Multiple-Outcome Proof Number Search

We present Multiple-Outcome Proof Number Search (MOPNS), a Proof Number based algorithm able to prove positions in games with multiple outcomes. MOPNS is a direct generalization of Proof Number Search (PNS) in the sense that both behave exactly the same way in games with two outcomes. However, MOPNS targets a wider class of games. When a game features more than two outcomes, PNS can be used multiple times with different objectives to finally deduce the value of a position. On the contrary, MOPNS is called only once to produce the same information. We present experimental results on solving various positions of the games CONNECT FOUR and WOODPUSH showing that in most problems, the total number of node creations of MOPNS is lower than the cumulative number of node creations of PNS, even in the best case where PNS does not need to perform a binary search.