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### AuthorTopic: More data mining: Answering Dominion questions with data  (Read 11580 times)

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#### TheExpressicist

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##### More data mining: Answering Dominion questions with data
« on: January 30, 2015, 03:40:32 pm »
+3

Update:
There have been a few requests for additional data and I've done some more research that I wanted to share but I don't want to create yet another thread. I'll update this first post with additional data as I collect it.

Card "Strength"

This uses the data gathered from the "Individual Player Analysis" tool, from the games of the Top-20 players as ranked by Isotropish.

Preface:
Firstly, I use the term "strength" quite loosely. In laymen's terms, this chart is a graph of how often a card is gained combined with how often games are won with that card. Each card is assigned a score that will always be a value between 0 and 100. A score of 100 would mean that the card is gained in 100% of the games and you win 100% of the time you gain it. Secondly, the chart uses "Adjusted Win Rate", which is just (Card Win Rate) minus (Average Win Rate). An Adjusted Win Rate of 0% means the card is completely average. (For what it's worth , the average win rate is like 65%).

I feel the need to highlight this: there are many, many, many explanations for why a card with a LOW win%/gain%. There are much fewer explanations for why a card has a HIGH win%/gain%. So although it is safe to assume that a card with a high score is a good card, it is NOT a reasonable assumption that a card with a low score is a bad card..

To reiterate: I would be very careful about how you interpret cards at the middle-to-lower end of the scale. There's a lot more room for cause-effect here: certain cards may make sense to buy only when you're already in a losing position. This does not necessarily reflect on the strength of the card itself.

 Card Name SCORE Adjusted Win% Gain% Butcher: 93.1 5.7% 83% King'sCourt: 93.1 5.9% 82.2% CandlestickMaker: 90.3 5% 79.3% Squire: 90.2 4.6% 81.5% Peddler: 88.4 5.5% 73.6% Forager: 88.4 3.4% 86.1% WanderingMinstrel: 88.3 4% 80.7% Goons: 87.9 3.1% 89.6% Chapel: 87.7 3.1% 88% GrandMarket: 86.8 4.7% 73.5% Ambassador: 86.1 2.9% 84.8% BorderVillage: 86 2.8% 86.5% Haggler: 83.9 5.2% 67.3% Menagerie: 83.1 3.3% 74.7% Hermit: 82.2 2.6% 78.4% Conspirator: 81.9 4.1% 68.5% Remake: 81.8 3.1% 73.3% City: 81.3 2.9% 73.6% Festival: 80.3 4.8% 63.9% Witch: 79.9 2.2% 76.9% Baker: 79.7 2.9% 71.5% Apprentice: 78.1 3.4% 66.4% Pawn: 77.9 4.3% 62.4% Market: 77.6 4.5% 61.3% Inn: 77.5 3.9% 63.3% Plaza: 76.9 1.1% 82.6% Hamlet: 76.8 1.1% 82.3% NativeVillage: 76 3.9% 61.5% BanditCamp: 75.9 4.1% 60.8% Counterfeit: 75.9 1.5% 76.2% Tactician: 75.7 3.6% 62.2% FarmingVillage: 75.5 4.7% 58.5% Cellar: 75.4 3.6% 61.9% Fortress: 75.1 2.5% 66.7% Wharf: 74.5 0.3% 88.9% ThroneRoom: 74.3 2% 69.1% Masquerade: 74.2 0.4% 87.3% Scheme: 73.2 1.1% 74.7% FishingVillage: 72.4 0.2% 83.4% Ill-GottenGains: 72.2 3.9% 57.1% MerchantGuild: 72.1 2.9% 61.3% Remodel: 72 4.7% 54.6% Minion: 71.7 0.3% 80.1% Altar: 71.6 2.5% 62.3% HuntingParty: 71.4 0.1% 82.4% Cultist: 71.2 1% 72.5% MarketSquare: 71.1 1% 71.5% ScryingPool: 70 1.5% 66.8% GreatHall: 69.8 0.7% 72.5% MiningVillage: 68 1% 67.6% WishingWell: 67.2 2.5% 57.2% Vineyard: 66.8 3.4% 53.1% JunkDealer: 66.7 -0.3% 76.3% Courtyard: 66.3 -0.1% 73.9% Tunnel: 65.8 0.6% 67.5% Bridge: 64.6 0.7% 64.9% Mint: 64.1 3.3% 50.4% HornofPlenty: 64 5% 44.9% JackOfAllTrades: 64 -0.3% 72% GhostShip: 63.8 1.9% 56.5% Apothecary: 63.6 4.6% 45.4% Tournament: 63.3 -2% 93.9% HuntingGrounds: 63.3 4.6% 45% Worker'sVillage: 63.2 -1.1% 78.3% Margrave: 63.2 0% 67.9% Crossroads: 63.1 -0.9% 75.7% Lighthouse: 62.6 -0.5% 71.7% Mountebank: 62.6 -1.7% 85.7% Jester: 62.3 3.1% 49.3% Journeyman: 62.3 4.4% 44.4% Quarry: 61.7 0.8% 61% Nobles: 61.7 -1.4% 78.2% Bazaar: 61.2 -0.3% 67.9% Warehouse: 61.1 -1.7% 81.2% Stables: 61.1 -0.5% 68.8% TradeRoute: 60.8 3.3% 46.7% Caravan: 60.5 -0.9% 71.6% Treasury: 60.3 4.9% 40.8% Moneylender: 60.2 2.7% 48.6% Possession: 60 6.3% 37.3% Haven: 60 -0.5% 67.8% Ironworks: 59.6 0.8% 58.1% Alchemist: 58.2 1.9% 50.4% Salvager: 58.1 -0.4% 64.3% Herald: 57.3 -2.1% 76.9% Advisor: 56.9 1.9% 48.9% SeaHag: 56.9 0.7% 55.9% Steward: 56.9 -2.5% 79.7% Swindler: 56.4 -2.7% 80.2% Island: 56.3 -1.3% 68.1% Armory: 56.1 4.8% 35.3% Cartographer: 56.1 2.4% 45.4% Upgrade: 56.1 -1.9% 72.6% Beggar: 55.5 5.3% 32.7% Scavenger: 55.3 1.9% 47.1% ShantyTown: 54.5 -1.8% 69.6% Stonemason: 54.3 -1.6% 67.9% BandofMisfits: 54.2 2.3% 44% Watchtower: 53.7 -0.7% 60.7% Village: 53.5 -1.1% 63.4% Herbalist: 53.5 6.4% 25.5% YoungWitch: 53.2 1.2% 48.8% Laboratory: 53.1 -1.7% 66.9% Highway: 52.6 -2.2% 69.4% Expand: 52.5 2.3% 42% Bishop: 52 0.8% 50% Embargo: 51.8 2.4% 40.6% Oasis: 51.7 -1.4% 62.9% Library: 51.3 3% 36.5% Militia: 51.2 -0.8% 58.8% Storeroom: 50.7 1.8% 42.3% Vagrant: 49.9 -1.7% 62.6% Doctor: 49.8 -0.2% 53.4% Lookout: 49.8 0.4% 50.1% Contraband: 49.7 6.7% 9.6% Urchin: 49.6 -4.3% 77.6% Harvest: 49.3 6.5% 8.6% Baron: 49.2 2% 39.3% Ironmonger: 48.7 -6.2% 84.7% Rebuild: 48.6 -2.8% 67.6% SpiceMerchant: 48.5 -2.9% 68% Sage: 48.3 -1.1% 57.2% MerchantShip: 48.2 3.4% 28.8% Mandarin: 48 5.2% 13.7% Outpost: 47.5 3.3% 27.8% Rabble: 47.5 0.6% 46.3% Mystic: 47.1 1.6% 39.2% Farmland: 46.7 -0.5% 52.3% Procession: 45.5 1.6% 37.1% Familiar: 45 -1.2% 54.1% Monument: 44.9 -1.6% 56.3% Develop: 44.8 1.6% 36% Workshop: 44.4 1.8% 34.2% Torturer: 43.9 -2% 57.4% Fool'sGold: 43.1 -2.7% 60% Catacombs: 42.7 -0.8% 49.6% Duchess: 41.8 0.7% 38.6% PearlDiver: 41.8 -1.3% 51.3% TradingPost: 41.7 0.4% 40.6% Bank: 41.5 0.8% 37.1% Gardens: 40.2 -3% 58.3% Explorer: 40.1 2.2% 20.3% Smithy: 40 -1.4% 50% Smugglers: 39.6 -1.2% 48.5% HorseTraders: 39.5 -3.5% 59.5% Fairgrounds: 38.7 -2% 51.5% University: 37.6 -5.2% 62.6% Rogue: 37.5 0.4% 34.9% Count: 36.9 -5.7% 62.9% Feast: 36.6 0.6% 31.2% Marauder: 35.5 -3.6% 55.2% CouncilRoom: 35.2 -1.8% 46.7% SilkRoad: 33.8 -3% 51.2% Harem: 32.9 -2.2% 46.3% Taxman: 32.7 0.7% 22.2% Soothsayer: 32.7 -4.5% 55.1% FortuneTeller: 32.4 0.3% 26.6% CountingHouse: 30.7 0.8% 9.1% Masterpiece: 29.6 -0.1% 25.3% Embassy: 29.4 -2.8% 45.3% Trader: 29.2 -1.4% 36.9% Hoard: 28.9 -4.9% 52.1% Golem: 26.2 -2.5% 39.6% Duke: 26.1 -4.5% 47.8% Moat: 25.8 -3.3% 43.5% Feodum: 25.3 -2.4% 38.2% DeathCart: 24.9 -1.2% 28.2% Philosopher'sStone: 24 -0.4% 9.9% Oracle: 23.5 -4.1% 43.6% Venture: 23.1 -1.6% 28.6% Woodcutter: 22.8 -1.3% 24% Vault: 22.1 -5.2% 45.2% PoorHouse: 21.7 -2.6% 34% NomadCamp: 21.6 -4.2% 41.6% RoyalSeal: 20.6 -1.3% 17.9% Navigator: 19.1 -1.7% 18.7% Loan: 19.1 -3.8% 36.9% Forge: 16.9 -4.8% 37.5% Scout: 16.8 -1.8% 8.6% Chancellor: 15.7 -2.3% 16.3% Cutpurse: 14.7 -4.7% 34.2% Spy: 14.5 -3.2% 24.8% PirateShip: 13.7 -2.5% 12% Mine: 12.1 -2.9% 11.5% SecretChamber: 11.3 -4.1% 24.2% Rats: 9.9 -8.4% 33.2% Talisman: 9.8 -4.8% 25.3% NobleBrigand: 9 -4.9% 23.6% Pillage: 8.1 -5.1% 22% Graverobber: 7.9 -9.2% 30.2% Tribute: 5.7 -6% 19.9% Coppersmith: 4.7 -5.2% 7.5% Saboteur: 3.7 -8.4% 19.5% Transmute: 3.6 -5.8% 6.5% Adventurer: 3.6 -5.8% 6.1% Bureaucrat: 3.5 -6.3% 11.4% TreasureMap: 3.2 -8.5% 17.5% Cache: 1.2 -10.3% 8.9% Thief: 1.1 -17.2% 8.5%

*Score is calculated as follows:
(CDF[((Card Win%)-(Average Win%))/(Win% StDev))]+CDF[((Card Gain%)-(Average Gain%))/(Gain% StDev))])*50

In other words: I convert the card's Win and Gain% to a Z-score, then convert that Z-score to a cumulative distribution. I add the cumulative distribution for Wins and Gains together. This results in a number on a scale of 0-2. I multiply that by 50 to result in a scale of 0-100.

In laymen's terms: if the cards were all lined up and ranked according to their gain% and win% (e.g. the most gained card would be 1, the least would be 200something), and you added those two ranks together.

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Win Rates for cards when they are only gained by one player. *Note: The average win rate for top-20 players is 65%. Naturally, the average win rate for all players is 50%.
 Card Name All Players% Top-20 Players Only% Colony: 78.6% 93.5% Goons: 68.2% 87.5% Butcher: 67.4% 85.3% Province: 66.7% 85.3% Minion: 66.6% 77.1% Vineyard: 65.3% 80.2% King'sCourt: 65.3% 77.6% Witch: 62.5% 77.7% Baker: 61.5% 74.4% Journeyman: 61.3% 76.3% GrandMarket: 60.8% 73.2% Masterpiece: 60.6% 67.6% Mountebank: 60.2% 80.7% Peddler: 59.9% 79.6% Platinum: 59.3% 81.8% BorderVillage: 58.1% 80.4% Wharf: 57.9% 72.7% Margrave: 57.8% 75.3% WishingWell: 57.5% 69% Catacombs: 57.2% 70.6% Governor: 57.1% 73.9% MerchantGuild: 57% 74.2% Beggar: 56.8% 75.6% GhostShip: 56.2% 77.1% Explorer: 55.9% 72.5% HornofPlenty: 55.8% 76.3% Mint: 55.8% 78.8% Library: 55.8% 69.9% HuntingParty: 55.7% 70.3% HuntingGrounds: 54.7% 78.6% Ill-GottenGains: 54.5% 66.3% MerchantShip: 54.4% 69.2% Estate: 54.1% 69.9% Laboratory: 54.1% 75.9% MiningVillage: 53.5% 70.4% Bazaar: 53.3% 72% Masquerade: 53.2% 76.3% Rogue: 52.9% 75.4% Warehouse: 52.8% 61.6% Pawn: 52.8% 73.3% Festival: 52.8% 75.6% Nobles: 52.8% 71.2% Farmland: 52.8% 72% ScryingPool: 52.7% 72.1% Armory: 52.7% 70.6% Apothecary: 52.6% 73% Stonemason: 52.6% 63.2% Possession: 52.5% 73.2% Crossroads: 52.3% 68.8% CountingHouse: 52.2% 69.7% Menagerie: 52.1% 71.4% JackOfAllTrades: 52% 63.4% Copper: 52% 67.8% CandlestickMaker: 51.9% 66.2% Embassy: 51.7% 68.5% WanderingMinstrel: 51.6% 66.7% Hamlet: 51.4% 64.8% Apprentice: 51.3% 71.6% Altar: 51.3% 68% BanditCamp: 51.2% 66.7% Chancellor: 51% 69.6% Familiar: 51% 74.7% Scheme: 50.9% 69.3% Mystic: 50.9% 65.5% Hermit: 50.7% 64.3% Scavenger: 50.6% 66.7% Conspirator: 50.5% 72.2% Quarry: 50.5% 67.4% Highway: 50.5% 68.3% Oracle: 50.3% 57.6% HorseTraders: 50.3% 62.5% Vault: 50% 60.2% Fairgrounds: 50% 61.5% ThroneRoom: 50% 64.8% Harem: 49.9% 67.1% Bridge: 49.9% 74.3% Herald: 49.9% 62.9% Counterfeit: 49.8% 70% Workshop: 49.8% 62.3% PearlDiver: 49.8% 65.4% Worker'sVillage: 49.8% 66.7% PoorHouse: 49.7% 62.7% TradingPost: 49.7% 68.7% JunkDealer: 49.7% 66.7% Market: 49.7% 63.6% City: 49.5% 80.9% GreatHall: 49.5% 61.9% FishingVillage: 49.5% 68.1% Duchess: 49.4% 65.3% Watchtower: 49.3% 68.1% Inn: 49.3% 72% Duke: 49.1% 64.6% Treasury: 49% 71.2% Contraband: 49% 75.8% Rabble: 48.9% 72.9% Fool'sGold: 48.8% 64.1% Venture: 48.7% 67.7% FarmingVillage: 48.7% 74.1% Herbalist: 48.6% 72.1% Ironmonger: 48.6% 62.5% Stables: 48.6% 62.7% Steward: 48.6% 54.8% Courtyard: 48.6% 64.7% Salvager: 48.5% 72.6% Tournament: 48.5% 80% Torturer: 48.4% 67.9% Fortress: 48.3% 66.7% Ambassador: 48.2% 62.5% Sage: 48.1% 61.6% SeaHag: 48% 63.1% Squire: 47.9% 69.8% Village: 47.9% 62.3% Moneylender: 47.9% 75.6% RoyalSeal: 47.8% 60% Chapel: 47.8% 63.2% Haggler: 47.8% 66.2% BandofMisfits: 47.8% 65.8% Feast: 47.7% 64.8% Plaza: 47.7% 62.7% Count: 47.6% 56.8% Duchy: 47.6% 62.7% Haven: 47.5% 58.1% Swindler: 47.4% 65.2% Woodcutter: 47.4% 66.1% Gardens: 47.2% 62.2% Remodel: 47.2% 65.4% Mine: 46.9% 61.5% BlackMarket: 46.9% 69.1% Hoard: 46.9% 61.7% Adventurer: 46.8% 73.9% Gold: 46.8% 66.9% ShantyTown: 46.7% 62.1% Embargo: 46.6% 68.9% Outpost: 46.4% 69.2% Bank: 46.3% 65.3% Urchin: 46.2% 57.6% Smithy: 46.1% 66.4% Cultist: 46% 72.1% Lighthouse: 46% 58.8% Procession: 45.9% 63.5% NativeVillage: 45.9% 58% Remake: 45.8% 70.6% CouncilRoom: 45.8% 59.1% Doctor: 45.8% 59% NomadCamp: 45.6% 61.2% Loan: 45.6% 62.1% Mandarin: 45.5% 68% Rebuild: 45.4% 61.5% Vagrant: 45.4% 59.5% Tactician: 44.9% 63% Cartographer: 44.9% 62.8% Expand: 44.9% 64.1% TradeRoute: 44.8% 63.9% Ironworks: 44.7% 62% FortuneTeller: 44.7% 55.3% Militia: 44.6% 57.5% Marauder: 44.5% 68.3% Baron: 44.4% 63.1% Navigator: 44.3% 56.3% Cellar: 44.1% 68.1% Monument: 44% 71% Bureaucrat: 43.9% 58.3% Upgrade: 43.8% 57.1% Taxman: 43.6% 71.2% Potion: 43.6% 64.2% Storeroom: 43.6% 59.7% Moat: 43.5% 66.7% Graverobber: 43.3% 51.9% MarketSquare: 43.2% 60.5% Caravan: 43.2% 69.2% Island: 43% 57.9% Lookout: 42.7% 64.6% Smugglers: 42.6% 61.6% Cutpurse: 42.6% 56.5% Cache: 42.5% 46.4% Harvest: 42.2% 71.4% YoungWitch: 42% 64.7% Advisor: 41.6% 64.4% Alchemist: 41.6% 71.4% Silver: 41.5% 54.8% Golem: 41.5% 58.9% Soothsayer: 41.5% 57.4% TreasureMap: 41.4% 54% Bishop: 41.3% 61% Curse: 41.3% 54.3% Feodum: 41.2% 55.4% Trader: 41% 66.7% DeathCart: 41% 56.8% Develop: 40.9% 63% Tunnel: 40.8% 62.5% SpiceMerchant: 40.7% 63.2% Pillage: 40.7% 60.3% Rats: 40.5% 46.5% Oasis: 40.4% 56.2% Spy: 40.3% 53.1% SilkRoad: 40.2% 43.3% Philosopher'sStone: 39.3% 53.1% SecretChamber: 38.8% 50% Forager: 38.7% 52% Forge: 38.2% 57.6% Jester: 38% 59.4% NobleBrigand: 37.7% 47.3% Talisman: 37.5% 53.3% Transmute: 36% 60.9% Saboteur: 35.9% 50.9% Thief: 35.7% 38.9% Scout: 35.6% 62.9% University: 33.1% 41.1% Coppersmith: 32.5% 54.2% Tribute: 31.1% 54.1% PirateShip: 24.3% 46.4%

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Impact of First-Shuffle Luck on Win %
In other words, how big of an impact does missing one or both of your T1/T2 purchases before the second reshuffle have on the Win % of the Top-20 players? Measured in "Adjusted Win %", see first post for explanation.

When opening Action/Action (63.5% of the time):
Hit Both Actions: +4%
Hit One Action: -3%
Hit Neither Action: -11%

When opening Action/Treasure (32% of the time):
Hit Action + Treasure: +1.5%
Hit Treasure Only: -11%
Hit Action Only: -0.5%
Hit Neither: -11%

When opening Treasure/Treasure (4.5% of the time):
Hit Both Treasures: +2%
Hit 1 Treasure: -12%
Hit Neither Treasure: -40%

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Top-20 players' "adjusted win rate" compared to when they played their first \$5 card.

T3/T4/T5: +4%
T6/T7: +0%
T8/T9 +0%
T10+: -3%

Of course, this is across the board and doesn't target specific high-value \$5 cards like Witch or Mountebank.

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Adjusted Win Rate of 5/2 vs. 4/3:
5/2: + 3.5%
4/3:  - 1%

« Last Edit: February 02, 2015, 07:07:08 am by TheExpressicist »
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#### werothegreat

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##### Re: More data mining: Card "strength"
« Reply #1 on: January 30, 2015, 03:48:08 pm »
0

Huh.  I don't think I've ever actually bought a Butcher.
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#### jsh357

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##### Re: More data mining: Card "strength"
« Reply #2 on: January 30, 2015, 03:56:47 pm »
+8

Butcher is pretty powerful, you should work on that.
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#### LastFootnote

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##### Re: More data mining: Card "strength"
« Reply #3 on: January 30, 2015, 04:05:28 pm »
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I'm pretty shocked that Candlestick Maker is so high.
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#### JW

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##### Re: More data mining: Card "strength"
« Reply #4 on: January 30, 2015, 04:19:50 pm »
+1

I'm pretty shocked that Candlestick Maker is so high.

Pawn stands out too. I'd attribute this to the fact that this is a data set of Top 20 players who win most of their games and are better than most of their opponents. In games where Candlestick Maker and Pawn are gained, it is more likely to be an engine-friendly board on which higher skill players excel (Candlestick Maker is not a strong Big Money card to take over Silver, for example, but is a good source of +buy for an engine). These also have a high gain rate due to being nonterminals costing \$2 (for example, the lowly Pearl Diver is bought on 51% of boards, vs. 62% for Pawn and 79% for Candlestick Maker).

Quote
CandlestickMaker:   90.3   5%   79.3%
Pawn:   77.9   4.3%   62.4%

Similarly, a card like Beggar has a very high Adjusted Win % of 5.3% because the sloggy boards where the top players buy it are complicated, but Beggar isn't bought that often because it's not a strong card most of the time. Possession is another card where if it's bought, that's an indication of a complex board and a high adjusted win %, but top players buy it on only 37% of boards.

Quote
Possession:   60   6.3%   37.3%
Beggar:   55.5   5.3%   32.7%
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#### microman

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##### Re: More data mining: Card "strength"
« Reply #5 on: January 30, 2015, 04:20:04 pm »
0

I'm pretty shocked that Candlestick Maker is so high.
I actually am not.  Its cheapness, +buy, +action, makes it very spamable and then it makes it very deadly as a 3 pile ender where a 3 pile game maybe wasnt an option.  Not to mention its most important function, those very useful coin tokens.  Its a must buy for me almost everytime!
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#### -Stef-

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##### Re: More data mining: Card "strength"
« Reply #6 on: January 30, 2015, 04:34:56 pm »
+7

I'm pretty shocked that Candlestick Maker is so high.
I actually am not.  Its cheapness, +buy, +action, makes it very spamable and then it makes it very deadly as a 3 pile ender where a 3 pile game maybe wasnt an option.  Not to mention its most important function, those very useful coin tokens.  Its a must buy for me almost everytime!

Candlestick maker is very not-spammable.

The first one is great, the second one ok, the 3rd one bad and from there on they're all terrible.
I win a lot of games because my opponent just keeps buying them.
With vineyards sure, but otherwise no thanks.
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#### WanderingWinder

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##### Re: More data mining: Card "strength"
« Reply #7 on: January 30, 2015, 04:39:04 pm »
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How are you calculating the Standard Deviation? It's the St Dev across... what?

#### TheExpressicist

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##### Re: More data mining: Card "strength"
« Reply #8 on: January 30, 2015, 04:54:04 pm »
0

How are you calculating the Standard Deviation? It's the St Dev across... what?

It's the SD of the "Gain %" column. Likewise with "Win %" column.

in other words: StDev{ (Card A Games Bought)/(Card A Games Available), (Card B Games Bought)/(Card B Games Available), (Card C Games Bought)/(Card C Games Available), .... etc.}
or for Win%: StDev{ (Card A Games Won)/(Card A Games Bought), (Card B Games Won)/(Card B Games Bought), (Card C Games Won)/(Card C Games Bought), .... etc.}
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#### WanderingWinder

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##### Re: More data mining: Card "strength"
« Reply #9 on: January 30, 2015, 05:13:46 pm »
0

How are you calculating the Standard Deviation? It's the St Dev across... what?

It's the SD of the "Gain %" column. Likewise with "Win %" column.

in other words: StDev{ (Card A Games Bought)/(Card A Games Available), (Card B Games Bought)/(Card B Games Available), (Card C Games Bought)/(Card C Games Available), .... etc.}
or for Win%: StDev{ (Card A Games Won)/(Card A Games Bought), (Card B Games Won)/(Card B Games Bought), (Card C Games Won)/(Card C Games Bought), .... etc.}

So the standard deviation between cards? It's the same for every single card then?

#### TheExpressicist

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##### Re: More data mining: Card "strength"
« Reply #10 on: January 30, 2015, 05:42:31 pm »
+1

How are you calculating the Standard Deviation? It's the St Dev across... what?

It's the SD of the "Gain %" column. Likewise with "Win %" column.

in other words: StDev{ (Card A Games Bought)/(Card A Games Available), (Card B Games Bought)/(Card B Games Available), (Card C Games Bought)/(Card C Games Available), .... etc.}
or for Win%: StDev{ (Card A Games Won)/(Card A Games Bought), (Card B Games Won)/(Card B Games Bought), (Card C Games Won)/(Card C Games Bought), .... etc.}

So the standard deviation between cards? It's the same for every single card then?

Not sure what you mean by it being the same for every single card. It's the standard deviation of the set of all cards.
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#### TheExpressicist

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##### Re: More data mining: Card "strength"
« Reply #11 on: January 30, 2015, 06:11:19 pm »
0

PS. I tried to include as many disclaimers as possible to prevent people from misinterpreting the data (e.g. BUY MORE CANDLESTICK MAKERS). I'm very aware of the limitations of 1. trying to objectively quantify a subjective concept like "strength". 2. Trying to model a complex system with a few simple variables. 3. Mixing abstract and concrete numbers. 4. Creating custom "metrics". 5. Trying to combine two fundamentally different measurements, etc.

But, all that said, I deliberately made the "Score" rating as abstract as possible so as to try to prevent people from trying to use those numbers to draw spurious, concrete conclusions.
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#### WanderingWinder

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##### Re: More data mining: Card "strength"
« Reply #12 on: January 30, 2015, 06:56:21 pm »
0

How are you calculating the Standard Deviation? It's the St Dev across... what?

It's the SD of the "Gain %" column. Likewise with "Win %" column.

in other words: StDev{ (Card A Games Bought)/(Card A Games Available), (Card B Games Bought)/(Card B Games Available), (Card C Games Bought)/(Card C Games Available), .... etc.}
or for Win%: StDev{ (Card A Games Won)/(Card A Games Bought), (Card B Games Won)/(Card B Games Bought), (Card C Games Won)/(Card C Games Bought), .... etc.}

So the standard deviation between cards? It's the same for every single card then?

Not sure what you mean by it being the same for every single card. It's the standard deviation of the set of all cards.
Ok, cool. My point is that when you are caulculating your 'score' metric, you divide by a st dev, then take the Normal CDF. But in that formula, the st dev you are dividing by is the same for all cards.

Edit: Which isn't inherently wrong, just I don't know that this is what you want to do/something which is really meaningful. Mostly still just trying to wrap my head around what it really means.
« Last Edit: January 30, 2015, 06:59:46 pm by WanderingWinder »
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#### JW

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##### Re: More data mining: Card "strength"
« Reply #13 on: January 30, 2015, 07:13:13 pm »
0

Pawn stands out too. I'd attribute this to the fact that this is a data set of Top 20 players who win most of their games and are better than most of their opponents. In games where Candlestick Maker and Pawn are gained, it is more likely to be an engine-friendly board on which higher skill players excel (Candlestick Maker is not a strong Big Money card to take over Silver, for example, but is a good source of +buy for an engine). These also have a high gain rate due to being nonterminals costing \$2 (for example, the lowly Pearl Diver is bought on 51% of boards, vs. 62% for Pawn and 79% for Candlestick Maker).

Candlestick maker is very not-spammable.

The first one is great, the second one ok, the 3rd one bad and from there on they're all terrible.
I win a lot of games because my opponent just keeps buying them.

Or as Stef alludes to, another explanation for why Candlestick Maker is so high up is that the top players know not to buy too many, but everyone else buys far too many Candlestick Makers and thus loses to the top players disproportionately on Candlestick Maker boards (in which the top player buys a judicious number of Candlestick Makers). This could help explain Squire's stats too. Just because it's easy to use Squire to get two more Squire doesn't mean that you want so many non-drawing cards.

Quote
Squire:   90.2   4.6%   81.5%
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#### TheExpressicist

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##### Re: More data mining: Card "strength"
« Reply #14 on: January 30, 2015, 07:21:13 pm »
0

How are you calculating the Standard Deviation? It's the St Dev across... what?

It's the SD of the "Gain %" column. Likewise with "Win %" column.

in other words: StDev{ (Card A Games Bought)/(Card A Games Available), (Card B Games Bought)/(Card B Games Available), (Card C Games Bought)/(Card C Games Available), .... etc.}
or for Win%: StDev{ (Card A Games Won)/(Card A Games Bought), (Card B Games Won)/(Card B Games Bought), (Card C Games Won)/(Card C Games Bought), .... etc.}

So the standard deviation between cards? It's the same for every single card then?

Not sure what you mean by it being the same for every single card. It's the standard deviation of the set of all cards.
Ok, cool. My point is that when you are caulculating your 'score' metric, you divide by a st dev, then take the Normal CDF. But in that formula, the st dev you are dividing by is the same for all cards.

Edit: Which isn't inherently wrong, just I don't know that this is what you want to do/something which is really meaningful. Mostly still just trying to wrap my head around what it really means.

The effect I'm approximating is similar to if you ranked each card , then added the two ranks together. That actually would have been a much easier way to do it. Such is the statistician's curse
: taking the most complex and circuitous route to explaining something that common sense could tell you.

My goal was to create a metric that is abstract enough to avoid people drawing incorrect conclusions like "X% of a players skill can be explained by Y" as we saw in the other data mining thread. I definitely sacrificed some statistical rigor but I think that's okay since we are already dealing with a lot of fuzziness.
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#### Throwaway_bicycling

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##### Re: More data mining: Card "strength"
« Reply #15 on: January 30, 2015, 08:04:57 pm »
+1

How are you calculating the Standard Deviation? It's the St Dev across... what?

It's the SD of the "Gain %" column. Likewise with "Win %" column.

in other words: StDev{ (Card A Games Bought)/(Card A Games Available), (Card B Games Bought)/(Card B Games Available), (Card C Games Bought)/(Card C Games Available), .... etc.}
or for Win%: StDev{ (Card A Games Won)/(Card A Games Bought), (Card B Games Won)/(Card B Games Bought), (Card C Games Won)/(Card C Games Bought), .... etc.}

So the standard deviation between cards? It's the same for every single card then?

Not sure what you mean by it being the same for every single card. It's the standard deviation of the set of all cards.

I am clearly not Wandering Winder, but I think I share his confusion. What I took his question to be is that the denominator of the first term contributing to score and the second term contributing to score (the SD of the relevant columns) is the same for every card that has a score. And that seems to be the case. So...you don't really need it? I mean, you're taking the CDF for both terms, which varies between 0 and 1, which is how you get a 0-100 scale after you multiply by 50. Normalizing first doesn't really get you anything. Unless I'm missing something.

I also see a deeper confusion here, which is the distinction between how strong a card is by itself and how much it allows a strong player to amplify his or her skill. So Rebuild has a pretty mediocre win_rate here, but it's hardly a weak card; the problem is that there is only so much you can do to eek out extra wins against competent opposition, since shuffle luck is clearly important. Similarly, Swindler looks like a bad card here by win_rate...but that's because your opponent can swindle, too, and is similarly swingy. Also Highway: a very good card, but even a nimrod like me can use it effectively (it was key on the one board where I beat a Top 20 player). Indeed, for the strength of cards alone, in many cases, negative means the card itself is so strong that, in combination with shuffle luck even a top-rated player is going to have a hard time coming out ahead. Similarly, cards that excel in BM games are not going to look good here because it is easier for most to play BM well.

What is clear here is that cards that are best in well-constructed engines will look really good on this list because the strongest players are waaaaay better at constructing engines than even pretty good players, so they actually amplify the value of those cards.

And actually, the really interesting cards are the ones that are not bought much by strong players, but, when they are, impart impressive benefits. Contraband is +6.7% and Harvest is +6.5%, which I guess is a 71% overall win rate or so.

That said, I think there are a few cards here that might be legitimately traps for better players, at least right now. I have personally beaten stronger players more often than not when they indulge in Golem, for example. If I am right, the -2.5% performance here mostly comes from games where the strong player buys Golem, the weaker one ignores it, and capitalizes on the slowness; maybe not enough to win a lot, but more than expected. Graverobber is another card that I think sometimes looks better on paper than in your deck. Also maybe Forge, although I guess that could be bought a lot in high junk games with not much other trashing, which would impede engine building, which is the Strong player's comparative advantage.

And all those Scout buys *must* come from really sloggy games where desperation sets in. :-)
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#### WanderingWinder

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##### Re: More data mining: Card "strength"
« Reply #16 on: January 30, 2015, 08:11:14 pm »
0

How are you calculating the Standard Deviation? It's the St Dev across... what?

It's the SD of the "Gain %" column. Likewise with "Win %" column.

in other words: StDev{ (Card A Games Bought)/(Card A Games Available), (Card B Games Bought)/(Card B Games Available), (Card C Games Bought)/(Card C Games Available), .... etc.}
or for Win%: StDev{ (Card A Games Won)/(Card A Games Bought), (Card B Games Won)/(Card B Games Bought), (Card C Games Won)/(Card C Games Bought), .... etc.}

So the standard deviation between cards? It's the same for every single card then?

Not sure what you mean by it being the same for every single card. It's the standard deviation of the set of all cards.

I am clearly not Wandering Winder, but I think I share his confusion. What I took his question to be is that the denominator of the first term contributing to score and the second term contributing to score (the SD of the relevant columns) is the same for every card that has a score. And that seems to be the case. So...you don't really need it? I mean, you're taking the CDF for both terms, which varies between 0 and 1, which is how you get a 0-100 scale after you multiply by 50. Normalizing first doesn't really get you anything. Unless I'm missing something.
You're missing something. He's dividing before taking the Normal CDF.

#### Throwaway_bicycling

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##### Re: More data mining: Card "strength"
« Reply #17 on: January 30, 2015, 08:49:15 pm »
0

How are you calculating the Standard Deviation? It's the St Dev across... what?

It's the SD of the "Gain %" column. Likewise with "Win %" column.

in other words: StDev{ (Card A Games Bought)/(Card A Games Available), (Card B Games Bought)/(Card B Games Available), (Card C Games Bought)/(Card C Games Available), .... etc.}
or for Win%: StDev{ (Card A Games Won)/(Card A Games Bought), (Card B Games Won)/(Card B Games Bought), (Card C Games Won)/(Card C Games Bought), .... etc.}

So the standard deviation between cards? It's the same for every single card then?

Not sure what you mean by it being the same for every single card. It's the standard deviation of the set of all cards.

I am clearly not Wandering Winder, but I think I share his confusion. What I took his question to be is that the denominator of the first term contributing to score and the second term contributing to score (the SD of the relevant columns) is the same for every card that has a score. And that seems to be the case. So...you don't really need it? I mean, you're taking the CDF for both terms, which varies between 0 and 1, which is how you get a 0-100 scale after you multiply by 50. Normalizing first doesn't really get you anything. Unless I'm missing something.
You're missing something. He's dividing before taking the Normal CDF.

Yes, I saw that like three seconds after I posted. A victim of my own R coding practices of yore, where I generally used ecdf (the empirical CDF). And then I saw TheExpressicist's post that ranks would be basically as good, and I agree there.

But I'm still not sure what you gain from making a single index here. Especially when we are talking about *card* strength.

Imagine a card called "Winner" that costs \$0 and allows you to win when played. Everybody would gain it like crazy (100% gain, for the purposes of this thread) and it would be (nearly?) a total crap shoot to win with it, so I guess it would be like -15% or something in this scheme and its score might even be somewhere south of Rebuild's.
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#### TheExpressicist

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##### Re: More data mining: Card "strength"
« Reply #18 on: January 30, 2015, 09:38:04 pm »
+1

Incidentally, if you take the "Gain % Rank" and subtract the "Win % Rank" you get a pretty reasonable illustration of the "swingiest" cards:

1. Ironmonger (?? I don't quite get this one.)
2. Urchin (Makes sense; whoever collides their Urchins first has a huge advantage).
3. Tournament (duh.)
4. Swindler (also duh.)
5. Mountebank (also also duh.)

The justification being; these are cards powerful enough to justify top-tier players buying them more often than not. But also brainless enough that anyone can play them and have a decent shot at winning.

IN OTHER WORDS: WHEN YOU PLAY GOOD PEOPLE BUY ALL THE URCHINS AND SWINDLERSSSS

« Last Edit: January 30, 2015, 09:59:27 pm by TheExpressicist »
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#### c4master

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##### Re: More data mining: Card "strength"
« Reply #19 on: January 31, 2015, 08:38:53 am »
0

I'm pretty shocked that Candlestick Maker is so high.
I actually am not.  Its cheapness, +buy, +action, makes it very spamable and then it makes it very deadly as a 3 pile ender where a 3 pile game maybe wasnt an option.  Not to mention its most important function, those very useful coin tokens.  Its a must buy for me almost everytime!

Candlestick maker is very not-spammable.

The first one is great, the second one ok, the 3rd one bad and from there on they're all terrible.
I win a lot of games because my opponent just keeps buying them.
With vineyards sure, but otherwise no thanks.

CM enables, or rather: supports, a lot of double Tactician boards.

It's also great with draw-to-X-engines although I would be careful about spamming them here. You can still get your share of 4-6 CMs, but you shouldn't buy all of them in order to not stall with a hand full of CMs.

At least, that's my experience.

-----------

Incidentally, if you take the "Gain % Rank" and subtract the "Win % Rank" you get a pretty reasonable illustration of the "swingiest" cards:

1. Ironmonger (?? I don't quite get this one.)
2. Urchin (Makes sense; whoever collides their Urchins first has a huge advantage).
3. Tournament (duh.)
4. Swindler (also duh.)
5. Mountebank (also also duh.)

The justification being; these are cards powerful enough to justify top-tier players buying them more often than not. But also brainless enough that anyone can play them and have a decent shot at winning.

IN OTHER WORDS: WHEN YOU PLAY GOOD PEOPLE BUY ALL THE URCHINS AND SWINDLERSSSS

Ironmonger is just almost always a good card. It's a Village in a thinned engine-deck. It's more than a Peddler in almost any other kind of deck because of it's discard ability. It's a good opener.

I don't think, it's a card that signals any specific strategy. So I guess, it's win rate should be about average, right?

edit: No, I'm wrong. It has -6.2% win rate, but more than 88% gain rate. That's really strange. Maybe it's just overrated even by the top players?
« Last Edit: January 31, 2015, 08:43:45 am by c4master »
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#### -Stef-

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##### Re: More data mining: Card "strength"
« Reply #20 on: January 31, 2015, 12:02:22 pm »
0

Ironmonger is just almost always a good card. It's a Village in a thinned engine-deck. It's more than a Peddler in almost any other kind of deck because of it's discard ability. It's a good opener.

I don't think, it's a card that signals any specific strategy. So I guess, it's win rate should be about average, right?

edit: No, I'm wrong. It has -6.2% win rate, but more than 88% gain rate. That's really strange. Maybe it's just overrated even by the top players?

Suppose we're playing a board with Mountebank and Ironmonger. I open with Ironmonger and you don't. Most likely scenario is that I'm way behind now.

Not saying that that is the reason, but it is really tricky to draw any conclusions at all based on these kinds of numbers.
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#### TheExpressicist

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##### Re: More data mining: Card "strength"
« Reply #21 on: January 31, 2015, 12:14:59 pm »
+1

Blaah. That post about "swingiest cards" was supposed to be a new post. I guess I edited over my old post. I'll try to do the condensed version:

How are you calculating the Standard Deviation? It's the St Dev across... what?

It's the SD of the "Gain %" column. Likewise with "Win %" column.

in other words: StDev{ (Card A Games Bought)/(Card A Games Available), (Card B Games Bought)/(Card B Games Available), (Card C Games Bought)/(Card C Games Available), .... etc.}
or for Win%: StDev{ (Card A Games Won)/(Card A Games Bought), (Card B Games Won)/(Card B Games Bought), (Card C Games Won)/(Card C Games Bought), .... etc.}

So the standard deviation between cards? It's the same for every single card then?

Not sure what you mean by it being the same for every single card. It's the standard deviation of the set of all cards.

I am clearly not Wandering Winder, but I think I share his confusion. What I took his question to be is that the denominator of the first term contributing to score and the second term contributing to score (the SD of the relevant columns) is the same for every card that has a score. And that seems to be the case. So...you don't really need it? I mean, you're taking the CDF for both terms, which varies between 0 and 1, which is how you get a 0-100 scale after you multiply by 50. Normalizing first doesn't really get you anything. Unless I'm missing something.
You're missing something. He's dividing before taking the Normal CDF.

Yes, I saw that like three seconds after I posted. A victim of my own R coding practices of yore, where I generally used ecdf (the empirical CDF). And then I saw TheExpressicist's post that ranks would be basically as good, and I agree there.

But I'm still not sure what you gain from making a single index here. Especially when we are talking about *card* strength.

Imagine a card called "Winner" that costs \$0 and allows you to win when played. Everybody would gain it like crazy (100% gain, for the purposes of this thread) and it would be (nearly?) a total crap shoot to win with it, so I guess it would be like -15% or something in this scheme and its score might even be somewhere south of Rebuild's.

It's a perfectly valid point which is why I tried to drench this thing with as many disclaimers as possible.

It raises the need to consider what this metric is actually measuring: cards that confer an advantage on good players. Take the "Winner" card. Yes, it has what would be the most powerful effect in the game. But, it would actually make good players worse because it drags their win rate from 65% down to closer to 50%.

In general, cards that are powerful but simple enough to use that they barely require any skill are dangerous to good players because it removes their primary advantage: skill. I would venture a guess that cards that are gained at a very high rate by good players but do not have a correspondingly high win-rate are cards that fall under this category. (Note: this was the context and lead-in to the 'swingiest cards' post).
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#### WanderingWinder

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##### Re: More data mining: Card "strength"
« Reply #22 on: January 31, 2015, 12:28:14 pm »
0

Yeah. I think this list has a very (very) rough relationship with how good the cards are, but that isn't really good for much at all.

More important, these are overall rankings. On any given board, you can throw them out the window - it doesn't matter that 195 other cards exist which might make card X good or bad. You only have the other 9 which exist right then and there, and that's basically always going to be a lot different than the general case.

It's a similar phenomenon to MtG, where what format is super important in determining how good a card is. Mental Misstep is unplayable in limited, because nobody runs 1-drops, certainly not impactful ones, but it's ubiquitous in Vintage, where you are countering things like Ancestral Recall for free.

Stef: You think Ironmonger is bad on Mountebank boards? Really? And you think it's significantly worse than, say, silver?

Re: the metric itself. The source of my head-scratching is, you applied a normal CDF to it. People do this all the time, and I'm not sure why - my guess is that it's because they did it all the time in their one stats course. But the thing is, most data isn't normally-distributed. So I can kind of understand wanting to do some kind of normalization to get things on the same scale, and I can kind of understand how how often the card is gained and how much you win when it is vs when it isn't are related to how good the card is, but even beyond the limitations of the approach from that perspective, I can't really get behind applying the Gaussian transformation.

#### TheOthin

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##### Re: More data mining: Card "strength"
« Reply #23 on: January 31, 2015, 12:46:36 pm »
0

Despite Ironmonger's frequent Village function later, it's not so bad as an opener, is it? An Ironmonger play after opening Ironmonger/Village means it has good odds of producing at least \$2, like a Silver; it'll only fall short of that if it draws one or more Estates. Plus it cycles. I can see it being weaker than opening Silver/Silver if you don't want the chance of falling short of a potential \$5, and it doesn't like hitting Curses, but...

Plus, the fact that Ironmonger is worried about drawing Estates means it gets better if you have an Estate in your hand in the first place, which is when you need a \$2 card to hit \$5.
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#### Awaclus

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##### Re: More data mining: Card "strength"
« Reply #24 on: January 31, 2015, 12:48:16 pm »
+6

Stef: You think Ironmonger is bad on Mountebank boards? Really? And you think it's significantly worse than, say, silver?

The player who doesn't open Ironmonger probably opens Mountebank.
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#### theright555J

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##### Re: More data mining: Card "strength"
« Reply #25 on: January 31, 2015, 12:51:53 pm »
+1

Ironmonger is bad on Mountebank boards? Really? And you think it's significantly worse than, say, silver?

I'm pretty sure it's not that Ironmonger is a bad card, but rather if your opponent doesn't open with it, s/he probably got. 5/2 and just bought Mountebank.

EDIT: Ninja'd by Awaclus.
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#### TheExpressicist

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##### Re: More data mining: Card "strength"
« Reply #26 on: January 31, 2015, 01:08:03 pm »
0

Yeah. I think this list has a very (very) rough relationship with how good the cards are, but that isn't really good for much at all.

More important, these are overall rankings. On any given board, you can throw them out the window - it doesn't matter that 195 other cards exist which might make card X good or bad. You only have the other 9 which exist right then and there, and that's basically always going to be a lot different than the general case.

Agreed. I think what it's good for is looking at the cards with high gain rates and say, "Okay, so, good people buy this card in 8 out of 10 kingdoms. Is this kingdom I'm playing in really the exception to that?"

Quote
Re: the metric itself. The source of my head-scratching is, you applied a normal CDF to it. People do this all the time, and I'm not sure why - my guess is that it's because they did it all the time in their one stats course. But the thing is, most data isn't normally-distributed. So I can kind of understand wanting to do some kind of normalization to get things on the same scale, and I can kind of understand how how often the card is gained and how much you win when it is vs when it isn't are related to how good the card is, but even beyond the limitations of the approach from that perspective, I can't really get behind applying the Gaussian transformation.

It's normal-ish. The main reason for applying the CDF was to minimize the impact of the outliers; cards that were gained <10% of the time or so. Something that's, say, 5 SD away from the mean is accounted for roughly the same as something that's 3SD away from the mean. As I mentioned earlier, a much simpler way of doing it would have just been to take the actual ranking of the card (e.g. the 2nd least gained card has a score of 2, the 10th least gained card has a score of 10, etc.). I re-ran the numbers doing it that way and the scores are more or less the same. The most any card gained or lost was 4 "points" and the average difference was like 1.5 points.
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#### WanderingWinder

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##### Re: More data mining: Card "strength"
« Reply #27 on: January 31, 2015, 01:42:20 pm »
0

Yeah. I think this list has a very (very) rough relationship with how good the cards are, but that isn't really good for much at all.

More important, these are overall rankings. On any given board, you can throw them out the window - it doesn't matter that 195 other cards exist which might make card X good or bad. You only have the other 9 which exist right then and there, and that's basically always going to be a lot different than the general case.

Agreed. I think what it's good for is looking at the cards with high gain rates and say, "Okay, so, good people buy this card in 8 out of 10 kingdoms. Is this kingdom I'm playing in really the exception to that?"

Quote
Re: the metric itself. The source of my head-scratching is, you applied a normal CDF to it. People do this all the time, and I'm not sure why - my guess is that it's because they did it all the time in their one stats course. But the thing is, most data isn't normally-distributed. So I can kind of understand wanting to do some kind of normalization to get things on the same scale, and I can kind of understand how how often the card is gained and how much you win when it is vs when it isn't are related to how good the card is, but even beyond the limitations of the approach from that perspective, I can't really get behind applying the Gaussian transformation.

It's normal-ish. The main reason for applying the CDF was to minimize the impact of the outliers; cards that were gained <10% of the time or so. Something that's, say, 5 SD away from the mean is accounted for roughly the same as something that's 3SD away from the mean. As I mentioned earlier, a much simpler way of doing it would have just been to take the actual ranking of the card (e.g. the 2nd least gained card has a score of 2, the 10th least gained card has a score of 10, etc.). I re-ran the numbers doing it that way and the scores are more or less the same. The most any card gained or lost was 4 "points" and the average difference was like 1.5 points.

It's really not the same as taking ranks. I suppose it 'smooths outliers', but that presumes those things shouldn't be so far out, and my intuition doesn't tell me that's correct.

If you have things 5 st dev from the mean, it's NOT normal-ish.

And I fully understand how the Gaussian CDF works - I work as a statistician, and I went to school for physics - you compute the integrals  for Quantum Mechanics.

#### TheExpressicist

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##### Re: More data mining: Card "strength"
« Reply #28 on: January 31, 2015, 04:17:54 pm »
0

It's really not the same as taking ranks. I suppose it 'smooths outliers', but that presumes those things shouldn't be so far out, and my intuition doesn't tell me that's correct.

In the general sense, it's not. But in this case, it does approximate just taking ranks. Which as I mentioned before, was the effect I was shooting for. (See my previous post regarding the fact that using rankings resulted in approximately the same score +-2 points). We're not trying to draw any standard statistical conclusions here; it's an invented metric that's deliberately abstract in order to discourage people from trying to apply the score where it's not appropriate to do so.

P.S. I also do stats for a living.
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#### popsofctown

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##### Re: More data mining: Card "strength"
« Reply #29 on: January 31, 2015, 04:26:24 pm »
0

Incidentally, if you take the "Gain % Rank" and subtract the "Win % Rank" you get a pretty reasonable illustration of the "swingiest" cards:

1. Ironmonger (?? I don't quite get this one.)
2. Urchin (Makes sense; whoever collides their Urchins first has a huge advantage).
3. Tournament (duh.)
4. Swindler (also duh.)
5. Mountebank (also also duh.)

The justification being; these are cards powerful enough to justify top-tier players buying them more often than not. But also brainless enough that anyone can play them and have a decent shot at winning.

IN OTHER WORDS: WHEN YOU PLAY GOOD PEOPLE BUY ALL THE URCHINS AND SWINDLERSSSS
This is a very useful post, and it's interesting to see these commonplace beliefs statistically verified somehow.

Ironmonger makes a lot of sense if you consider how it can be kind of braindead to buy it instead of Silver.  Maybe even braindead to buy it over most other <5\$ engine pieces for your engine.  That probably has more to do with it than randomly hitting Estates, although that might be a factor too.
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#### WanderingWinder

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##### Re: More data mining: Card "strength"
« Reply #30 on: January 31, 2015, 04:37:44 pm »
0

It's really not the same as taking ranks. I suppose it 'smooths outliers', but that presumes those things shouldn't be so far out, and my intuition doesn't tell me that's correct.

In the general sense, it's not. But in this case, it does approximate just taking ranks. Which as I mentioned before, was the effect I was shooting for. (See my previous post regarding the fact that using rankings resulted in approximately the same score +-2 points). We're not trying to draw any standard statistical conclusions here; it's an invented metric that's deliberately abstract in order to discourage people from trying to apply the score where it's not appropriate to do so.

P.S. I also do stats for a living.

Eh, that's fair I suppose. This isn't how I would do it, but I don't have anything to particularly say that the way I would do it is any better.

#### Throwaway_bicycling

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##### Re: More data mining: Card "strength"
« Reply #31 on: January 31, 2015, 05:44:08 pm »
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Yeah. I think this list has a very (very) rough relationship with how good the cards are, but that isn't really good for much at all.

So I find some additional usefulness in the two components that I don't get from the composite. Knowing what cards are more likely to be gained by the strongest players (modulo the high situation-dependency you note) can be useful for the rest of us, and the hard data are better than our fallible memories. So if Qvist's rankings have two \$4 villages in one order and the objective data has them in the opposite order by a decent margin...stuff like that would be revealing.

The other component, which shows how much more mileage strong players get out of specific cards, may also be interesting. This is really even more interesting for the more rarely gained cards (e.g., what are you all doing with Harvest? Maybe I should look.) But a lot of it seems to indicate how much better engine building gets for the Level 40 crowd, which many of us aspire to.

Quote
More important, these are overall rankings. On any given board, you can throw them out the window - it doesn't matter that 195 other cards exist which might make card X good or bad. You only have the other 9 which exist right then and there, and that's basically always going to be a lot different than the general case.

I agree in the general case, but there are some splits (Attacks present vs. not; Villages present vs. not, maybe others) where difference in gain rates and success given gain could be instructive.

(I skip the Magic references and shout out to Stef.)

Quote
Re: the metric itself. The source of my head-scratching is, you applied a normal CDF to it. People do this all the time, and I'm not sure why - my guess is that it's because they did it all the time in their one stats course.

That baffled me, too, which is why I mentally inserted a call to an empirical CDF function instead of the normal in my comment above. :-) I suppose if we were going to plug this into some analysis that really really cared about normality...but we're not.

So again: I see some value in the two rates separately (gain rate and win|gained), but no strong rationale for normality or for forming a single index. And I would like to see win|not_gained.
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#### SCSN

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##### Re: More data mining: Card "strength"
« Reply #32 on: January 31, 2015, 06:04:15 pm »
0

Incidentally, if you take the "Gain % Rank" and subtract the "Win % Rank" you get a pretty reasonable illustration of the "swingiest" cards:

1. Ironmonger (?? I don't quite get this one.)
2. Urchin (Makes sense; whoever collides their Urchins first has a huge advantage).
3. Tournament (duh.)
4. Swindler (also duh.)
5. Mountebank (also also duh.)

The justification being; these are cards powerful enough to justify top-tier players buying them more often than not. But also brainless enough that anyone can play them and have a decent shot at winning.

IN OTHER WORDS: WHEN YOU PLAY GOOD PEOPLE BUY ALL THE URCHINS AND SWINDLERSSSS
This is a very useful post, and it's interesting to see these commonplace beliefs statistically verified somehow.

I've always considered people complaning about Urchin's swinginess to be idiots. My winrate in Urchin mirrors is 63%, guess I'm just very lucky when it comes to colliding them!

I don't think Mountebank is very swingy either, as the blocking levels the playing field quite a bit. Looking at my own stats I'm winning 58.7% of Mountebank mirrors, versus just 51.8% for Witch.

Quote
Knowing what cards are more likely to be gained by the strongest players (modulo the high situation-dependency you note) can be useful for the rest of us

I doubt this is very useful, if someone 20 levels below me were to copy my exact gain %s he'd almost certainly be getting worse results than he's getting now.
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#### WanderingWinder

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##### Re: More data mining: Card "strength"
« Reply #33 on: January 31, 2015, 06:05:06 pm »
+1

Here's a fairly simple metric I'd like to see: Take the games in which exactly one player gains a card, then find in what percentage of those games the player who got the card won. Obviously this won't tell the entire story (true of any metric), but I like simple, intuitive things in general, when people can both understand the metric and its limitations.

#### dondon151

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##### Re: More data mining: Card "strength"
« Reply #34 on: January 31, 2015, 06:12:19 pm »
+3

I've always considered people complaning about Urchin's swinginess to be idiots. My winrate in Urchin mirrors is 63%, guess I'm just very lucky when it comes to colliding them!

I've always considered people complaining about people complaining about Urchin's swinginess to be idiots. I mean, they could just be better players, go figure.
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#### TheExpressicist

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##### Re: More data mining: Card "strength"
« Reply #35 on: January 31, 2015, 06:51:07 pm »
+4

Here's a fairly simple metric I'd like to see: Take the games in which exactly one player gains a card, then find in what percentage of those games the player who got the card won. Obviously this won't tell the entire story (true of any metric), but I like simple, intuitive things in general, when people can both understand the metric and its limitations.

I have that data. I'll post it shortly.
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#### SCSN

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##### Re: More data mining: Card "strength"
« Reply #36 on: January 31, 2015, 06:52:26 pm »
0

I've always considered people complaning about Urchin's swinginess to be idiots. My winrate in Urchin mirrors is 63%, guess I'm just very lucky when it comes to colliding them!

I've always considered people complaining about people complaining about Urchin's swinginess to be idiots. I mean, they could just be better players, go figure.

Next time you try to pick a fight make sure you actually have a point, lol. Having an above average winrate with a card is pretty damning evidence against its being swingy if your average opponent is worse than you.
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#### Throwaway_bicycling

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##### Re: More data mining: Card "strength"
« Reply #37 on: January 31, 2015, 07:01:10 pm »
0

Here's a fairly simple metric I'd like to see: Take the games in which exactly one player gains a card, then find in what percentage of those games the player who got the card won. Obviously this won't tell the entire story (true of any metric), but I like simple, intuitive things in general, when people can both understand the metric and its limitations.

Yes, that would be interesting. It would give you something like the relative risk of winning with Card X when there is a difference of opinion on strategy. A lot of that could be a wash, but some of it might be revealing. I think also the RR of winning|gain X vs. winning|not_gain X could be interesting.
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#### pacovf

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##### Re: More data mining: Card "strength"
« Reply #38 on: January 31, 2015, 07:08:22 pm »
0

I've always considered people complaning about Urchin's swinginess to be idiots. My winrate in Urchin mirrors is 63%, guess I'm just very lucky when it comes to colliding them!

I've always considered people complaining about people complaining about Urchin's swinginess to be idiots. I mean, they could just be better players, go figure.

Next time you try to pick a fight make sure you actually have a point, lol. Having an above average winrate with a card is pretty damning evidence against its being swingy if your average opponent is worse than you.

No. It is pretty damning evidence that you average opponent is worse than you. A swingy card can not lower your average winrate below 50% (edit: or increase your average winrate above 50%).

EDIT: after rereading your post, I see you weren't saying what I thought you were saying, so my point doesn't apply. Still, there are other explanations for what you are saying.
« Last Edit: January 31, 2015, 07:21:02 pm by pacovf »
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#### dondon151

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##### Re: More data mining: Card "strength"
« Reply #39 on: January 31, 2015, 07:14:35 pm »
+1

Next time you try to pick a fight make sure you actually have a point, lol. Having an above average winrate with a card is pretty damning evidence against its being swingy if your average opponent is worse than you.

Next time you choose to pursue a fight make sure you actually understand the point, lol. CR stats show that I had an above average winrate with Swindler on Iso; it's still a swingy card even if I could be expected to beat less able opponents to a pulp with or without it in the kingdom. You could be better than the average opponent at adapting to less favorable outcomes with Urchin, which makes up for the occasions where you have worse Urchin luck than your opponent, but that doesn't make Urchin less swingy.

But dude, you've been way more caustic than usual lately.
« Last Edit: January 31, 2015, 07:17:50 pm by dondon151 »
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#### Donald X.

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##### Re: More data mining: Card "strength"
« Reply #40 on: January 31, 2015, 07:29:40 pm »
+2

You could do lists that evaluate basic interactions. What is the win rate for a card sans +2 Actions, vs. the win rate when paired with +2 Actions? Or +1 Buy?
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#### Throwaway_bicycling

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##### Re: More data mining: Card "strength"
« Reply #41 on: January 31, 2015, 07:31:12 pm »
+1

Quote
Knowing what cards are more likely to be gained by the strongest players (modulo the high situation-dependency you note) can be useful for the rest of us

I doubt this is very useful, if someone 20 levels below me were to copy my exact gain %s he'd almost certainly be getting worse results than he's getting now.

Absolutely true, but that's not what I would be using it for.

One thing I noticed from the previous posted list of gain stats for stronger players and my personal gain stats is that I over-gain the "strong" cards and under-gain the "weak" cards, in a statistical sense. This could potentially happen for a lot of reasons, but looking a bit more closely, I think it usually means one of three things:

1) I under-appreciate the situational utility of some cards that are generically weak, maybe because I don't quite realize what they really could do. So I think more about those cards, re-check the wiki, maybe look up some games where they were in the kingdom and gained by strong players, and look at my own games where I gained or ignored them. So it can give me something concrete to think about while contemplating the general reasons why I am 20 levels weaker than (say) you.

2) I sometimes buy what could be "strong" cards without a complete understanding of how they would fit into my eventual plan. So there seems to be some evidence that I am way too enthusiastic about Farming Village. Might want to look into that.

3) Sometimes with some cards I apparently have No Idea. You buy it at 80%, I buy it at 30%. Or vice versa. No way should I gain it at the same rate as you until I figure it out, but that's an obvious place to look in general.
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#### TheExpressicist

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##### Re: More data mining: Card "strength"
« Reply #42 on: January 31, 2015, 07:48:42 pm »
+6

Win Rates for cards when they are only gained by one player. *Note: The average win rate for top-20 players is 65%. Naturally, the average win rate for all players is 50%.
 Card Name All Players% Top-20 Players Only% Colony: 78.6% 93.5% Goons: 68.2% 87.5% Butcher: 67.4% 85.3% Province: 66.7% 85.3% Minion: 66.6% 77.1% Vineyard: 65.3% 80.2% King'sCourt: 65.3% 77.6% Witch: 62.5% 77.7% Baker: 61.5% 74.4% Journeyman: 61.3% 76.3% GrandMarket: 60.8% 73.2% Masterpiece: 60.6% 67.6% Mountebank: 60.2% 80.7% Peddler: 59.9% 79.6% Platinum: 59.3% 81.8% BorderVillage: 58.1% 80.4% Wharf: 57.9% 72.7% Margrave: 57.8% 75.3% WishingWell: 57.5% 69% Catacombs: 57.2% 70.6% Governor: 57.1% 73.9% MerchantGuild: 57% 74.2% Beggar: 56.8% 75.6% GhostShip: 56.2% 77.1% Explorer: 55.9% 72.5% HornofPlenty: 55.8% 76.3% Mint: 55.8% 78.8% Library: 55.8% 69.9% HuntingParty: 55.7% 70.3% HuntingGrounds: 54.7% 78.6% Ill-GottenGains: 54.5% 66.3% MerchantShip: 54.4% 69.2% Estate: 54.1% 69.9% Laboratory: 54.1% 75.9% MiningVillage: 53.5% 70.4% Bazaar: 53.3% 72% Masquerade: 53.2% 76.3% Rogue: 52.9% 75.4% Warehouse: 52.8% 61.6% Pawn: 52.8% 73.3% Festival: 52.8% 75.6% Nobles: 52.8% 71.2% Farmland: 52.8% 72% ScryingPool: 52.7% 72.1% Armory: 52.7% 70.6% Apothecary: 52.6% 73% Stonemason: 52.6% 63.2% Possession: 52.5% 73.2% Crossroads: 52.3% 68.8% CountingHouse: 52.2% 69.7% Menagerie: 52.1% 71.4% JackOfAllTrades: 52% 63.4% Copper: 52% 67.8% CandlestickMaker: 51.9% 66.2% Embassy: 51.7% 68.5% WanderingMinstrel: 51.6% 66.7% Hamlet: 51.4% 64.8% Apprentice: 51.3% 71.6% Altar: 51.3% 68% BanditCamp: 51.2% 66.7% Chancellor: 51% 69.6% Familiar: 51% 74.7% Scheme: 50.9% 69.3% Mystic: 50.9% 65.5% Hermit: 50.7% 64.3% Scavenger: 50.6% 66.7% Conspirator: 50.5% 72.2% Quarry: 50.5% 67.4% Highway: 50.5% 68.3% Oracle: 50.3% 57.6% HorseTraders: 50.3% 62.5% Vault: 50% 60.2% Fairgrounds: 50% 61.5% ThroneRoom: 50% 64.8% Harem: 49.9% 67.1% Bridge: 49.9% 74.3% Herald: 49.9% 62.9% Counterfeit: 49.8% 70% Workshop: 49.8% 62.3% PearlDiver: 49.8% 65.4% Worker'sVillage: 49.8% 66.7% PoorHouse: 49.7% 62.7% TradingPost: 49.7% 68.7% JunkDealer: 49.7% 66.7% Market: 49.7% 63.6% City: 49.5% 80.9% GreatHall: 49.5% 61.9% FishingVillage: 49.5% 68.1% Duchess: 49.4% 65.3% Watchtower: 49.3% 68.1% Inn: 49.3% 72% Duke: 49.1% 64.6% Treasury: 49% 71.2% Contraband: 49% 75.8% Rabble: 48.9% 72.9% Fool'sGold: 48.8% 64.1% Venture: 48.7% 67.7% FarmingVillage: 48.7% 74.1% Herbalist: 48.6% 72.1% Ironmonger: 48.6% 62.5% Stables: 48.6% 62.7% Steward: 48.6% 54.8% Courtyard: 48.6% 64.7% Salvager: 48.5% 72.6% Tournament: 48.5% 80% Torturer: 48.4% 67.9% Fortress: 48.3% 66.7% Ambassador: 48.2% 62.5% Sage: 48.1% 61.6% SeaHag: 48% 63.1% Squire: 47.9% 69.8% Village: 47.9% 62.3% Moneylender: 47.9% 75.6% RoyalSeal: 47.8% 60% Chapel: 47.8% 63.2% Haggler: 47.8% 66.2% BandofMisfits: 47.8% 65.8% Feast: 47.7% 64.8% Plaza: 47.7% 62.7% Count: 47.6% 56.8% Duchy: 47.6% 62.7% Haven: 47.5% 58.1% Swindler: 47.4% 65.2% Woodcutter: 47.4% 66.1% Gardens: 47.2% 62.2% Remodel: 47.2% 65.4% Mine: 46.9% 61.5% BlackMarket: 46.9% 69.1% Hoard: 46.9% 61.7% Adventurer: 46.8% 73.9% Gold: 46.8% 66.9% ShantyTown: 46.7% 62.1% Embargo: 46.6% 68.9% Outpost: 46.4% 69.2% Bank: 46.3% 65.3% Urchin: 46.2% 57.6% Smithy: 46.1% 66.4% Cultist: 46% 72.1% Lighthouse: 46% 58.8% Procession: 45.9% 63.5% NativeVillage: 45.9% 58% Remake: 45.8% 70.6% CouncilRoom: 45.8% 59.1% Doctor: 45.8% 59% NomadCamp: 45.6% 61.2% Loan: 45.6% 62.1% Mandarin: 45.5% 68% Rebuild: 45.4% 61.5% Vagrant: 45.4% 59.5% Tactician: 44.9% 63% Cartographer: 44.9% 62.8% Expand: 44.9% 64.1% TradeRoute: 44.8% 63.9% Ironworks: 44.7% 62% FortuneTeller: 44.7% 55.3% Militia: 44.6% 57.5% Marauder: 44.5% 68.3% Baron: 44.4% 63.1% Navigator: 44.3% 56.3% Cellar: 44.1% 68.1% Monument: 44% 71% Bureaucrat: 43.9% 58.3% Upgrade: 43.8% 57.1% Taxman: 43.6% 71.2% Potion: 43.6% 64.2% Storeroom: 43.6% 59.7% Moat: 43.5% 66.7% Graverobber: 43.3% 51.9% MarketSquare: 43.2% 60.5% Caravan: 43.2% 69.2% Island: 43% 57.9% Lookout: 42.7% 64.6% Smugglers: 42.6% 61.6% Cutpurse: 42.6% 56.5% Cache: 42.5% 46.4% Harvest: 42.2% 71.4% YoungWitch: 42% 64.7% Advisor: 41.6% 64.4% Alchemist: 41.6% 71.4% Silver: 41.5% 54.8% Golem: 41.5% 58.9% Soothsayer: 41.5% 57.4% TreasureMap: 41.4% 54% Bishop: 41.3% 61% Curse: 41.3% 54.3% Feodum: 41.2% 55.4% Trader: 41% 66.7% DeathCart: 41% 56.8% Develop: 40.9% 63% Tunnel: 40.8% 62.5% SpiceMerchant: 40.7% 63.2% Pillage: 40.7% 60.3% Rats: 40.5% 46.5% Oasis: 40.4% 56.2% Spy: 40.3% 53.1% SilkRoad: 40.2% 43.3% Philosopher'sStone: 39.3% 53.1% SecretChamber: 38.8% 50% Forager: 38.7% 52% Forge: 38.2% 57.6% Jester: 38% 59.4% NobleBrigand: 37.7% 47.3% Talisman: 37.5% 53.3% Transmute: 36% 60.9% Saboteur: 35.9% 50.9% Thief: 35.7% 38.9% Scout: 35.6% 62.9% University: 33.1% 41.1% Coppersmith: 32.5% 54.2% Tribute: 31.1% 54.1% PirateShip: 24.3% 46.4%
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#### Throwaway_bicycling

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##### Re: More data mining: Card "strength"
« Reply #43 on: January 31, 2015, 09:19:47 pm »
+2

Okay, so this might be getting interesting. First, I will note that there are *no* cards where the Top 20 have a lower win rate than everybody when they are the only buyer.

But there are some cards where they do appear to (in some cases grossly) underperform when they are the only buyer, which makes these potential "trap" cards. Unfortunately, there is an important confound in the data here present also in the dataset provided: the Top 20 play a very different set of people than the population at large. If the Top 20 were to play the same mix of people that the population played, their win rate on average would be *much* higher. So although below there are columns for Everybody, Top 20, and the difference between them, the two performance columns really aren't directly comparable and so their difference is a bit suspect, too. But I think it is reasonable to point out that if there are cards where Top 20 players achieve a win rate less than 0.500 against any competition (even or particularly just each other), than this should give one pause, for sure.
`Card                All    Top 20  DiffThief                0.357 0.389 0.032University           0.331 0.411 0.080SilkRoad             0.402 0.433 0.031Cache                0.425 0.464 0.039PirateShip           0.243 0.464 0.221Rats                 0.405 0.465 0.060NobleBrigand         0.377 0.473 0.096`

So for the above cards, something was almost certainly wrong with your strategy if you were the only buyer, no matter who you were. The only card here where there is really strong evidence of vastly superior use by stronger players is...Pirate Ship! Apparently still very frequently a mistake overall to buy it, but the Elite almost scrape back to even when they buy it. More could be gleaned, but not by me tonight.
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#### Merudo

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##### Re: More data mining: Card "strength"
« Reply #44 on: February 01, 2015, 01:44:07 am »
0

I'm surprised how well Scout, Transmute & Adventurer can be according to this last list.

Then again, I always believed Adventurer can be amazing on some boards .
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#### Awaclus

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##### Re: More data mining: Card "strength"
« Reply #45 on: February 01, 2015, 03:52:09 am »
0

My winrate in Urchin mirrors is 63%, guess I'm just very lucky when it comes to colliding them!

Is that higher or lower than your overall winrate?
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#### Rabid

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##### Re: More data mining: Card "strength"
« Reply #46 on: February 01, 2015, 07:23:11 am »
+2

SilkRoad             0.402 0.433 0.031

I think this will be because if Silk Road is good it can be mirrored.
Or at least a few will be denied.
So a lot of the time if you are the only player to buy one, it was a late game \$4 hand that you wish was a duchy.
« Last Edit: February 01, 2015, 07:27:02 am by Rabid »
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#### WanderingWinder

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##### Re: More data mining: Card "strength"
« Reply #47 on: February 01, 2015, 07:54:33 am »
+2

My winrate in Urchin mirrors is 63%, guess I'm just very lucky when it comes to colliding them!

Is that higher or lower than your overall winrate?
It's lower by about 5%. The thing you have to realize, though, is that just because a card is swingy doesn't mean there can't also be some skill. Clearly there is some skill with the card, it's not 'roll a die, if you get higher you win'. We had the same discussions with Tournament (though I think Urchin is worse). And SCSN deals with the card better.

Actually, I think the argument SCSN should be making isn't that Urchin isn't swingy, it's Mic_qsenoch's common point that everything is swingy. And he's right. I just think the Urchin is a bit more swingy, because it makes a pretty big difference and, importantly, you're very close to 50% hit rate on that first shuffle, which gives you close to maximum percentage to the two players having significantly different outcomes by turn 5.

SilkRoad             0.402 0.433 0.031

I think this will be because if Silk Road is good it can be mirrored.
Or at least a few will be denied.
So a lot of the time if you are the only player to buy one, it was a late game \$4 hand that you wish was a duchy.

The thing about SR in high-level games is, it's a card you often go to if you're way behind. "I'm very far behind - if I'm going to win, it will have to go long enough for SR to be good (better than duchy anyway), so SR it is". Desperation moves are going to look bad, even if they may up your winrate in the situation you get them.

#### TheExpressicist

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##### Re: More data mining: Card "strength"
« Reply #48 on: February 01, 2015, 08:21:51 am »
+1

Quote from: Wandering Winder
The thing about SR in high-level games is, it's a card you often go to if you're way behind. "I'm very far behind - if I'm going to win, it will have to go long enough for SR to be good (better than duchy anyway), so SR it is". Desperation moves are going to look bad, even if they may up your winrate in the situation you get them.

Yes, this. I've been trying to think up a way to account for this. Something I'm considering is establishing an arbitrary turn limit, like, only counting cardS purchased before turn 10 or something. I *think* this should sufficiently account for deliberate strategies, and weed out ad hoc desperation tactics. Thoughts?
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#### Awaclus

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##### Re: More data mining: Card "strength"
« Reply #49 on: February 01, 2015, 08:33:18 am »
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It's lower by about 5%. The thing you have to realize, though, is that just because a card is swingy doesn't mean there can't also be some skill. Clearly there is some skill with the card, it's not 'roll a die, if you get higher you win'. We had the same discussions with Tournament (though I think Urchin is worse). And SCSN deals with the card better.

Well, I don't think Urchin itself is a very difficult card, but trashing and hand size attacks usually make skill-intensive strategies better.
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Bomb, Cannon, and many of the Gunpowder cards can strongly effect gameplay, particularly in a destructive way

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#### WanderingWinder

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##### Re: More data mining: Card "strength"
« Reply #50 on: February 01, 2015, 09:59:16 am »
0

Quote from: Wandering Winder
The thing about SR in high-level games is, it's a card you often go to if you're way behind. "I'm very far behind - if I'm going to win, it will have to go long enough for SR to be good (better than duchy anyway), so SR it is". Desperation moves are going to look bad, even if they may up your winrate in the situation you get them.

Yes, this. I've been trying to think up a way to account for this. Something I'm considering is establishing an arbitrary turn limit, like, only counting cardS purchased before turn 10 or something. I *think* this should sufficiently account for deliberate strategies, and weed out ad hoc desperation tactics. Thoughts?

My thoughts are that you really can't come up with a solution to do it based on a scripted kind of numerical analysis. Only counting the first X turns will sometimes include desperation plays and sometimes not include real strategic decisions. Essentially, things are on far too much of a case-by-case basis to 'correct for' everything - you won't get there, and you lose the simplicity of a nice little metric. I mean, you can do whatever you want, but after very far at all, I don't see what the point is, personally.

#### Throwaway_bicycling

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##### Re: More data mining: Card "strength"
« Reply #51 on: February 01, 2015, 10:01:08 am »
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SilkRoad             0.402 0.433 0.031

I think this will be because if Silk Road is good it can be mirrored.
Or at least a few will be denied.
So a lot of the time if you are the only player to buy one, it was a late game \$4 hand that you wish was a duchy.

That sounds right to me. Do you have a Pirate Ship theory that fits the data? Only thing I can think of without combing through lots of actual games is when a Top 20 player buys it, he or she buys it relatively late and has a way to play it 2 or 3 times per turn in an engine, uses it to "mast" an opponent by taking down the money then grabs \$2-3 every turn (maybe times 2 or 3) and is immune to the mirror because their deck has no money.

Meanwhile, there are some cards where Top 20 players actually outperform their overall win rate (given as 65% here) when they alone gain, although the caveat here is that for some of these cards, overall win rate on the board that contains them could be overall higher or lower than 65%.
`Card                 All   Top20 DiffSwindler             0.474 0.652 0.178Bank                 0.463 0.653 0.190Duchess              0.494 0.653 0.159PearlDiver           0.498 0.654 0.156Remodel              0.472 0.654 0.182Mystic               0.509 0.655 0.146BandofMisfits        0.478 0.658 0.180Woodcutter           0.474 0.661 0.187CandlestickMaker     0.519 0.662 0.143Haggler              0.478 0.662 0.184Ill-GottenGains      0.545 0.663 0.118Smithy               0.461 0.664 0.203BanditCamp           0.512 0.667 0.155Fortress             0.483 0.667 0.184JunkDealer           0.497 0.667 0.170Moat                 0.435 0.667 0.232Scavenger            0.506 0.667 0.161Trader               0.410 0.667 0.257WanderingMinstrel    0.516 0.667 0.151Worker'sVillage      0.498 0.667 0.169Gold                 0.468 0.669 0.201Harem                0.499 0.671 0.172Quarry               0.505 0.674 0.169Masterpiece          0.606 0.676 0.070Venture              0.487 0.677 0.190Copper               0.520 0.678 0.158Torturer             0.484 0.679 0.195Altar                0.513 0.680 0.167Mandarin             0.455 0.680 0.225Cellar               0.441 0.681 0.240FishingVillage       0.495 0.681 0.186Watchtower           0.493 0.681 0.188Highway              0.505 0.683 0.178Marauder             0.445 0.683 0.238Embassy              0.517 0.685 0.168TradingPost          0.497 0.687 0.190Crossroads           0.523 0.688 0.165Embargo              0.466 0.689 0.223WishingWell          0.575 0.690 0.115`

So some of these cards are ones that lower-rated players (that is, players overall) do well with when they are the sole gainers as well (e.g., Wishing Well, Crossroads, Highway, Altar, Copper (?), Quarry, Embassy, Scavenger and Mystic). Except for Copper, all of those basically make sense to me since they can work well with building up engines, so any time you are building one and opponent isn't or you are building a better one...makes sense. And gaining Embassy curses your opponent. :-)

But others of these cards seem to be just more magic in the deck of a Top 20 player, the top ten of those in sorted order:
`Card                 All   Top20 DiffTrader               0.410 0.667 0.257Cellar               0.441 0.681 0.240Marauder             0.445 0.683 0.238Moat                 0.435 0.667 0.232Mandarin             0.455 0.680 0.225Embargo              0.466 0.689 0.223Smithy               0.461 0.664 0.203Gold                 0.468 0.669 0.201Torturer             0.484 0.679 0.195Venture              0.487 0.677 0.190`

Moat does not top this list, but would have been a good guess. :-)

Finally, there are cards that the Top20 just crush with if they are the only ones to gain them:
`Card                 All   Top20 DiffColony               0.786 0.935 0.149Goons                0.682 0.875 0.193Province             0.667 0.853 0.186Butcher              0.674 0.853 0.179Platinum             0.593 0.818 0.225City                 0.495 0.809 0.314Mountebank           0.602 0.807 0.205BorderVillage        0.581 0.804 0.223Vineyard             0.653 0.802 0.149Tournament           0.485 0.800 0.315`

I think most of these are pretty obvious. The relative top player advantage with City and Tournament is pretty striking, though.

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#### Rabid

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##### Re: More data mining: Card "strength"
« Reply #52 on: February 01, 2015, 10:22:33 am »
+1

That sounds right to me. Do you have a Pirate Ship theory that fits the data?

My guesses for this are: small sample size, fun, testing or learning.

Copper (?)
I guess this would be mostly Goons, and also people buying random copper on the winning turn.
The all data will also be dragged down by new players using up all the buys.
« Last Edit: February 01, 2015, 10:28:28 am by Rabid »
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#### Throwaway_bicycling

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##### Re: More data mining: Card "strength"
« Reply #53 on: February 01, 2015, 10:41:38 am »
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That sounds right to me. Do you have a Pirate Ship theory that fits the data?
My guesses for this are: small sample size, fun, testing or learning.
Good point; it still is below .500, so the "F it, I'm going Pirate Ship, Arrr!" Theory is good. Less good players are probably acquiring it for very different reasons.

Copper (?)
I guess this would be mostly Goons, and also people buying random copper on the winning turn.
The all data will also be dragged down by new players using up all the buys.
Goons was my best guess, too, except I would have thought most Top20 games would have been Goons mirrors, where copper buying is not unheard of. But you're right that these could be last turn buys of (say) 11 Coppers to gain 44 VP or something.

Would have been cooler if it were due to some trippy Coppersmith megaturn engine, but speaking of small sample sizes...

Expressicist: what are the sample sizes of the game base you are working with?
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#### WanderingWinder

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##### Re: More data mining: Card "strength"
« Reply #54 on: February 01, 2015, 10:48:03 am »
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That sounds right to me. Do you have a Pirate Ship theory that fits the data?
My guesses for this are: small sample size, fun, testing or learning.
Good point; it still is below .500, so the "F it, I'm going Pirate Ship, Arrr!" Theory is good. Less good players are probably acquiring it for very different reasons.

Copper (?)
I guess this would be mostly Goons, and also people buying random copper on the winning turn.
The all data will also be dragged down by new players using up all the buys.
Goons was my best guess, too, except I would have thought most Top20 games would have been Goons mirrors, where copper buying is not unheard of. But you're right that these could be last turn buys of (say) 11 Coppers to gain 44 VP or something.

Would have been cooler if it were due to some trippy Coppersmith megaturn engine, but speaking of small sample sizes...

Expressicist: what are the sample sizes of the game base you are working with?

The other thing for coppers, more than goons, is going to be mountebank. You also sometimes get them in slogs and for Apothecary or counting house or as additional fuel for trashers. But the biggest thing is, good players know that buying copper is awful, so when they do it, they are probably doing really well, whereas their opponents can often write it off entirely.

#### TheExpressicist

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##### Re: More data mining: Card "strength"
« Reply #55 on: February 01, 2015, 02:52:51 pm »
+4

I'm gonna update the thread title from being just about card strength to the general subject of trying to answer Dominion questions using game data. I have some more data but I don't really want to start yet another thread.

Impact of First-Shuffle Luck on Win %
In other words, how big of an impact does missing one or both of your T1/T2 purchases before the second reshuffle have on the Win % of the Top-20 players? Measured in "Adjusted Win %", see first post for explanation.

When opening Action/Action (63.5% of the time):
Hit Both Actions: +4%
Hit One Action: -3%
Hit Neither Action: -11%

When opening Action/Treasure (32% of the time):
Hit Action + Treasure: +1.5%
Hit Treasure Only: -11%
Hit Action Only: -0.5%
Hit Neither: -11%

When opening Treasure/Treasure (4.5% of the time):
Hit Both Treasures: +2%
Hit 1 Treasure: -12%
Hit Neither Treasure: -40%
« Last Edit: February 01, 2015, 02:58:55 pm by TheExpressicist »
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#### JW

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##### Re: More data mining: Answering Dominion questions with data
« Reply #56 on: February 01, 2015, 04:28:10 pm »
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Do those stats take into account that the number of cards you draw depends on how you open? So Silver-Silver is drawn less than Silver-smithy because your smithy might help draw your silver?
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#### TheExpressicist

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##### Re: More data mining: Answering Dominion questions with data
« Reply #57 on: February 01, 2015, 05:47:40 pm »
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Do those stats take into account that the number of cards you draw depends on how you open? So Silver-Silver is drawn less than Silver-smithy because your smithy might help draw your silver?

It simply looks for if you played one or both of the cards you opened with on or before T4. So, for example if you open Smithy-Silver, you're guaranteed to play both this is wrong.
« Last Edit: February 01, 2015, 08:20:25 pm by TheExpressicist »
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#### JW

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##### Re: More data mining: Answering Dominion questions with data
« Reply #58 on: February 01, 2015, 07:12:14 pm »
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Do those stats take into account that the number of cards you draw depends on how you open? So Silver-Silver is drawn less than Silver-smithy because your smithy might help draw your silver?

It simply looks for if you played one or both of the cards you opened with on or before T4. So, for example if you open Smithy-Silver, you're guaranteed to play both.

If you open double terminal and they collide, that's not the same luck of the draw as having one miss the shuffle. And another factor is that you might choose not to play a drawing action you opened with so that it doesn't trigger a bad shuffle.

Side note, you aren't guaranteed to see both Silver and Smithy if smithy is at the bottom of your deck.
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#### TheExpressicist

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##### Re: More data mining: Answering Dominion questions with data
« Reply #59 on: February 01, 2015, 08:23:31 pm »
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Do those stats take into account that the number of cards you draw depends on how you open? So Silver-Silver is drawn less than Silver-smithy because your smithy might help draw your silver?

It simply looks for if you played one or both of the cards you opened with on or before T4. So, for example if you open Smithy-Silver, you're guaranteed to play both.

If you open double terminal and they collide, that's not the same luck of the draw as having one miss the shuffle. And another factor is that you might choose not to play a drawing action you opened with so that it doesn't trigger a bad shuffle.

Side note, you aren't guaranteed to see both Silver and Smithy if smithy is at the bottom of your deck.

Yup, good catch. I edited my post re: silver/smithy.

Re: double terminals, it's not the same luck of the draw, but, regardless there's a luck component. You've got about a 33% chance of two non-drawing terminals colliding. (55% if you have a 2-draw, and 66% if you have a 3-draw). The player who doesn't collide those terminals is going to have an advantage over the player who does, which is what I was trying to quantify.
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#### TheExpressicist

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##### Re: More data mining: Answering Dominion questions with data
« Reply #60 on: February 01, 2015, 08:31:06 pm »
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Along the same lines of how much luck plays an impact, I also analyzed Top-20 players' "adjusted win rate" compared to when they played their first \$5 card.

T3/T4/T5: +4%
T6/T7: +0%
T8/T9 +0%
T10+: -3%

Of course, this is across the board and doesn't target specific high-value \$5 cards like Witch or Mountebank.

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#### liopoil

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##### Re: More data mining: Answering Dominion questions with data
« Reply #61 on: February 01, 2015, 09:47:35 pm »
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You know, I'm not really sure which is better on average, 5/2 or 4/3. What you just posted suggests 5/2, and I guess that's about right. Can you just look at which opening split is better?
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#### TheExpressicist

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##### Re: More data mining: Answering Dominion questions with data
« Reply #62 on: February 02, 2015, 07:05:05 am »
+4

You know, I'm not really sure which is better on average, 5/2 or 4/3. What you just posted suggests 5/2, and I guess that's about right. Can you just look at which opening split is better?

Adjusted Win Rate of 5/2 vs. 4/3:
5/2: + 3.5%
4/3:  - 1%
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#### Merudo

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##### Re: More data mining: Answering Dominion questions with data
« Reply #63 on: February 07, 2015, 12:35:03 am »
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Update:
There have been a few requests for additional data and I've done some more research that I wanted to share but I don't want to create yet another thread. I'll update this first post with additional data as I collect it.

It would be wonderful if you could post the win rates of 1st vs 2nd player. I'm especially curious about the importance of player order in games with expert players, as well as games with powerful cards (militia, sea hag, cutpurse) that are even better for player 1.

It may be selective retention, but I feel that against players of comparable skills, most of my wins occur when I have 1 extra turn, while most of my loses happen when I had one less turn.
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#### JW

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##### Re: More data mining: Answering Dominion questions with data
« Reply #64 on: February 07, 2015, 02:03:07 am »
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In his data set as a whole, which I believe was games involving top 100 players, P1 won 57-43.
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