Searching for periodicity in Officers

Officers is a take-and-break game in which a move consists of removing a bean from a heap and leaving the remaining beans from that heap in exactly one or two nonempty heaps. It is an open question as to whether or not the Grundy values of this game are eventually periodic; answering this question in the positive for take-and-break games generally requires computing enough Grundy values to explicitly find the period. We contribute to this search by presenting two novel parallelization strategies that, combined with additional optimizations, accelerate the computation of Grundy values by nearly 60 times compared to the previous state of the art. The resulting implementation computes over 5 million values per second, and has computed a total of more than 140 trillion values over the course of 18 months. To date, no period has been found.