Question 1
Suppose that there are initially eight townspeople and one goon. One of the eight townspeople is named Jester. If Jester is sent to jail during some morning, then the game ends immediately in his sole victory. (However, the Jester does not win if he is sent to jail during some night.)
Find the probability that only the Jester wins.
Official shared rules: Start in the morning; $t,g$ count townspeople/goons. Morning: uniformly jail one survivor; stop if $g=0$ or $t=0$. Otherwise evening: uniformly jail one townsperson; stop if $g\ge t$.
Official preamble, page 1: https://hmmt-archive.s3.amazonaws.com/tournaments/2014/nov/thm/problems.pdf
Find the probability that only the Jester wins.
Official shared rules: Start in the morning; $t,g$ count townspeople/goons. Morning: uniformly jail one survivor; stop if $g=0$ or $t=0$. Otherwise evening: uniformly jail one townsperson; stop if $g\ge t$.
Official preamble, page 1: https://hmmt-archive.s3.amazonaws.com/tournaments/2014/nov/thm/problems.pdf