Abstract
We present a complete solution to a card game with historical origins. Our analysis exploits the convexity properties in the payoff matrix, allowing this discrete game to be resolved by continuous methods.
Similar content being viewed by others
References
HALD, A., A History of Probability and Statistics and Their Applications Before 1750, John Wiley and Sons, New York, NY, 1990.
DRESHER, M., Games of Strategy, Mathematics Magazine, Vol. 25, pp. 93–99, 1951.
DRESHER, M., Games of Strategy: Theory and Applications, Prentice-Hall, Englewood Cliffs, New Jersey, 1961.
FISHER, R. A., Randomization and an Old Enigma of Card Play, Mathematical Gazette, Vol. 18, pp. 294–297, 1934.
TODHUNTER, I., A History of the Mathematical Theory of Probability, Chelsea, New York, NY, 1949 (Reprint).
KARLIN, S., Mathematical Methods and Theory in Games, Programming, and Economics, Vol. 1, Addison-Wesley, Reading, Massachusetts, 1959.
BENJAMIN, A. T., and GOLDMAN, A. J., Le Her, Preprint, 1992.
HOWARD, J. V., A Geometrical Method of Solving Certain Games, Naval Research Logistics, Vol. 41, pp. 133–136, 1994.
BENJAMIN, A. T., and GOLDMAN, A. J., Localization of Optimal Strategies in Certain Games, Naval Research Logistics, Vol. 41, pp. 669–676, 1994.
FAN, K., Minimax Theorems, Proceedings of the National Academy of Science, Vol. 39, pp. 42–47, 1953.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Benjamin, A., Goldman, A. Analysis of the N-Card Version of the Game Le Her. Journal of Optimization Theory and Applications 114, 695–704 (2002). https://doi.org/10.1023/A:1016035315396
Issue Date:
DOI: https://doi.org/10.1023/A:1016035315396