We show how classic conditional probability puzzles, such as the Monty Hall problem, are intimately related to the recently discovered hot hand selection bias. We explain the connection by way of the principle of restricted choice, an intuitive inferential rule from the card game bridge, which we show is naturally quantified as the updating factor in the odds form of Bayes's rule. We illustrate how, just as the experimental subject fails to use available information to update correctly when choosing a door in the Monty Hall problem, researchers may neglect analogous information when designing experiments, analyzing data, and interpreting results.

中文翻译：

---

从蒙蒂·霍尔到热手的桥梁：限制选择的原则

我们展示了经典的条件概率难题，例如Monty Hall问题，与最近发现的热手选择偏向密切相关。我们通过受限选择的原理（一种来自纸牌游戏桥的直观推断规则）来解释这种联系，我们证明了自然地将其量化为贝叶斯规则赔率形式中的更新因子。我们举例说明，就像实验对象在选择蒙蒂·霍尔（Monty Hall）问题中的一扇门时未能利用可用信息正确更新一样，研究人员在设计实验，分析数据和解释结果时可能会忽略类似的信息。