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This paper rebuilds the inference rules of a strong Skat (trick-taking card game) player as a declarative, domain-specific language, then adds cardinality constraints and confidence-weighted belief updates. The self-play gains are modest in scope, limited to one game and one engine, but the work is a concrete example of making hand-coded game AI knowledge auditable and extensible. Readers interested in symbolic-probabilistic hybrids for imperfect-information settings should find the design choices more useful than the win-rate numbers.
Source coveringarXiv

Inner-Learning: From Hand-Coded Beliefs to Declarative Knowledge in Trick-Taking Games

arXiv2 min read

arXiv:2610.38304v1 Announce Type: new Abstract: We present a declarative approach to belief-state modeling in trick-taking card games. Starting from a state-of-the-art Skat player, we automatically extract its hand-coded inference rules into a domain-specific language built on the primitive $\neg\mathsf{holds}(P,C)$, denoting that player $P$ cannot hold any card in set $C$. Round-trip code generation verifies that the extracted rules reproduce the original engine's intended behavior, up to three audited bugs in the original that the declarative engine corrects. We then grow the rule base through symmetric derivation and annotation of an expert strategy document---unifying code, symmetry, and expertise in one representation. We extend the knowledge representation with \emph{cardinality constraints}: at-most-$k$ and at-least-$k$ bounds on the cards a player holds from a named group, expressed in the same declarative language and enforced at world-generation time. Confidence parameters connect symbolic rules to probabilistic belief updates. Self-play evaluation shows the declarative engine measurably improving winning percentage and score over the original hand-coded engine, with the extracted rules, the human-annotated rules, and the cardinality constraints each contributing to the effect.

Abstract:We present a declarative approach to belief-state modeling in trick-taking card games. Starting from a state-of-the-art Skat player, we automatically extract its hand-coded inference rules into a domain-specific language built on the primitive $\neg\mathsf{holds}(P,C)$, denoting that player $P$ cannot hold any card in set $C$. Round-trip code generation verifies that the extracted rules reproduce the original engine's intended behavior, up to three audited bugs in the original that the declarative engine corrects. We then grow the rule base through symmetric derivation and annotation of an expert strategy document---unifying code, symmetry, and expertise in one representation. We extend the knowledge representation with \emph{cardinality constraints}: at-most-$k$ and at-least-$k$ bounds on the cards a player holds from a named group, expressed in the same declarative language and enforced at world-generation time. Confidence parameters connect symbolic rules to probabilistic belief updates. Self-play evaluation shows the declarative engine measurably improving winning percentage and score over the original hand-coded engine, with the extracted rules, the human-annotated rules, and the cardinality constraints each contributing to the effect.

Artificial Intelligence (cs.AI)

arXiv:2610.38304 [cs.AI]

(or arXiv:2610.38304v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2610.38304 Focus to learn more arXiv-issued DOI via DataCite

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Full text under the publisher's open licence · 262 words