标题： 在拼字游戏中欺骗 显示英文标题

标题： Bluffing in Scrabble

摘要： 众所周知，在信息不完全的游戏中，如扑克，以一定概率进行虚张声势可能是最优策略的一部分。 然而，据我们所知，没有人曾经展示过一个拼字游戏（Scrabble）局面，其中最优策略涉及虚张声势，甚至没有展示过一个最优策略是混合（即随机化）策略的拼字游戏局面。 我们提出一个精心构建的拼字游戏局面，这在比赛中可能实际出现，且没有使用无效单词。在这种情况下，最优策略（假设平局时分数均分，不采用所谓的“扩散分数”作为决胜机制）是以1/3的概率进行移动A，以2/3的概率进行移动B。 移动B可以合理地被称为虚张声势，因为在这一移动中设置了一个威胁，但玩家实际上无法执行该威胁，而对手可能无法排除这种可能性。 显示英文摘要

摘要： 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, in which the optimal strategy (assuming that a tied score leads to the point being split equally, with no recourse to so-called "spread points" as a tie-breaking mechanism) is to make Move A with probability 1/3 and to make Move B with probability 2/3. Move B can reasonably be called a bluff, in the sense that it sets up a threat which the player cannot in fact execute, but which the opponent may not be able to rule out.