-7. Is there any reason to not play a spade here? Maybe I should draw trump instead. But that doesn't seem great. I play a spade. Q-J of hearts-3 of diamonds-4. Declarer draws my trump. K-6 of clubs-6-T. He ruffs a club away. 2-5-7 of hearts-8. He ruffs a spade back to hand. 7-8-8 of hearts-4 of diamonds. Another club ruff. T-9-Q of hearts-2 of diamonds. Then it turns out declarers clubs are set up so he's up. Down 1. Partner pitched a club or they'd be down 2. (Though declarer can take a ruffing finesse if he has to.)
Professor Jack agrees with me all the way! With both opponents bidding crazily with minimums I'm not the one he should be criticizing here anyway.
The auction is the same at the other table and they take the same tricks for down 1.
Nick: 100
Jack: 100
IMPs: 0 (+3 total)
My hand: ♠ A Q T 9 8 6 ♥ T 4 ♦ K 5 2 ♣ A 8
West opens 1 heart and East raises to 2. I bid 2 spades. West bids 3 hearts and East goes to 4 with partner staying silent the whole time. I'm probably down 3 doubled if I bid again which is worse than their game, so I pass. Partner leads the 5 of spades.
NORTH ♠ 5 | ||
| EAST ♠ 7 4 3 2 ♥ Q 7 6 3 ♦ A 9 7 6 ♣ 4 | ||
| SOUTH ♠ A Q T 9 8 6 ♥ T 4 ♦ K 5 2 ♣ A 8 |
| West | North | East | South |
| 1♥ | Pass | 2♥ | 2♠ |
| 3♥ | Pass | 4♥ | All Pass |
5-2-A-J. Declarer likely has the K of spades so I can give partner a ruff. 6-K-5 of hearts-3. I hope partner realizes my lowest spade means I have a club entry. Instead he cashes the A of hearts. A-3-4-2. Now partner shifts to a club. 3-4-A-7. Is there any reason to not play a spade here? Maybe I should draw trump instead. But that doesn't seem great. I play a spade. Q-J of hearts-3 of diamonds-4. Declarer draws my trump. K-6 of clubs-6-T. He ruffs a club away. 2-5-7 of hearts-8. He ruffs a spade back to hand. 7-8-8 of hearts-4 of diamonds. Another club ruff. T-9-Q of hearts-2 of diamonds. Then it turns out declarers clubs are set up so he's up. Down 1. Partner pitched a club or they'd be down 2. (Though declarer can take a ruffing finesse if he has to.)
| NORTH ♠ 5 ♥ A 5 ♦ Q T 8 4 3 ♣ Q 9 6 5 3 | ||
| WEST ♠ K J ♥ K J 9 8 2 ♦ J ♣ K J T 7 2 | EAST ♠ 7 4 3 2 ♥ Q 7 6 3 ♦ A 9 7 6 ♣ 4 | |
| SOUTH ♠ A Q T 9 8 6 ♥ T 4 ♦ K 5 2 ♣ A 8 |
Professor Jack agrees with me all the way! With both opponents bidding crazily with minimums I'm not the one he should be criticizing here anyway.
The auction is the same at the other table and they take the same tricks for down 1.
Nick: 100
Jack: 100
IMPs: 0 (+3 total)
Thursday, January 06, 2011
Cylon Leaders
The second Battlestar Galactica board game expansion came out last week and it just happened to be New Year's Eve so of course it got picked up and played at Andrew's place. There are a lot of new mechanics so we wanted to minimize the impact of the first expansion but we ended up with 7 players and hence had to use a cylon leader. I rolled relatively high and got to pick second and decided if one of us had to be a cylon leader it might as well be me.
For those who may not know the game it's a team game where you don't know who's on your team at the start of the game. You get dealt secret cards indicating which team you're on both at the start of the game and halfway through the game. Everyone starts out as a human but some people are actually cylons in disguise. The humans are just trying to survive to game end; the cylons are trying to commit genocide in any of a variety of ways. You take a lot of hidden actions so people try to use logic to deduce who is actually evil based on imperfect information. It's pretty interesting but hard to balance with 7 people. 4 humans against 3 cylons is pretty much a slaughter for the cylons. 5 humans against 2 cylons is pretty much a guaranteed win for the humans. So what they did was they made the "cylon leader" who doesn't take part in the hidden team part of the game the way the other players do. They act as a cylon most of the time but can also turn into a human and help them if they want. Their motivation is derived from a secret agenda card which tells them what their win conditions are. They either need the humans to win while having done things to hurt them or they need the cylons to win with a lot of complications tacked on. In theory it makes the balance more like 4.5 vs 2.5 but in practice it doesn't always work out that way. I think it warps games but it's a reasonable solution to the problem of the game only being balanced with 5 players by default.
At any rate, an interesting situation arose in the game we played. It became pretty clear that I was a cylon-wins cylon leader since every overt action I took for the first 2 hours of the game was attacking the humans. It also became pretty clear that the humans were dead. They were in danger of losing on 5 of the 6 losing conditions and were a long way from the end. But I hadn't completed my special objectives yet, so we were basically just playing it out to see if I could win or not. Assuming I actually am a cylon-wins character there are 4 possible options for what I could need to accomplish. The question then is, how should the other players act?
The 4 humans should hope for a miracle and keep trying to survive as long as possible. I'd actually started helping them near the end and a couple lucky draws and maybe they could have pulled it off. Alternatively, if they've really given up they could try to work out my win condition and fight to keep me from getting it. The cylons win, no need to have the cylon leader win.
What should the 2 cylons do? If they get me working with them again they definitely win. Ignore me and they almost certainly win. If they work at it they might be able to screw me out of my goal, but should they even worry about it? There is certainly some risk involved, since the further they take me from my goal the more I need to prolong the game in order to win.
For me the answer is clear. I need to achieve my goal and then blow the humans up. If I'm not going to win I have to keep them alive, if I am I want them dead. I'm not spite playing here, if that matters, but maximizing my own winningness. This sort of thing came up in Republic of Rome too. Is it 'better' for the humans to have me lose too? Is it 'worse' if I win? Or once they've lost should it be irrelevant to them?
As it turned out I had to help the humans survive one card that was guaranteed to kill them if I hadn't helped. My criteria was met shortly thereafter and then we blew them up. No one even put any thought into what I could be trying to accomplish or tried to help/hinder me in any way. The game was a little long and I think most people just wanted it over, but I'm not sure they could have colluded to keep me from winning even if they knew my goal. (Not without just throwing in the towel long before they were practically guaranteed death.) I'm pretty sure I had the hardest secret objective (cylons win, 3 or less morale, 4 or more Galactica locations damaged) and it was pretty tricky trying to pull both of the requirements off. But I was essentially a better cylon from the start of the game to the end and only helped the humans once, so they didn't have a lot of hope of winning, sadly. Which is the problem with the cylon leaders in general. I had a great game but the humans (Andrew, Byung, Dee, and Heather) had a lot of trouble and the two cylons (Adam and Duncan) had an easier time than they should have. This isn't to say they didn't play well (Adam managed to take some bad actions as a hidden cylon without being ousted and I didn't think Duncan was a cylon either until he revealed) but the game balance was skewed in their favour because of the cylon leader. It's always great to be the cylon leader, so if I played a lot of games and everyone rotated being the cylon leader I think it would be a reasonable mechanic. But I don't play enough and some people refuse to be a cylon leader so I'm not much of a fan. Even if you can call me Al.
For those who may not know the game it's a team game where you don't know who's on your team at the start of the game. You get dealt secret cards indicating which team you're on both at the start of the game and halfway through the game. Everyone starts out as a human but some people are actually cylons in disguise. The humans are just trying to survive to game end; the cylons are trying to commit genocide in any of a variety of ways. You take a lot of hidden actions so people try to use logic to deduce who is actually evil based on imperfect information. It's pretty interesting but hard to balance with 7 people. 4 humans against 3 cylons is pretty much a slaughter for the cylons. 5 humans against 2 cylons is pretty much a guaranteed win for the humans. So what they did was they made the "cylon leader" who doesn't take part in the hidden team part of the game the way the other players do. They act as a cylon most of the time but can also turn into a human and help them if they want. Their motivation is derived from a secret agenda card which tells them what their win conditions are. They either need the humans to win while having done things to hurt them or they need the cylons to win with a lot of complications tacked on. In theory it makes the balance more like 4.5 vs 2.5 but in practice it doesn't always work out that way. I think it warps games but it's a reasonable solution to the problem of the game only being balanced with 5 players by default.
At any rate, an interesting situation arose in the game we played. It became pretty clear that I was a cylon-wins cylon leader since every overt action I took for the first 2 hours of the game was attacking the humans. It also became pretty clear that the humans were dead. They were in danger of losing on 5 of the 6 losing conditions and were a long way from the end. But I hadn't completed my special objectives yet, so we were basically just playing it out to see if I could win or not. Assuming I actually am a cylon-wins character there are 4 possible options for what I could need to accomplish. The question then is, how should the other players act?
The 4 humans should hope for a miracle and keep trying to survive as long as possible. I'd actually started helping them near the end and a couple lucky draws and maybe they could have pulled it off. Alternatively, if they've really given up they could try to work out my win condition and fight to keep me from getting it. The cylons win, no need to have the cylon leader win.
What should the 2 cylons do? If they get me working with them again they definitely win. Ignore me and they almost certainly win. If they work at it they might be able to screw me out of my goal, but should they even worry about it? There is certainly some risk involved, since the further they take me from my goal the more I need to prolong the game in order to win.
For me the answer is clear. I need to achieve my goal and then blow the humans up. If I'm not going to win I have to keep them alive, if I am I want them dead. I'm not spite playing here, if that matters, but maximizing my own winningness. This sort of thing came up in Republic of Rome too. Is it 'better' for the humans to have me lose too? Is it 'worse' if I win? Or once they've lost should it be irrelevant to them?
As it turned out I had to help the humans survive one card that was guaranteed to kill them if I hadn't helped. My criteria was met shortly thereafter and then we blew them up. No one even put any thought into what I could be trying to accomplish or tried to help/hinder me in any way. The game was a little long and I think most people just wanted it over, but I'm not sure they could have colluded to keep me from winning even if they knew my goal. (Not without just throwing in the towel long before they were practically guaranteed death.) I'm pretty sure I had the hardest secret objective (cylons win, 3 or less morale, 4 or more Galactica locations damaged) and it was pretty tricky trying to pull both of the requirements off. But I was essentially a better cylon from the start of the game to the end and only helped the humans once, so they didn't have a lot of hope of winning, sadly. Which is the problem with the cylon leaders in general. I had a great game but the humans (Andrew, Byung, Dee, and Heather) had a lot of trouble and the two cylons (Adam and Duncan) had an easier time than they should have. This isn't to say they didn't play well (Adam managed to take some bad actions as a hidden cylon without being ousted and I didn't think Duncan was a cylon either until he revealed) but the game balance was skewed in their favour because of the cylon leader. It's always great to be the cylon leader, so if I played a lot of games and everyone rotated being the cylon leader I think it would be a reasonable mechanic. But I don't play enough and some people refuse to be a cylon leader so I'm not much of a fan. Even if you can call me Al.
Wednesday, January 05, 2011
Yahtzee Jr.
I played a kid's game this weekend and thought I was quite clever in figuring out a way to get a slight edge. I ended up beating Andrew and his two children twice (probably mostly through luck) but I wanted to see how slight that edge was.
The game is a very simplified version of Yahtzee in that you have 5 dice and 3 rolls to make your best 'hand' which you put on the scoring chart. All you're collecting is sets. There are no straights or full houses or anything like that. (In fact the dice all had pictures on them so the concept of a straight is right out.) There are two twists compared to normal Yahtzee. First, the dice each have the 5 main characters on them that you're collecting and 1 wild value. Second, one of the wilds is actually an anti-wild. It counts as nothing and can't be rerolled at all.
My 'trick' was to find the die with the anti-wild on it and keep it if I had a choice. To make things clearer, assume I'm using standard D6s and the 1s are wild. One of the dice has the 1 scratched off and replaced by something else to represent the anti-wild. I make my first roll and it comes out 1-2-2-3-3. Should I collect 2s or 3s? Normally in Yahtzee the answer to that question depends on what you've filled in on your scorecard but it often doesn't really matter. You have the same odds of getting 5-of-a-kind with either 2s or 3s. In this variant, however, I should find the die with the anti-wild on it. If it's on one of the dice current showing a 2 I should keep the 2s. If it's on a die currently showing a 3 I should keep it. I'm always keeping the wild as well. What sort of edge am I getting by choosing this way as opposed to always rerolling the anti-wild?
Well, I get to reroll each of the dice twice. The first die is 1/3 to give me what I want on the first roll and 2/3*1/3=2/9 to give me what I want on the second roll for a total of 5/9 to turn out good. The odds are the same for the second die. So, my overall odds are 16/81 - 3-of-a-kind. 40/81 - 4-of-a-kind. 25/81 - 5-of-a-kind.
What if I keep the anti-wild in play? The first die has the same odds as above but the second one is 1/6 to give me what I want on the first roll and 4/6*1/6=1/9 to give me what I want on the second roll. Overall that's 5/18 to give me what I want as opposed to 5/9 with the normal die. My overall odds here are 52/162 - 3-of-a-kind. 85/162 - 4-of-a-kind. 25/162 - 5-of-a-kind.
My expected value score in the first case is 4.1111. My expected value in the second case is 3.8333.
How about if my first roll is worse? (Simplify things a little and assume you can't switch horses in mid stream, so even if you roll 3-3-3-3 on your second roll it doesn't help if you kept a 2 to start.) 2-3-4-5-6, say? Pick out the bad die and keep it and you end up with 256/6561 - 1-of-a-kind. 1280/6561 - 2-of-a-kind. 2400/6561 - 3-of-a-kind. 2000/6561 - 4-of-a-kind. 625/6561 - 5-of-a-kind. Run with something else and you end up with 832/13122 - 1-of-a-kind. 3440/13122 - 2-of-a-kind. 5100/13122 - 3-of-a-kind. 3125/13122 - 4-of-a-kind. 625/13122 - 5-of-a-kind.
My expected value in the first case is 3.2222. My expected value in the second case is 2.9444. I am happy but not too surprised to see the difference is the same. A gain a little more than a quarter of a point by making this choice over making the wrong choice. Someone who isn't aware of this is going to pick right half the time, so my edge is .1389 points. This is, of course, assuming that I didn't roll the anti-wild in my first roll and that the die it's on is one of my potential best picks.
Or does it? What if I roll 2-2-3-4-5? Should I keep the 3 if it's the anti-wild? I already know my expected value in that case, so I need to work out the results when I keep the 2-2. Well, my odds are 208/1458 - 2-of-a-kind. 600/1458 - 3-of-a-kind. 525/1458 - 4-of-a-kind. 125/1458 - 5-of-a-kind. Or an expected value of 3.3889. This is bigger than the 3.2222 where I keep just the anti-wild die, so no unexpected diversions in strategy here. Keep the bigger raw number, only use the location of the anti-wild to break ties. This was my gut feeling at the time, so I'm glad it pans out in reality.
Now the real question is should I really be looking for edges in order to beat 6 and 7 year old kids at board games? Now that I have the edge, should I use it? Should I try to explain it to them? Should I only use it if Andrew is also playing?
The game is a very simplified version of Yahtzee in that you have 5 dice and 3 rolls to make your best 'hand' which you put on the scoring chart. All you're collecting is sets. There are no straights or full houses or anything like that. (In fact the dice all had pictures on them so the concept of a straight is right out.) There are two twists compared to normal Yahtzee. First, the dice each have the 5 main characters on them that you're collecting and 1 wild value. Second, one of the wilds is actually an anti-wild. It counts as nothing and can't be rerolled at all.
My 'trick' was to find the die with the anti-wild on it and keep it if I had a choice. To make things clearer, assume I'm using standard D6s and the 1s are wild. One of the dice has the 1 scratched off and replaced by something else to represent the anti-wild. I make my first roll and it comes out 1-2-2-3-3. Should I collect 2s or 3s? Normally in Yahtzee the answer to that question depends on what you've filled in on your scorecard but it often doesn't really matter. You have the same odds of getting 5-of-a-kind with either 2s or 3s. In this variant, however, I should find the die with the anti-wild on it. If it's on one of the dice current showing a 2 I should keep the 2s. If it's on a die currently showing a 3 I should keep it. I'm always keeping the wild as well. What sort of edge am I getting by choosing this way as opposed to always rerolling the anti-wild?
Well, I get to reroll each of the dice twice. The first die is 1/3 to give me what I want on the first roll and 2/3*1/3=2/9 to give me what I want on the second roll for a total of 5/9 to turn out good. The odds are the same for the second die. So, my overall odds are 16/81 - 3-of-a-kind. 40/81 - 4-of-a-kind. 25/81 - 5-of-a-kind.
What if I keep the anti-wild in play? The first die has the same odds as above but the second one is 1/6 to give me what I want on the first roll and 4/6*1/6=1/9 to give me what I want on the second roll. Overall that's 5/18 to give me what I want as opposed to 5/9 with the normal die. My overall odds here are 52/162 - 3-of-a-kind. 85/162 - 4-of-a-kind. 25/162 - 5-of-a-kind.
My expected value score in the first case is 4.1111. My expected value in the second case is 3.8333.
How about if my first roll is worse? (Simplify things a little and assume you can't switch horses in mid stream, so even if you roll 3-3-3-3 on your second roll it doesn't help if you kept a 2 to start.) 2-3-4-5-6, say? Pick out the bad die and keep it and you end up with 256/6561 - 1-of-a-kind. 1280/6561 - 2-of-a-kind. 2400/6561 - 3-of-a-kind. 2000/6561 - 4-of-a-kind. 625/6561 - 5-of-a-kind. Run with something else and you end up with 832/13122 - 1-of-a-kind. 3440/13122 - 2-of-a-kind. 5100/13122 - 3-of-a-kind. 3125/13122 - 4-of-a-kind. 625/13122 - 5-of-a-kind.
My expected value in the first case is 3.2222. My expected value in the second case is 2.9444. I am happy but not too surprised to see the difference is the same. A gain a little more than a quarter of a point by making this choice over making the wrong choice. Someone who isn't aware of this is going to pick right half the time, so my edge is .1389 points. This is, of course, assuming that I didn't roll the anti-wild in my first roll and that the die it's on is one of my potential best picks.
Or does it? What if I roll 2-2-3-4-5? Should I keep the 3 if it's the anti-wild? I already know my expected value in that case, so I need to work out the results when I keep the 2-2. Well, my odds are 208/1458 - 2-of-a-kind. 600/1458 - 3-of-a-kind. 525/1458 - 4-of-a-kind. 125/1458 - 5-of-a-kind. Or an expected value of 3.3889. This is bigger than the 3.2222 where I keep just the anti-wild die, so no unexpected diversions in strategy here. Keep the bigger raw number, only use the location of the anti-wild to break ties. This was my gut feeling at the time, so I'm glad it pans out in reality.
Now the real question is should I really be looking for edges in order to beat 6 and 7 year old kids at board games? Now that I have the edge, should I use it? Should I try to explain it to them? Should I only use it if Andrew is also playing?
Tuesday, January 04, 2011
Bridge Match 1 - Board 99
Board 99 – Dealer South – NS Vul
My hand: ♠ 9 6 ♥ A T 8 7 ♦ 8 6 2 ♣ K 9 5 4
West opens 1 diamond in 2nd seat. Partner bids 1 heart and East bids 1 spade. I abide by the law so I bid 3 hearts. West bids 4 diamonds and East goes to 5. Partner leads the 4 of hearts.
4-J-A-2. Declarer should be out of hearts now, so I could go for a tap. He could pitch and float around to dummy's Q if he needs 2 pitches, though. Alternatively I can play a club in the hopes that partner has the A, or the Q, or the J and declarer misguesses. That seems like a better plan. I play the 9 of clubs. 9-J-Q-3.
Partner foolishly cashes the K of hearts, establishing the Q on board. K-6-7-9 of diamonds. Declarer draws trump. T-4-3-2. J-3 of hearts-5-6. Then declarer switches to a spade. J-K-A-6. Declarer is up because he gets to pitch his 4th club on the Q of hearts. Making 5.
Professor Jack disagrees with my club play. He wants me to lead low. He then disagrees with my spade play and wants me to play high to show 2. I thought that would help declarer more than partner is why I didn't.
The bidding is the same on the replay. My hand returns a low club and North again cashes the K of hearts like a moron. Also making 5. I go back and make partner return a club but he ends up getting squeezed. I go back and force my hand to return a heart instead of a club at trick 2. Declarer ruffs but still gets the squeeze off because my hand fires back a club and not a heart when declarer ducks a club. I go back and make him play another heart to eliminate that threat. My hand then pitches a club letting declarer establish that suit. I make him keep his clubs but then declarer just crossruffs the hand. I guess there's actually nothing to do to set them.
Nick: -600
Jack: -600
IMPs: +0 (+3 total)
My hand: ♠ 9 6 ♥ A T 8 7 ♦ 8 6 2 ♣ K 9 5 4
West opens 1 diamond in 2nd seat. Partner bids 1 heart and East bids 1 spade. I abide by the law so I bid 3 hearts. West bids 4 diamonds and East goes to 5. Partner leads the 4 of hearts.
NORTH ♥ 4 | ||
| EAST ♠ A Q 8 7 5 ♥ Q J 6 ♦ 7 5 3 ♣ 7 3 | ||
| SOUTH ♠ 9 6 ♥ A T 8 7 ♦ 8 6 2 ♣ K 9 5 4 |
| West | North | East | South |
| Pass | |||
| 1♦ | 1♥ | 1♠1 | 3♥ |
| 4♦ | Pass | 5♦ | All Pass |
| 1At least 5 spades | |||
4-J-A-2. Declarer should be out of hearts now, so I could go for a tap. He could pitch and float around to dummy's Q if he needs 2 pitches, though. Alternatively I can play a club in the hopes that partner has the A, or the Q, or the J and declarer misguesses. That seems like a better plan. I play the 9 of clubs. 9-J-Q-3.
Partner foolishly cashes the K of hearts, establishing the Q on board. K-6-7-9 of diamonds. Declarer draws trump. T-4-3-2. J-3 of hearts-5-6. Then declarer switches to a spade. J-K-A-6. Declarer is up because he gets to pitch his 4th club on the Q of hearts. Making 5.
| NORTH ♠ K T 4 3 ♥ K 9 5 4 3 ♦ 4 ♣ Q T 2 | ||
| WEST ♠ J 2 ♥ 2 ♦ A K Q J T 9 ♣ A J 8 6 | EAST ♠ A Q 8 7 5 ♥ Q J 6 ♦ 7 5 3 ♣ 7 3 | |
| SOUTH ♠ 9 6 ♥ A T 8 7 ♦ 8 6 2 ♣ K 9 5 4 |
Professor Jack disagrees with my club play. He wants me to lead low. He then disagrees with my spade play and wants me to play high to show 2. I thought that would help declarer more than partner is why I didn't.
The bidding is the same on the replay. My hand returns a low club and North again cashes the K of hearts like a moron. Also making 5. I go back and make partner return a club but he ends up getting squeezed. I go back and force my hand to return a heart instead of a club at trick 2. Declarer ruffs but still gets the squeeze off because my hand fires back a club and not a heart when declarer ducks a club. I go back and make him play another heart to eliminate that threat. My hand then pitches a club letting declarer establish that suit. I make him keep his clubs but then declarer just crossruffs the hand. I guess there's actually nothing to do to set them.
Nick: -600
Jack: -600
IMPs: +0 (+3 total)
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