3 PLAYER KUHN POKER ERNESTO DIAZ FELIPE ZUNIGA

3 -PLAYER KUHN POKER ERNESTO DIAZ FELIPE ZUNIGA SEBASTIAN BUCCOLLINI

INTRODUCTION • Poker is a game of skill and strategy that usually involves betting, randomness and competition. Players are dealt cards from a deck, each player receives a certain amount of cards (usually 2) and must place a bet that he/she will win the pot (sum of all the players bets). • The rules of poker make it perfect for studying it from a mathematical perspective. The study of how conflict and cooperation between rational agents affect the outcome of a predetermined mathematical model is known as game theory [1].

INTRODUCTION CONT. • Kuhn poker is an extremely simplified version of poker that serves as a zero-sum, imperfect information game. In this version of poker the deck includes three cards (King, Queen, Jack) and one card is dealt to each player. The game includes one round of betting and players can place bets like in standard poker [2]. • This game is included in the Annual Computer Poker Competition, which is as the name implies, a poker tournament for intelligent agents [2].

METHODOLOGY • To implement our intelligent agent we used the python interface (Git. Hub repository provided by instructor) for the ACPC server. By conforming to the interface provided in this repository, one can write code in python that communicates with the official competition server for the ACPC. • Our initial strategy involved using the Gambit interface for python so as to compute a Nash equilibrium. While this could be the optimal strategy our implementation took much too long to compile so we opted for another strategy. • Our strategy is quite simple, our agent bets only under certain conditions so as to ensure optimal gains.

ANALYSIS • If the agent is dealt an Ace the agent always bets because this is the highest card. When the agent is dealt the lowest card, Jack, the agent will only bet if the other players fold because this way the agent can still win the pot. • For the rest of the cards, King and Queen, the agent will bet based on a random factor (pseudo random number from 0 to 1) generated using python’s random library. • By adding this random factor we can limit the amount of times our agent bets based on the card it has been dealt.

CONCLUSION • In this paper, we have shown that by simply limiting agent bets and intertwining random factors into the equations we can gain profitable results. • Although we were not able to implement the Gambit interface and compute a Nash equilibrium and perhaps sacrifice some optimality, we were able to find a simple but effective strategy through which our agent makes its betting decisions. • With more time, in the future, and a better implementation could potentially be made, but that will require further study.

REFERENCES • [1] Artificial Intelligence: A Modern Approach (3 rd Edition) (11 December 2009) by Stuart Russell, Peter Norvig • [2] Annual Computer Poker Competition. Retrieved December 07, 2017, from http: //www. computerpokercompetition. org/