Best play in Dots and Boxes endgames
نویسندگان
چکیده
We give very simple algorithms for best play in the simplest kind of Dots and Boxes endgames: those that consist entirely loops long chains. In every such endgame we compute margin victory, assuming both players maximize numbers boxes they capture, specify a move leads to result. improve on results by Buzzard Ciere same problem: our examine only current position do not need consider game tree at all.
منابع مشابه
Solving Dots-And-Boxes
Dots-And-Boxes is a well-known and widely-played combinatorial game. While the rules of play are very simple, the state space for even very small games is extremely large, and finding the outcome under optimal play is correspondingly hard. In this paper we introduce a Dots-And-Boxes solver which is significantly faster than the current state-of-the-art: over an order-of-magnitude faster on seve...
متن کاملSolving 4x5 Dots-And-Boxes
Dots-And-Boxes is a well-known and widely-played combinatorial game. While the rules of play are very simple, the state space for even small games is extremely large, and finding the outcome under optimal play is correspondingly hard. In this paper we introduce a Dots-And-Boxes solver which is significantly faster than the current state-of-the-art: over an order-of-magnitude faster on several l...
متن کاملNarrow Misère Dots-and-Boxes
We study misère Dots-and-Boxes, where the goal is to minimize score, for narrow boards. In particular, we characterize the winner for 1× n boards with an explicit winning strategy for the first player with a score of b(n − 1)/3c. We also give preliminary results for 2 × n and for Swedish 1× n (where the boundary is initially drawn).
متن کاملEvolution of Neural Networks to Play the Game of Dots-and-Boxes
Dots-and-Boxes is a child’s game which remains analytically unsolved. We implement and evolve arti cial neural networks to play this game, evaluating them against simple heuristic players. Our networks do not evaluate or predict the nal outcome of the game, but rather recommend moves at each stage. Superior generalisation of play by co-evolved populations is found, and a comparison made with ne...
متن کاملVariations on Narrow Dots-and-Boxes and Dots-and-Triangles
We verify a conjecture of Nowakowski and Ottaway that closed 1×n Dots-and-Triangles is a first-player win when n 6= 2 [2]. We also prove that in both the open and closed 1× n Dots-and-Boxes games where n is even, the first player can guarantee a tie.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Game Theory
سال: 2021
ISSN: ['1432-1270', '0020-7276']
DOI: https://doi.org/10.1007/s00182-020-00730-4