![]() The optimal strategy for $A$ is to play once and try to double, resulting in a winning probability $\approx \frac14$.Īdmittedly, the optimality of this strategy for $A$ is not rigorously shown and especially there may be some gains from exploiting the detailed shape of $B$'s winnign probability function, but I am pretty sure this is a not-too-bad approximation. As seen for example here, the probability of $B$ reaching this target is maximized by this strategy and depends only on the initial proportion $\alpha:=\frac$, so the total probability of $A$ winning is approximatelyĪnd this is maximized precisely when $T=200$. That is, aim for a target sum of $a \epsilon$ and bet what is needed to reach this goal exactly or bet all, whatever is less. ![]() Flip A Coin is easy to use, just put your phone in your pocket and start flipping You can even go live with others by joining a chat room. This app is great for people who like to play games like flipping coins, and it’s also great for people who like to give others a chance to win. Once $A$ has finished playing, ending with an amount $a$, the strategy for $B$ is simple and well-known: Use bold play. Flip A Coin is a new app that allows you to flip virtual coins. What would be the optimal strategy for $A$? Obviously the optimal strategy for player $B$ involves playing until $B$ either goes bankrupt or has more money than $A$ (although it's not obvious what bet sizes to use). It allows you to virtually flip a coin as if you’re flipping a real coin.
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