How reactive gambling can backfire: ruin probability is increasing in $p$, Hölder continuous in initial fortune

Aditya Guha Roy, Yuval Peres, Shuo Qin +1

A gambler with an initial fortune $x$ starts by betting a dollar, then doubles the bet after every win and halves the bet after every loss. Let $p\in (0,1)$ be the probability of w…