204.Twenty Up or Ten Down
★★★random walksJane Street
A counter starts at 0. A fair coin is flipped repeatedly, adding 1 on heads and subtracting 1 on tails. Play stops when the counter reaches +20 or -10. What is the probability that it reaches +20 first?
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In a fair walk the counter is a martingale, so its expected final value equals its starting value.
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