论文标题
猜测卡有完整的反馈
Guessing cards with complete feedback
论文作者
论文摘要
我们将以下游戏视为测试超体感知声明（ESP）的一种方式。给出了一个$ MN $卡的甲板，其中包括$ n $不同类型的每种类型，每种类型恰好出现$ m $ times：该甲板被改组，然后从顶部到底部一次从甲板上丢弃卡片。在每个步骤中，一个玩家（正在测试其心理力量）试图猜测当前最高的卡的类型，然后在被丢弃之前向玩家揭示。我们研究了玩家可以做出的正确预测的预期数量$ s_ {n，m} $：人们总是可以猜测完全相同的卡片，这表明可以实现$ s_ {n，m}> m $。我们证明，最佳（非心理）策略略高于此策略，并在$ n，m $以合适的价格生长时找到一阶校正。这与$ m $固定并且$ n $大的情况大不相同（He＆Ottolini），并且与固定$ n $和$ m $的情况相似（Graham＆Diaconis）。情况$ m = n $回答了diaconis的问题。
We consider the following game that has been used as a way of testing claims of extrasensory perception (ESP). One is given a deck of $mn$ cards comprised of $n$ distinct types each of which appears exactly $m$ times: this deck is shuffled and then cards are discarded from the deck one at a time from top to bottom. At each step, a player (whose psychic powers are being tested) tries to guess the type of the card currently on top, which is then revealed to the player before being discarded. We study the expected number $S_{n,m}$ of correct predictions a player can make: one could always guess the exact same type of card which shows that one can achieve $S_{n,m}>m$. We prove that the optimal (non-psychic) strategy is just slightly better than that and find the first order correction when $n, m$ grows at suitable rates. This is very different from the case where $m$ is fixed and $n$ is large (He & Ottolini) and similar to the case of fixed $n$ and $m$ is large (Graham & Diaconis). The case $m=n$ answers a question of Diaconis.
