🎲 Gambler's Ruin

Win probability p 0.48 Starting capital W₀ 50 Target fortune T 100 Simulation paths 50

—

Ruin probability

—

Analytic P(ruin)—

MC P(ruin)—

E[duration]—

E[win] if survive—

Kelly fraction f*

—

Optimal bet per round

If p < 0.5, the house has edge. Even starting with half the target, ruin is near-certain over enough time.

Kelly criterion: f* = 2p − 1 — bet this fraction of wealth each round to maximise log-wealth growth.

Ruined Reached target In progress