Could the Declarer Have Discarded It? Refined Anticipation of Cards in Skat

In this paper we refine the concept of anticipation within a card game, taking the Nullspiel in Skat as a running example. We generate the belief space of all distributions of cards according to the assumption on plausible play of the declarer. Using a selection of open-card searches in a two-stage knowledge filtering we improve the play of the two opponents to find forced wins. In the voting scheme to combine the open-card analyses of the possible worlds, we additionally use the search tree size and depth to prefer short proofs. In hundreds of thousands human ouvert games replayed by our AIs over 99% matched the predictions of the open-card solver, with only 0.21% of games known lost for the declarer were not won by the AIs, both trademarks outperforming human play.