Card counting meets hidden Markov models
Steven J. Aragon · UNM’s Digital Repository (University of New Mexico) · 2011
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.'