$\textbf{Mafia}$
You are captured by a mafia. He puts two bullets in adjacent chambers of a standard $6$-chamber revolver. Then he points the gun at your head, and pulls the trigger. You survives. He thinks you may be a lucky man and thus promises to free you if you can survive the second shot. Meanwhile, he also gives you the option to re-spin the revolver before he pulls the trigger again. Should you accept his offer?
$\textbf{Answer}$
No.
$\textbf{Analysis}$
Let's first list all the possibilities of two bullets in adjacent chambers whereas the first position indicates the next firing chamber: $$\begin{array}{rcccccc}1\rightarrow&B&B&\_&\_&\_&\_\\2\rightarrow&\_&B&B&\_&\_&\_\\3\rightarrow&\_&\_&B&B&\_&\_\\4\rightarrow&\_&\_&\_&B&B&\_\\5\rightarrow&\_&\_&\_&\_&B&B\\6\rightarrow&B&\_&\_&\_&\_&B\end{array}$$
Among these six cases, two will kill the person in the next firing: $1$ and $6$. Therefore, the probability of being killed after a re-spin is $\frac{1}{3}$.
Now, given the first firing is empty, these two cases are eliminated. Therefore, the initial status must be one of four cases: $2$ to $5$. Among them, only one case will kill in the second round: $2$, which gives a probability of $\frac{1}{4}$.
Therefore, continue without re-spinning will result in a smaller probability of being killed.