I am recently playing a billiard game where you can play a series of exciting tournaments. In each tournament, you pay an entrance fee of, for example, \(\$500\), to potentially win a prize of, say, \(\$2500\). There are various kinds of tournaments with different entrance fees ranging from \(\$100\) up to over \(\$10000\). After hundreds of games, my winning rate stablized around \(58\%\), which is actually pretty good as it significantly beats random draws. A natural concept therefore came into my mind: Is there an optimal strategy?