Motivated by the results for Magic: The Gathering presented in [CBH20] and [Bid20], we study a (different) computability problem about winning strategies in Yu-Gi-Oh! Trading Card Game, a popular card game developed and published by Konami. We show that the problem of establishing whether, from a given game state, a given computable strategy is winning is undecidable. In particular, not only do we prove that the Halting Problem can be reduced to this problem, but also that this problem is actually $Π^1_1$-complete. We extend this last result to all strategies with a reduction on the set of countable well orders, a classic $\boldsymbolΠ^1_1$-complete set. For these reductions, we present two legal decks (according to the current Forbidden & Limited List of Yu-Gi-Oh! Trading Card Game) that can be used by the player who goes first to perform them.

翻译：受[CBH20]与[Bid20]中关于《万智牌》研究结果的启发，我们针对科乐美公司开发并发行的热门卡牌游戏《游戏王》集换式卡牌，研究了一个（不同的）关于必胜策略的可计算性问题。我们证明：在给定游戏状态下，判定特定可计算策略是否为必胜策略的问题是不可判定的。具体而言，我们不仅证明了停机问题可归约至该问题，更证明了该问题实际上是$Π^1_1$-完全的。通过将问题归约至经典$\boldsymbolΠ^1_1$-完全集——可数良序集，我们将最终结论推广至所有策略。针对这些归约过程，我们提出了两套符合《游戏王》集换式卡牌游戏现行禁限卡表规则的卡组，可供先手玩家用于实现归约操作。