THE SPRAGUE-GRUNDY FUNCTION FOR SOME SELECTIVE COMPOUND GAMES.

We analyze the Sprague-Grundy functions for a class of almost disjoint selective compound games played on Nim heaps. Surprisingly, we find that these functions behave chaotically for smaller Sprague-Grundy values of each component game yet predictably when any one heap is sufficiently large. In particular, we prove some conjectures of Boros et al. and make progress on others. We conjecture some periodicity results for almost disjoint union of games which relate to Conway’s conjecture that all bounded octal games have periodic Sprague-Grundy functions. [ABSTRACT FROM AUTHOR]