Bluffing in Scrabble
Nick Ballard, Timothy Y. Chow
众所周知,在信息不完善(如扑克)的游戏中,以某种概率虚张声势可能是最佳策略的组成部分。 然而,据我们所知,没有人曾经表现出一个拼字游戏的位置,其中最优策略涉及虚张声势,甚至是拼字游戏位置,其中最优策略是混合(即随机)策略。 我们展示了一个精心构建的拼字游戏位置,实际上可能会出现在锦标赛中,没有播放无效的单词,其中最佳策略(假设绑分数导致点平分,没有使用所谓的“点差”作为平局破损机制)是使A以概率1/3和概率为2/3的移动B。 移动B可以合理地称为虚张声势,因为它设置了玩家实际上无法执行的威胁,但对手可能无法排除。
It is well known that in games with imperfect information, such as poker, bluffing with some probability can be a component of the optimal strategy. However, as far as we know, nobody has ever exhibited a Scrabble position in which the optimal strategy involves bluffing, or even a Scrabble position in which the optimal strategy is a mixed (i.e., randomized) strategy. We present a carefully constructed Scrabble position, that could actually arise in a tournament game with no invalid words played,...