Semi-Strongly solved: a New Definition Leading Computer to Perfect Gameplay
Hiroki Takizawa

TL;DR
The paper introduces semi-strong solving, an intermediate game-solving concept that certifies optimal play within a specific region, balancing the thoroughness of strong solving and the efficiency of weak solving.
Contribution
It proposes a new semi-strong solving framework with a specialized alpha-beta search algorithm, providing verifiable solutions and resource bounds for perfect-information games.
Findings
Semi-strong solutions support exact value queries and move selection.
The approach reduces resource requirements compared to strong solving.
Experimental results on Othello and Connect Four demonstrate efficiency and scalability.
Abstract
Strong solving of perfect-information games certifies optimal play from every reachable position, but the required state-space coverage is often prohibitive. Weak solving is far cheaper, yet it certifies correctness only at the initial position and provides no formal guarantee for optimal responses after arbitrary deviations. We define semi-strong solving, an intermediate notion that certifies correctness on a certified region R: positions reachable from the initial position under the explicit assumption that at least one player follows an optimal policy while the opponent may play arbitrarily. A fixed tie-breaking rule among optimal moves makes the target deterministic. We propose reopening alpha-beta, a node-kind-aware Principal Variation Search/Negascout scheme that enforces full-window search only where semi-strong certification requires exact values and a canonical optimal action,…
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Taxonomy
TopicsEducational Games and Gamification
