I study endogenous learning dynamics for people expecting systematic reversals from random sequences - the "gambler's fallacy." Biased agents face an optimal-stopping problem. They are uncertain about the underlying distribution and learn its parameters from predecessors. Agents stop when early draws are "good enough," so predecessors' experience contain negative streaks but not positive streaks. Since biased agents understate the likelihood of consecutive below-average draws, society converges to over-pessimistic beliefs about the distribution's mean and stops too early. Agents uncertain about the distribution's variance overestimate it to an extent that depends on predecessors' stopping thresholds. Subsidizing search partially mitigates long-run belief distortions.

翻译：我研究了人们期望从随机序列中系统地逆转的内在学习动态——“gambler的谬误” 。 被滥用的代理商面临一个最佳的阻止问题。 他们对于基本分布并不确定, 并从前身那里了解其参数。 代理商在早期抽取时停止, “ 足够好 ”, 所以前任代理商的经验包含负数, 而不是正数。 由于偏见的代理商低估了连续的低于平均的抽取的可能性, 社会会趋向于过度悲观的关于分配平均值的信念, 并过早停止。 代理商对分配差异的不确定性高估程度取决于前身的停止阈值。 补贴搜索会部分减轻长期的信仰扭曲。