Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-18T01:26:09.190Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal doubling strategy against a suboptimal opponent

Part of: Stochastic processes Game theory

Published online by Cambridge University Press:  14 July 2016

Konstantinos V. Katsikopoulos  and
Özgür Şimşek
Konstantinos V. Katsikopoulos*
Affiliation:
University of Massachusetts, Amherst and Max Planck Institute for Human Development
Özgür Şimşek*
Affiliation:
University of Massachusetts, Amherst
*
∗Postal address: Center for Adaptive Behavior and Cognition, Max Planck Institute for Human Development, Lentzeallee 94, Berlin, 14195, Germany. Email address: katsikop@mpib-berlin.mpg.de
∗∗Postal address: Department of Computer Science, University of Massachusetts, 140 Governors Drive, Amherst, MA 01003, USA.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For two-person zero-sum games, where the probability of each player winning is a continuous function of time and is known to both players, the mutually optimal strategy for proposing and accepting a doubling of the game value is known. We present an algorithm for deriving the optimal doubling strategy of a player who is aware of the suboptimal strategy followed by the opponent. We also present numerical results about the magnitude of the benefits; the results support the claim that repeated application of the algorithm by both players leads to the mutually optimal strategy.

Keywords

Gamblingdoublingoptimal strategy

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 91A05: 2-person games
Type
Short Communications
Information
Journal of Applied Probability , Volume 42 , Issue 3 , September 2005 , pp. 867 - 872
Copyright
© Applied Probability Trust 2005 

References

Jacoby, O. and Crawford, J. R. (1970). The Backgammon Book. Viking Press, New York.Google Scholar
Keeler, E. and Spencer, J. (1975). Optimal doubling in backgammon. Operat. Res. 23, 1063–1071.CrossRefGoogle Scholar
Luce, R. D. and Raiffa, H. (1957). Games and Decisions. John Wiley, New York.Google Scholar
Magriel, P. (1985). Backgammon. X-22 Publishing, New York.Google Scholar
Robertie, B. (1997). Backgammon for Serious Players, 2nd edn. Cardoza Publications, New York.Google Scholar
Zadeh, N. (1977). On doubling in tournament backgammon. Manag. Sci. 23, 986–993.Google Scholar
Zadeh, N. and Kobliska, G. (1977). On optimal doubling in backgammon. Manag. Sci. 23, 853–858.CrossRefGoogle Scholar