Risk of Ruin (RoR)
Scientific calculation of your bankruptcy probability. Crucial for portfolio survival.
Risk of Ruin: The Mathematics of Going Broke
Risk of ruin (RoR) is the probability that your bankroll hits a defined loss threshold before your edge has time to assert itself. It is the classic gambler's ruin problem: a bettor with a finite bankroll faces a market with effectively unlimited capital, and even a bettor with a genuine positive edge can be wiped out by an ordinary losing streak if stakes are too large. Ruin is absorbing — once the bankroll is gone, no future win rate can recover it — which is why professionals treat this number as their primary safety metric, checked before any bet is placed.
This calculator uses the classical gambler's ruin approximation. With win probability p, loss probability q = 1 − p, and net decimal odds b (decimal odds minus 1), your per-bet edge is p × b − q. If that edge is positive, the probability of losing U units of bankroll before grinding upward is approximately (q / (p × b))^U. The inputs map directly: staking 2% of bankroll with a 50% target loss means U = 50 ÷ 2 = 25 units — you would need to fall 25 net stake-units behind for the losing streak to hit your ruin threshold.
Variance is why ruin happens to winning bettors. At a 55% win rate on even-money odds, a 10-bet losing streak has probability 0.45¹⁰ ≈ 0.034% on any single sequence — but across 3,000 bets you should expect to run into roughly one such streak. The standard deviation of a single even-money bet is roughly your full stake, which dwarfs the per-bet expected profit (a tenth of a stake at a 10% edge). Short-term results are therefore almost entirely noise, and it is the size of that noise relative to your bankroll — not your edge — that determines whether you survive to realize the edge.
The exponent U is your lever. Because RoR = r^U with r < 1 for any positive edge, halving your stake doubles U and squares the ruin probability: 10% becomes 1%, and 1% becomes 0.01%. This exponential relationship means small reductions in stake size buy enormous amounts of safety at a modest cost to growth. The same math governs drawdowns: strategies that never formally ruin still see deep peak-to-trough declines — under full Kelly staking the probability of at some point halving your bankroll is about 50% — so size stakes for the drawdown you can psychologically tolerate, not just the ruin you can mathematically survive.
Pair this tool with the Kelly Criterion Calculator to translate your edge into a stake fraction, then stress-test that fraction across thousands of simulated bankroll paths in the Staking Plan Simulator.
Gambler's Ruin Formula
RoR = (q / (p × b))^U p = win probability (as a decimal) q = 1 − p (loss probability) b = decimal odds − 1 (net odds) U = units to ruin = target loss % ÷ stake % per bet Edge per bet = (p × b) − q If edge ≤ 0 → ruin is certain over time (RoR = 100%)
Worked Examples
p = 55%, decimal odds 2.00 (b = 1), stake 2%, target loss 50%. Edge = 0.55 − 0.45 = +10%. U = 50 ÷ 2 = 25 units. r = 0.45 ÷ 0.55 ≈ 0.818, so RoR ≈ 0.818²⁵ ≈ 0.7% — a streak deep enough to cost half the bankroll is very unlikely before the edge compounds.
Identical bettor, but staking 5% per bet with the same 50% loss threshold: U = 10 units, so RoR ≈ 0.818¹⁰ ≈ 13.4%. Multiplying the stake by 2.5 multiplied the ruin risk roughly 20×. The edge did not change — only the exposure to variance did.
Frequently Asked Questions
What is risk of ruin in sports betting?
Risk of ruin is the probability that your bankroll falls to a defined loss threshold — often 50% or 100% — before your positive edge has time to compound. It depends on three things: your win probability, the odds you take, and the fraction of bankroll you stake per bet. It is the single best measure of whether a staking plan is survivable.
Can I go broke even with a positive edge?
Yes. A positive edge only guarantees profit over a very long series of bets. With a finite bankroll and meaningful stake sizes, an ordinary losing streak can exhaust your capital before the edge asserts itself. Overstaking a winning strategy is one of the most common ways skilled bettors bust.
How does stake size affect risk of ruin?
Exponentially. Because RoR = r^U, where U is the number of stake-units between you and your ruin threshold, halving your stake doubles U and squares the ruin probability — turning, say, 10% into 1%. This is why professionals bet 1–2% of bankroll even with strong edges: safety is cheap when bought with smaller stakes.
What is an acceptable risk of ruin?
There is no universal number, but a common rule of thumb in bankroll-management writing is to keep risk of ruin below roughly 1–5% for a 50% drawdown threshold. If the calculator shows double digits, your stake percentage is too large for your actual edge — reduce it until the number is comfortable.
How is risk of ruin related to the Kelly criterion?
The Kelly criterion maximizes long-run bankroll growth, but full Kelly tolerates brutal swings — under full Kelly staking, the probability of at some point halving your bankroll is about 50%, a known property of the strategy. Most practitioners bet half or quarter Kelly, accepting slightly slower growth for a dramatic reduction in drawdown depth and ruin risk.
Why does the calculator show 100% risk of ruin?
Because your inputs imply zero or negative edge: p × (odds − 1) is less than or equal to 1 − p. With no edge, every staking plan loses over time — ruin becomes a mathematical certainty given enough bets, regardless of how small the stakes are.