Insight · ★★★★☆ · ~7 min
Random Walk (Gambler's Ruin)
Fair coin, start with $k, target $N — chance you hit N before going broke?
by MindYourPuzzle
A random walk starts at position k on the integers. At each step, it moves +1 (probability p) or -1 (probability 1-p). What is the probability it reaches N before reaching 0?
Hints