Gambler's Ruin Simulator
Probability of reaching a target bankroll before going broke, given a per-bet win probability and a fixed unit bet. Includes expected duration and a multi-session visualization.
Setup
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Result
Session trajectories
Each line = one session's bankroll over time. Lines that touch 0 = ruin; lines that reach the target line = success.
The formula this tool uses
The classical gambler's ruin formula gives the probability of reaching target T starting from S when each bet pays b:1 with win-probability p:
If p = 1/(b+1): P(reach T) = S / T
Otherwise: P(reach T) = (1 - r^S) / (1 - r^T), where r = (1-p)/(p·b)
Who uses it
- Educators illustrating the random walk and the surprising danger of small −EV bets over many trials.
- Quants modeling risk of ruin in trading strategies.
- Gamblers confronting the math (most find it sobering).
Limitations
- Assumes flat bets of 1 unit — no martingale or variable sizing.
- Assumes bets are independent — no hot/cold streak memory.
- Assumes infinite time. The simulation caps bets at 2000 to keep runtime fast; sessions that don't terminate in that many bets are counted as neither ruin nor target.