Conway's bounded octal game periodicity conjecture

An octal game is a game played with tokens divided into heaps, where a move either removes some or all tokens in one heap, or removes some but not all tokens from a heap and divides the remainder into two non-empty heaps. A bounded octal game is one in which the number of tokens removable from any single heap is bounded. Conway's conjecture. Every bounded octal game is periodic. The conjecture is supported by the threshold theorem and computational evidence, but it gives no upper bound on the period and remains unproved in general.