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Dominion League / Re: Season 6 - Results
« on: February 17, 2015, 02:39:49 pm »
TheExpressicist - 4, Vsiewnar - 2
Crossroads, Herbalist, University, Advisor, Bandit Camp, Count, Mandarin, Royal Seal, Tribute, Wharf
I don't think this is an issue. There are no rewards for doing well in the League, so there's no reason why anyone would cheat.
I mean, I don't think anyone is doing this in the league, but you think that there's no reason to cheat? For some people winning is really important, and they'd seek unfair advantages even in unrated non-league games (see, for instance, the Pirate Ship / King's Court setup board that someone or other plays over and over in Casual games). And in the league there are rewards for doing well: your name in lights on the leaderboard, the respect and admiration of other players...those can be more compelling than some smal monetary reward. So while, again, I don't think this is a serious issue that needs addressing, I don't agree at all that there's no reason anyone would cheat.
Transmute, Pearl Diver, Shanty Town, Swindler, Village, Smithy, Apprentice, Catacombs, Horn of Plenty, Grand Market
Moat, Watchtower, Cutpurse, Militia, Navigator, Spy, Band of Misfits, Mandarin, Margrave, Soothsayer
If you consider each card to be unique in a deck of cards, each ordering (of the 52 cards) has the same probability, right? The .5*X instance of one heads one tails comes because you're considering the orderings HT and TH to be the same.
But given an infinite number of shuffles don't we just get every ordering as much as any other?
Given a Bernoulli process (probability of success p), what is the chance that, given an infinite number of trials, after SOME point, the majority of trials have come up with success?
If I understand the question right ("given an infinite number of trials, what is the probability that at any point the number of successes outnumber the number of failures"), the probability is 1 for any p > 0.
A good rule of thumb is that whenever infinity is involved, you need to be very careful on your intuition. From the linked PDF, it turns out that the probability is 1 for p >= 1/2, and p / (1-p) for p < 1/2.
This sounds weird because if we do something an infinite number of times, surely we must have every possibility eventually happen. However, it turns out this isn't generally true. For example, a random walk in 2 dimensions returns to the origin with probability 1, but a random walk in 3 dimensions returns to the origin only around a third of the time. Usually, this comes down to the rate of growth for the two - for example, if the probability of getting a majority at time t+1 is 1/4 the probability of a majority at time t, then the probabilities decrease fast enough to make the sum across all times t not equal to 1.
Given a Bernoulli process (probability of success p), what is the chance that, given an infinite number of trials, after SOME point, the majority of trials have come up with success?
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?
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.
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?
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.
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% |
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.