Abstract/Details

Simplified poker and the evolutionarily stable strategy

Vamos, Bryan E. 
 University of Guelph (Canada) ProQuest Dissertations Publishing,  2007. NR24583.

Abstract (summary)

This thesis is an investigation of the viability of applying the concept of the evolutionarily stable strategy (ESS) to simplified forms of poker. One avenue towards the emergence of an ESS is to explore the dynamics over time as suggested by Taylor and Jonker (1978). The underlying assumption is that the gradient method could be used to find strategies with greater fitness. The approach, in this thesis, was to assume that all players play a common strategy, that they are all aware of the strategy employed in each generation of play, and that after each tournament the common strategy is updated based on the returns for each hand. Two general variants of poker are investigated using both computer algorithms and explicit solutions. In the first variant, the players bet simultaneously while in the second they bet sequentially.

The limiting strategy for the simultaneous bets game is dependent upon the number of players, the number of hands, and the size of the bet, and can be characterized as having one, two or three regions. Either a player bets with certainty for all hands or he bets with higher ranked hands and folds with lower ranked hands. Occasionally a hand with an intermediate betting probability may be sandwiched between these regions. The limiting strategy for the sequential bets game is more complex. The strategy for the first player involves bluffing, with a prescribed probability for each bet size, below a particular threshold, regardless of the rank of the hand. For games with multiple bet sizes the first player should bet more aggressively with a better hand above the threshold. The player playing second plays a simple two-region strategy of betting on higher ranked hands and folding on lower ranked hands with the split between these regions being such as to maximize his return. While the solutions for the sequential bets case have been obtained using other methods, the gradient approach worked well, which suggests that it may prove a useful method for solving variants with increased rounds of betting or with more players.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Evolutionarily stable strategy; Poker
Title
Simplified poker and the evolutionarily stable strategy
Author
Vamos, Bryan E.
Number of pages
199
Degree date
2007
School code
0081
Source
DAI-B 68/03, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
978-0-494-24583-5
University/institution
University of Guelph (Canada)
University location
Canada
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
NR24583
ProQuest document ID
304844942
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/304844942/abstract