Generalizing OOOOOOB

Abstract

We present three versions of the classic two-pile game \textsc{one-or-one-or-one-of-both} generalized to the multi-pile context. In each case, we explore the resulting $\mathcal{P}$-positions. In the first version, there is a simple pattern. In the other two versions, we find partial solutions in each case through two experimental routes. First by limiting the number of piles, then by limiting the number of tokens per pile.