coin tossing - 金融分析師

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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