In coinball each of the two players take turns flipping a coin and calling rush

Question

In coinball each of the two players take turns flipping a coin and calling rush or pass. If you win the toss then you get 1 point if you called a rush and 2 points if you called a pass. Similarly if you lose a coin toss your opponent get the aappropriate points ( if if you called rush, 2...). Who ever has the most points at the end wins. Suppose you and an opponent say, Joe Montana, are going to play 12 downs. Find the probability of winning if you both run every time. Find the probability of winning if Joe rushes every down and you pass every down. If you know Joe is going to rush everytime what would be your optimum startegy i.e. gives you the highest probability of winning.

Explanation / Answer

The probability of winning if you both run every time. Find the probability of winning if Joe rushes every down and you pass every down =2/12=1/6

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