[問題] coin tossing

[cjchen (cjchen)]

 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.

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 219.75.60.122
推 Lpspace:with probability 1, it is a simple random walk
→ Lpspace:every state space (integer) is recurrent
→ Lpspace:you should study stochastic process or probability
推 louis0407:1/2+1/2*1/2+1/2*1/2*1/2....loop=1/2/(1-1/2)=1=ans.