A Course On Poker?!? Information Games Principles Of Knowledge

cs6501: ImperfectInformation GamesA Course on Poker?!?There are few things that are sounpardonably neglected in ourcountry as poker. The upper classknows very little about it. Now andthen you find ambassadors whohave sort of a general knowledge ofthe game, but the ignorance of thepeople is fearful. Why, I have knownclergymen, good men,kind hearted, liberal, sincere, andall that, who did not know themeaning of a “flush”. It is enough tomake one ashamed of one’s species. Mark Twain(as quoted in A Bibliography of MarkTwain, Merle Johnson)PrinciplesOfKnowledgeEngineering &ReconstructionSpring 2010University of VirginiaDavid EvansA K Q Game (not von NeumannPoker)John von Neumann(1903 1957)Pure MathQuantum PhysicsAtomic BombsDesigner of Plutonium BombFission/Fusion Hydrogen BombComputer ScienceFirst Draft Report on EDVACvon Neumann ArchitectureMerge SortRandom Number generationGame TheoryTheory of Games and EconomicBehavior (with Morgenstern)Mutual Assured DestructionFlickr:cc MalkavA K Q Game RulesA K Q Game Rules 3 card deck: Ace King Queen 2 Players, each player gets one card face up Higher card winsWithout secrecy, stakes, betting, its not poker! 3 card deck: Ace King Queen2 Players, each player gets one card face downHigher card winsBetting: (half street game)– Ante: 1 chip– Player 1: bet 1, or check– Player 2: call or fold Stakes: scheduling signup order by chip countLoosely based on Bill Chen and Jerrod Ankenman, The Mathematics of Poker.

A K Q AnalysisGame PayoffsPlayer 1:Better to be player 1 or player 2?AceBetCheckKingBetCheckQueenBetCheckCallEasy Decisions:AcePlayer 2FoldHard Decisions:CallKingFoldCallQueenFoldGame Payoffs (Player 1, Player 2)Player 1:AceBetKingCheckZero-Sum GameQueenBetCheckBetCheckCall(-2, 2)(-1, 1)(-2, 2)(-1, 1)Fold( 1,-1)( 1, -1)( 1,-1)( 1,-1)Gain(p) 0Player 2AceCall( 2, -2) ( 1, -1)(-2, 2)(-1, 1)Fold( 1, -1) ( 1, -1)( 1,-1)( 1,-1)Call( 2, -2) ( 1, -1)( 2,-2)( 1,-1)Fold( 1, -1) ( 1, -1)( 1,-1)( 1, -1)p P layersKingQueenPayoffs for Player 1Player 1:AceBetKingCheckStrategic DominationQueenBetCheckBetCheckCall-2-1-2-1Fold 1 1 1 1Player 2AceCall 2 1-2-1Fold 1 1 1 1Call 2 1 2 1Fold 1 1 1 1KingQueenStrategy A dominates Strategy B if Strategy Aalways produces a better outcome thanStrategy B regardless of the other player’saction.

Eliminating Dominated StrategiesPlayer 1:AceBetKingCheckSimplified Payoff MatrixQueenBetCheckBetCheckCall-2-1-2-1Fold 1 1 1 1Player 1: Ace KingBetCall 2 1-2-1Fold 1 1 1 1Call 2 1 2 1Fold 1 1 1 1KingAcePlayer 2Player 2AceCallQueenCheckBetCheck-1-2-1Call 2-2-1Fold 1 1 1Fold 1KingQueen 1QueenThe Tough DecisionsPlayer 1: AceBetPlayer 2AceCallExpected ValueQueenBetCheck-2-1-1Call 2-2Fold 1 1EV P r(e)V alue(e)e EventsKingWhat if Player 1 never bluffs?Never Bluff StrategyEV1 AKQBetCheckCheck-1-1ACallKFold/Call 1QFold 113 (1) 1 13( 2 Player 1: AceBetPlayer 2Player 2Player 1:The Tough Decisions-1 1112 ) 3 ( 1)AceCallQueenBetCheck-2-1-1Call 2-2Fold 1 1King 0What if Player 1 always bluffs?

Always Bluff StrategyPlayer 2Player 1:AAKQBetCheckBet-1-2CallCall 2Fold 1 1Fold 1 1RecapIf player 1 never bluffs:EV1 0If player 1 always bluffs: EV1 16-2KQ 1Is this a break-even game for Player 1?EV1/CallK 13 ( 21 ( 2) 12 ( 1)) 13 ( 21 12 ) 13 ( 2) 16EV1/F oldK 13 (1) 13 ( 12 12 ) 13 ( 12 ( 2) 12 (1)) 16Course OverviewClass Leader Expectations At least two weeks* before your scheduled class: Topics– Game Theory– Machine Learning– Anything else relevant to building a poker bot Format: most classes will be student-led– Present a topic and/or research paper– Let me know what you are planning on doing (talk to meafter class or email) At least one week before your scheduled class:– Post on the course blog a description of the class topic andlinks to any reading/preparation materials At the class: lead an interesting class, bring any neededmaterials Later that day: post class materials on the course blog Follow-up: respond to any comments on the courseblog* If you signed up for Feb 1, you’re already late!Course ProjectMy (Lack of) QualificationsBuild a poker bot capable of competing in theSixth Annual Computer Poker / I do research in computer security I have very limited knowledge and experiencein game theory, machine learning, etc. I am (probably) a fairly lousy poker playerWork in small (2-4) person teamsA few preliminary projects earlierCombine ideas/code/results from best teamsThis course will be a shared learning experience,and will only work well if everyone contributes tomake it interesting and worthwhile.Note: overlaps with USENIX Security, August 9-12 (also in San Francisco)

Things to DoRecap Recap Submit course survey Print and sign course contract: bring toTuesday’s classIf player 1 never bluffs:EV1 0If player 1 always bluffs: EV1 16Looks like a break-even game for Player 1:is there a better strategy? Reading for Tuesday: Chapters 1 and 2 ofDarse Billings’ dissertationEverything will be posted on the course site (by ixed StrategyAKQBetCheckCheck-1-1ACallKFold/Call 1QFold 1Never Bluff-1 1EV1 0Player 1: ABetPlayer 2Player 2Player 1:StrategiesAKQCallCall 2Fold 1Always BluffKQCheckBet-1-2Player 1Player 2Call with KingFold with KingBluff with QueenCheck with Queen-2 1EV1 ( SBluf f , TCall ) 16 EV1 ( SBluf f , TF old ) EV1 16EV1 ( SCheck , TCall ) Pure strategy: always do the same action for a given input state.Mixed strategy: probabilistically select from a set of pure strategies.Nash Equilibrium1616EV1 ( SCheck , TF old ) 0Finding the best strategy for Player 1: assume Player 2 plays optimally.Nash Equilibrium Player 1 is making the best decision she can,taking into account Player 2’s decisions. Player 2 is making the best decision he can,taking into about Player 1’s decisions. Neither player can improve its expected valueby deviating from the strategy.John Nash (born 1928)Equilibrium Points in N-Person Games, 1950Hence, to find the best strategy for Player 1, we need to find a strategythat makes Player 2 indifferent between his options.

Winning the AKQ GameEV1 ( SBluf f , TCall ) 16EV1 ( SCheck , TCall ) CallFold16EV1 ( SBluf f , TF old ) Winning the AKQ Game16EV1 ( SCheck , TF old ) 0BluffCheck-1 1 10Player 1 wants to make Player 2 indifferent between TCall and TFoldCharge Submit course survey Print and sign course contract: bring toTuesday’s class Reading for Tuesday: Chapters 1 and 2 ofDarse Billings’ dissertationReadings posted now. Everything else will be posted on thecourse site (by f you are signed up for February 1, by tomorrow: contact me about plans for class.BluffCheckCall-1 1Fold 10Player 1 wants to make Player 2 indifferent between TCall and TFold

A Course on Poker?!? There are few things that are so unpardonably neglected in our country as poker. The upper class knows very little about it. Now and . The Mathematics of Poker. A K Q Analysis Better to be player 1 or player 2? Easy Decisions: Hard Decisions: Game Payoffs Player 1: Ace King Queen Bet Check Bet Check Bet Check Player 2 Ace