What is the probability of ruin?

The probability of ruin is the chance that your bankroll reaches zero before you reach your profit target. It depends on your edge, stake size relative to bankroll, and target. Larger stakes increase ruin probability dramatically.

How does stake size affect ruin probability?

Ruin probability is extremely sensitive to stake size. Staking 5% of bankroll per bet has a vastly higher ruin probability than staking 1%. Our simulator lets you compare these scenarios side by side.

What is the Gambler's Ruin formula?

For even-money bets, ruin probability = ((q/p)^N − (q/p)^B) ÷ ((q/p)^N − 1), where p is win probability, q is loss probability, B is current bankroll in units, and N is the target bankroll in units.

Can Monte Carlo validation differ from the formula?

Yes, slightly. The analytical formula assumes simple binary bets. Monte Carlo simulation handles any odds distribution and provides a more realistic estimate for bets at non-even money odds.

What ruin probability is acceptable?

Professional bettors generally target a ruin probability below 5%. For recreational bettors, below 20% is often considered acceptable. Any strategy with over 50% ruin probability should be reconsidered.

Ruin Probability Calculator

Win Probability (%)

Decimal Odds

Bankroll (units)

Stake (units)

Target Profit (units)

Simulations

Ruin Probability vs Stake Size

How bust probability changes as you increase stake from 1% to 10% of bankroll — the curve is dramatic

Sample Bankroll Paths

20 trajectories: green = reached target, red = went bust

Time to Target / Ruin Distribution

How many bets it takes to reach target or go bust

How to Use This Calculator

Enter Your Edge

Set your win probability and odds. At 55% and 1.90, you have a small but genuine edge.

Set Bankroll & Target

Define your bankroll in units and the profit target you want to reach.

Analyse Risk

Compare Monte Carlo results with the exact Gambler's Ruin formula. Find the maximum safe stake.

The Math Behind It

The Gambler's Ruin Formula

For a simple win/loss bet where you win 1 unit or lose 1 unit, the exact probability of ruin before reaching your target is given by the classic formula:

P(ruin) = ((q/p)^B - (q/p)^(B+T)) / (1 - (q/p)^(B+T))

Where p = win probability, q = 1-p, B = bankroll in units, and T = target profit in units. When p = q (no edge), the formula simplifies to P(ruin) = T / (B + T).

This formula assumes each bet is ±1 unit. For bets with different payoffs (like 1.90 odds where you win 0.9 units or lose 1 unit), the formula uses an adjusted q/p ratio based on the equivalent random walk.

Why Stake Size Is Everything

Even with a genuine edge, staking too high dramatically increases ruin probability. With a 55% edge at 1.90 odds and a 100-unit bankroll:

1-unit stakes: ~2-5% ruin probability
3-unit stakes: ~15-25% ruin probability
5-unit stakes: ~35-50% ruin probability
10-unit stakes: ~70-85% ruin probability

The relationship is exponential, not linear. Doubling your stake far more than doubles your ruin risk.

See Also: Manage your risk with the Kelly Criterion Calculator for optimal stake sizing. See how your chosen staking strategy performs over hundreds of bets in the Staking Strategy Comparison.

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Frequently Asked Questions

What's a safe stake size for my edge?

A common rule of thumb is to keep your ruin probability below 5%. For most edges (2-10%), this means staking between 1-3% of your bankroll. The Kelly Criterion provides the mathematically optimal answer, but many professionals use half-Kelly for added safety.

How reliable is the Gambler's Ruin formula?

The formula is exact for simple ±1 unit bets. For more complex payoff structures (different odds), we use an adjusted version that closely approximates the true probability. The Monte Carlo simulation validates the analytical result — you should see them agree closely.

Does the formula account for different odds?

The standard formula assumes symmetric ±1 bets. For bets where the win and loss amounts differ (e.g., 1.90 odds = win 0.90, lose 1.00), we adjust the ratio. The Monte Carlo simulation handles any payoff structure exactly.

Why does my ruin probability seem high even with an edge?

Small edges require large bankrolls relative to stake size. A 5% edge means you win 52.5% and lose 47.5% of the time. Over small samples, the losing scenarios can dominate. The cure is smaller stakes relative to bankroll — not a bigger edge.

Should I set a profit target or just keep betting?

In theory, with a genuine edge, you should keep betting forever (the expected value grows over time). The target in this calculator is useful for understanding risk over a defined period. In practice, having milestone targets helps with bankroll management and discipline.