부산대학교 도서관

Summary: ``Suppose Alice has a coin with heads probability $q$ and Bob has one with heads probability $p > q$. Now each of them will toss their coin $n$ times, and Alice will win if and only if she gets more heads than Bob does. Evidently the game favors Bob, but for the given $p,q$, what is the choice of $n$ that maximizes Alice's chances of winning? We show that there is an essentially unique value $N(q,p)$ of $n$ that maximizes the probability $f(n)$ that the weak coin will win, and it satisfies $\lfloor\frac1{2(p-q)}-\frac12\rfloor\le N(q,p)\le\lceil\frac{\max(1-p,q)}{p-q}\rceil$. The analysis uses the multivariate form of Zeilberger's algorithm to find an indicator function $J_n(q,p)$ such that $J>0$ if and only if $n