1 / 12

How to win at poker using game theory

How to win at poker using game theory. A review of the key papers in this field. The main papers on the issue. The first attempts Émile Borel : ‘Applications aux Jeux des Hazard’ (1938) John von Neumann and Oskar Morgenstern : ‘Theory of Games and Economic Behaviour’ (1944)

minya
Download Presentation

How to win at poker using game theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. How to win at poker using game theory A review of the key papers in this field

  2. The main papers on the issue • The first attempts • ÉmileBorel: ‘Applications aux Jeux des Hazard’ (1938) • John von Neumann and Oskar Morgenstern : ‘Theory of Games and Economic Behaviour’ (1944) • Extensions on this early model • Bellman and Blackwell (1949) • Nash and Shapley (1950) • Kuhn (1950) • Jason Swanson: Game theory and poker (2005) • Sundararaman (2009)

  3. Jargon buster • Fold: A Player gives up his/her hand. • Pot: All the money involved in a hand. • Check: A bet of ‘Zero’. • Call: Matching the bet of the previous player. • Ante: Money put into the pot before any cards have been dealt.

  4. Émile Borel: ‘Applications aux Jeux des Hazard’ (1938) • How the game is played • Two players • Two ‘cards’ • Each card is given a independent uniform value between 0 and 1 • Player 1’s card is X, Player 2’s Card is Y • No checking in this game • No raising or re-raising

  5. How the game is played Betting tree: outcomes for Player 1 • First both players ante £1 • The pot is now £2 • Player 1 starts first • Either Bets or Fold • Folding results in player 2 receiving £2 – wins £1 • Player 2 can either call or fold. • Folding results in player 1 receiving £3 – wins £1 • Then the cards are ‘turned over’ • The highest card wins the pot

  6. Émile Borel: ‘Applications aux Jeux des Hazard’ (1938) • Key assumptions • No checking • X≠Y (Cannot have same cards) • Money in the pot is an historic cost (sunk cost) and plays no part in decision making.

  7. Émile Borel: ‘Applications aux Jeux des Hazard’ (1938) Key Conclusions • Unique admissible optimal strategies exist for both players • Where no strategy does any better against one strategy of the opponent without doing worse against another – it’s the best way to take advantage of mistakes an opponent may make. • The game favours Player 2 in the long run • The expected winnings of player 2 is 11% when B=1 • The optimum strategies exists • player 1 is to bet unless X<0.11 where he should fold. • player 2 is to call unless Y<0.33 where he should fold • Player 1 can aim to capitalise on his opponents mistakes by bluffing

  8. John von Neumann and Oskar Morgenstern : ‘Theory of Games and Economic Behaviour’ (1944) • New key assumption: • Player 1 can now check • New conclusions • Player 1 should bluff with his worst hands • The optimum bet is size of the pot

  9. One Card Poker • 3 Cards in the Deck {Ace, Deuce, Trey} • 2 Players – One Card Each • Highest Card Wins • Players have to put an initial bet (‘ante’) before they receive their card • A round of betting occurs after the cards have been received • The ‘dealer’ always acts second

  10. One Card Poker • Assumptions • Never fold with a trey • Never call with the ace • Never check with the trey as the dealer • ‘Opener’ always checks with the deuce

  11. One Card Poker • Conclusions • Dealer should call with the deuce 1/3 of the time • Dealer should bluff with the ace 1/3 of the time • If the dealer plays optimally the whole time, then expected profit will be 5.56%

  12. Thank You for Listening!

More Related