Electrical and Computer Engineering ETDs

Publication Date



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.'


Hidden Markov models, Card counting, Blackjack (Game)

Document Type




Degree Name

Electrical Engineering

Level of Degree


Department Name

Electrical and Computer Engineering

First Advisor

Jordan, Ramiro

First Committee Member (Chair)

Jayaweera, Sudharman

Second Committee Member

Solomon, Otis Jr.