{"id":{"repo_id":"unm","oai_identifier":"oai:digitalrepository.unm.edu:ece_etds-1016"},"canonical_url":"https://search.dev.ndltd.org/etd/unm/oai:digitalrepository.unm.edu:ece_etds-1016","repository":{"repo_id":"unm","name":"University of New Mexico","base_url":"https://digitalrepository.unm.edu/do/oai/"},"display":{"title":"Card counting meets hidden Markov models","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.'","abstract_html":"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.'","abstract_has_math":false,"creators":["Aragon, Steven J."],"institution":null,"degree_name":"Electrical Engineering","degree_level":"Thesis","degree_discipline":"Electrical and Computer Engineering","degree_department":null,"school":null,"contributors":["Jordan, Ramiro","Jayaweera, Sudharman","Solomon, Otis Jr."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-02-07T08:00:00Z","date_published":"2011-02-07T08:00:00Z","updated_at":"2026-07-24T05:27:10Z","subjects":["Hidden Markov models","Card counting","Blackjack (Game)"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalrepository.unm.edu/ece_etds/17","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jordan, Ramiro","Jayaweera, Sudharman","Solomon, Otis Jr."]},{"key":"dc:creator","label":"Author","values":["Aragon, Steven J."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical and Computer Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis","Masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Electrical Engineering"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Hidden Markov models","Card counting","Blackjack (Game)"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalrepository.unm.edu/ece_etds/17"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.'"]},{"key":"dc:title","label":"Title","values":["Card counting meets hidden Markov models"]}]}],"canonical_facts":{"dc:contributor":["Jordan, Ramiro","Jayaweera, Sudharman","Solomon, Otis Jr."],"dc:creator":["Aragon, Steven J."],"dc:description.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.'"],"dc:identifier":["https://digitalrepository.unm.edu/ece_etds/17"],"dc:language":["English"],"dc:subject":["Hidden Markov models","Card counting","Blackjack (Game)"],"dc:title":["Card counting meets hidden Markov models"],"thesis:degree_discipline":["Electrical and Computer Engineering"],"thesis:degree_level":["Thesis","Masters"],"thesis:degree_name":["Electrical Engineering"]},"updated_at":"2026-07-24T05:27:10Z"}