Solving 9 Layer Triangular Nim

Abstract

Triangular Nim, one variant of the game Nim, is a common two-player game in Taiwan and China. In the past, Hsu strongly solved 7 layer Triangular Nim while some of the authors recently strongly solved 8 layer Triangular Nim. The latter required 8 gigabytes in memory and 8878 seconds.Using a retrograde method, this paper strongly solves 9 layer Triangular Nim. In our first version, the program requires four terabytes in memory and takes about 129.21 days aggregately. In our second version, improved by removing some rotated and mirrored positions, the program reduces the memory by a factor of 5.86 and the computation time by a factor of 4.38. Our experiment result also shows that the loss rate is only 5.0%. This is also used to help improve the performance.

XT Domineering: A new combinatorial game

“…Based on the theory, playing or solving many combinatorial games such as Nim [3,4], Triangular Nim [5], Clobber [6] and Cutthroat [7] may simply become mathematical calculations, such as summation, instead of a complex tree search.…”