Selection Search for Mean and Temperature of Multi-Branch Combinatorial Games

This paper shows a new algorithm to calculate the mean and temperature of multi-branch combinatorial games. The algorithm gradually, one node at a time, expands the offspring of a game. After each step of expansion, the lower and upper bounds of the mean and temperature of the game is re-calculated. As the expanding process continues, the range between the lower and upper bounds is narrowed. The key feature of the algorithm is its ability to generate a path whose outcome is most likely to reduce the distance between the lower and upper bounds.