The Number of Optimal Strategies in the Penney-Ante Game

zbMath1470.91063arXiv2107.06952MaRDI QIDQ4987405

Reed Phillips, Adolf Hildebrand

Publication date: 3 May 2021

Full work available at URL: https://arxiv.org/abs/2107.06952

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) 2-person games (91A05) Probabilistic games; gambling (91A60)

Uses Software

• OEIS
• NAIVE
• DAVID_IAN
• JODO
• BLANKS
• SYMGJ
• SPGJ
• GJseries
• GJSAW
• GJsqfree

Cites Work

• A martingale approach to the study of occurrence of sequence patterns in repeated experiments
• String overlaps, pattern matching, and nontransitive games
• On fair coin-tossing games
• Optimal Penney Ante strategy via correlation polynomial identities
• Renewal theory for several patterns
• How many random digits are required until given sequences are obtained?
• Optimal Strategy for the First Player in the Penney Ante Game
• The Goulden—Jackson cluster method: extensions, applications and implementations
• Waiting Times for Patterns and a Method of Gambling Teams

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