Impact of Rounding during Retrograde Analysis for a Game with Chance Nodes: Karl’s Race as a Test Case

Article type: Research Article

Authors: Hartisch, Michael¹

Affiliations: University of Siegen

Note: [1] Technology Management, Faculty of Business Administration, University of Siegen, Siegen, Germany, email: michael.hartisch@uni-siegen.de

Abstract: We investigate the game “Karl’s Race” which has elements of chance and is closely related to “Ein-Stein Würfelt Nicht!”. Its state space is significantly smaller, without losing its fascination and complex nature. This game can be analysed completely by using retrograde analysis and thus creates an excellent testing ground for other heuristics dealing with games with chance nodes. Since analysing games with chance nodes requires saving expected values, and thus rational numbers, an enormous amount of memory is required during the calculation and when saving the exact data. Therefore, we examine the effect of intentional rounding during the retrograde analysis. We find that certain types of rounding only slightly affect the playing strength of players using these data while reducing the required memory space to 25 percent.

DOI: 10.3233/ICG-2015-38203

Journal: ICGA Journal, vol. 38, no. 2, pp. 81-93, 2015