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coin tossing - 金融分析師

Linda avatarLinda · 2011-02-01

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Assume a coin is fair and your initial position is flat.
You gain $1 on a head and lose $1 on a tail.
You quit the game once you position is +$1.

Then what is the probability that the game terminates?

I tried to draw a binomial tree and realized that
the answer should be greater than 2/3,
but couldn't find out an analytical solution.

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All Comments

John avatarJohn2011-02-03
with probability 1, it is a simple random walk
Selena avatarSelena2011-02-07
every state space (integer) is recurrent
you should study stochastic process or probability
Jack avatarJack2011-02-08
1/2+1/2*1/2+1/2*1/2*1/2....loop=1/2/(1-1/2)=1=ans.