Winkler的帽子猜测游戏：不平衡帽子分布的更好结果
Winkler's Hat Guessing Game: Better Results for Imbalanced Hat Distributions
摘要：
在这篇文章中，我们给出了一个显式的多项式时间可执行策略的彼得温克勒的帽子猜测游戏，给出了优越的结果，如果帽子的分布是不平衡的。Winkler的策略保证了$n$参与者的$\lfloor n/2 \rfloor$在任何情况下都能正确猜测他们的帽子颜色，而我们的策略则保证了参与者对$r$红色和$b = n - r$蓝色帽子的任何分布都能产生$\max\{r,b\} - 1.2 n^{2/3} -2$正确的猜测。我们还表明，任何策略，确保$\max\{r,b\} - f(n)$正确的猜测必然有$f(n) = Ω(\sqrt n)$。
英文摘要：
In this note, we give an explicit polynomial-time executable strategy for Peter Winkler's hat guessing game that gives superior results if the distribution of hats is imbalanced. While Winkler's strategy guarantees in any case that $\lfloor n/2 \rfloor$ of the $n$ player guess their hat color correct, our strategy ensures that the players produce $\max\{r,b\} - 1.2 n^{2/3} -2$ correct guesses for any distribution of $r$ red and $b = n - r$ blue hats. We also show that any strategy ensuring $\max\{r,b\} - f(n)$ correct guesses necessarily has $f(n) = Ω(\sqrt n)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
