## Electrical and Computer Engineering ETDs

#### Publication Date

2-7-2011

#### 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 \uf070. 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, \uf070 represents the prior probability of beginning in a particular unobservable state. Three fundamental questions arise with respect to HMMs. First, given A, B, and \uf070, what is the probability a specific observation sequence will be seen? Second, given A, B, \uf070 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 \uf070. 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.'

#### Keywords

Hidden Markov models, Card counting, Blackjack (Game)

#### Document Type

Thesis

#### Language

English

#### Degree Name

Electrical Engineering

#### Level of Degree

Masters

#### Department Name

Electrical and Computer Engineering

#### First Advisor

Jordan, Ramiro

#### First Committee Member (Chair)

Jayaweera, Sudharman

#### Second Committee Member

Solomon, Otis Jr.

#### Recommended Citation

Aragon, Steven J.. "Card counting meets hidden Markov models." (2011). http://digitalrepository.unm.edu/ece_etds/17