Two players A and B, toss a fair coin. A, who starts the game. stakes a penny each time he throws the coin; B also stakes a penny at each of his throws. The first player to throw heads wins and gathers all the stakes. Find the probability that A wins the game. Explain why A, although he wins more frequently, loses money. Calculate his expected loss on 100 games
Hint: for |z| < 1, 1 + 2z + 3z^2 +4z^3 + ......= (1-z)^-2
I am able to get the probability of A winning is 2/3 by using sum to infinity formula. But now i am stucked at the remaining part of the question. Help please. Oh and do note that 100 games is not 100 consecutive throws. A game only ends when a player throws head. And then they start all over again, for 100 times
Hint: for |z| < 1, 1 + 2z + 3z^2 +4z^3 + ......= (1-z)^-2
I am able to get the probability of A winning is 2/3 by using sum to infinity formula. But now i am stucked at the remaining part of the question. Help please. Oh and do note that 100 games is not 100 consecutive throws. A game only ends when a player throws head. And then they start all over again, for 100 times
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