Gambler's Ruin: Hitting Probability

Level 4●●●○○ Medium~6 min

Problem

You start with

DOLLARk

and bet

DOLLAR1

per round on a game that pays

+1

with probability

p

and

-1

with probability

q=1-p

. You stop at

DOLLAR0

(ruin) or

DOLLARN

(target). What is the probability you reach

N

before

0

? Cover both the fair (

p=1/2

) and biased cases.

Start at k; a fair walk is absorbed at 0 (ruin) or N (target).

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