cs.AI updates on arXiv.org 10月07日
简化版2048游戏策略研究
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本文研究简化版2048游戏(4x3版)的强解,通过状态空间分割技术,分析了最常见初始状态下最优策略的期望得分,并确定了可达状态和后续状态的数量。

arXiv:2510.04580v1 Announce Type: new Abstract: 2048 is a stochastic single-player game involving 16 cells on a 4 by 4 grid, where a player chooses a direction among up, down, left, and right to obtain a score by merging two tiles with the same number located in neighboring cells along the chosen direction. This paper presents that a variant 2048-4x3 12 cells on a 4 by 3 board, one row smaller than the original, has been strongly solved. In this variant, the expected score achieved by an optimal strategy is about $50724.26$ for the most common initial states: ones with two tiles of number 2. The numbers of reachable states and afterstates are identified to be $1,152,817,492,752$ and $739,648,886,170$, respectively. The key technique is to partition state space by the sum of tile numbers on a board, which we call the age of a state. An age is invariant between a state and its successive afterstate after any valid action and is increased two or four by stochastic response from the environment. Therefore, we can partition state space by ages and enumerate all (after)states of an age depending only on states with the recent ages. Similarly, we can identify (after)state values by going along with ages in decreasing order.

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2048游戏 策略研究 状态空间分割 期望得分
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