Gambler’s Ruin

Why the house always wins

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Fair game with boundaries 0 and $N$, starting at $k$: $P(\text{reach } N) = k/N$.
• Even fair games usually ruin players aiming for big targets.
• With an unfavourable edge, ruin is virtually certain.

Steps

1. Walking to a boundary
2. Double or bust?
3. A slightly unfair coin
4. Forty-nine percent
5. How long does it last?
6. Against the casino