直到出现 HTHT 的期望抛掷次数

HTHT

个人笔记

一枚公平的 coin is 到ssed until the sequence HTHT is obtained. 的期望次数是多少到sses?

A fair coin is tossed until the sequence HTHT is obtained. What is the expected number of tosses?

解析

设 $N$ 为首次出现模式 HTHT 的抛掷次数。

用状态递推（按当前前缀匹配长度分状态）或用经典“博彩鞅 + 可选停止”方法，都可得到

\boxed{\mathbb{E}[N]=20}.

\boxed{\mathbb{E}[N]=20}.