Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/12022

Title: | Card counting meets hidden Markov models |

Author: | Aragon, Steven J. |

Advisor(s): | Jordan, Ramiro |

Committee Member(s): | Jayaweera, Sudharman Solomon, Otis Jr. |

Department: | University of New Mexico. Dept. of Electrical and Computer Engineering |

Subject(s): | Hidden Markov Models |

LC Subject(s): | Hidden Markov models Card counting Blackjack (Game) |

Degree Level: | Masters |

Abstract: | The Hidden Markov Model (HMM) is a stochastic process that involves an unobservable Markov Chain and an observable output at each state in the chain. Hidden Markov Models are described by three parameters: A, B, and . A is a matrix that holds the transition probabilities for the unobservable states. B is a matrix that holds the probabilities for the output of an observable event at each unobservable state. Finally, represents the prior probability of beginning in a particular unobservable state. Three fundamental questions arise with respect to HMM’s. First, given A, B, and , what is the probability a specific observation sequence will be seen? Second, given A, B, and an observation sequence, what is the most probable sequence of hidden states that produced the output? Finally, given a set of training data, estimate A, B, and . There are a number of tools that have been developed to answer these questions. Woolworth Blackjack is a variation of Blackjack played with a deck consisting of 20 fives and 32 tens. The object is to get a close to 20 as possible without going over. The player using a basic strategy loses to the dealer. The aim of this research is to develop a winning counting strategy for Woolworth Blackjack and then attempt to improve upon the counting strategy with a HMM using well-established HMM analysis tools. A secondary goal is to understand when to use counting strategies and when to use HMM’s. |

Graduation Date: | December 2010 |

URI: | http://hdl.handle.net/1928/12022 |

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