Risk of ruin calculator
Partial ruin is the real constraint, because it is where people quit. This prices the drawdown you might actually take, under both stakings and both horizons, and solves the fraction that keeps it tolerable.
Worked example — Chance of a 50% drawdown within 500 bets: 11.5%. Half-Kelly: 55.00000000000001% win probability at 2.00, 5% of bankroll a bet, exceeds your 5% tolerance by 6.5 pts
Half-Kelly at even money: The page’s current defaults and worked example
Advanced options 3
At 5% a bet you are at 0.50x Kelly, which is 10.00% for this edge. The bankroll never technically ruins under fractional staking, and yet losing half of it at some point is a 12.3% proposition. To hold that below 5%, size at 3.79%.
In plain English: the same average profit can be safe or dangerous depending on how wide each win and loss swings. The model writes average log growth as m = E[ln(1 + fX)] and per-bet variance as s2. It is conservative over short horizons because a smooth theoretical path can touch a level that a bankroll moving in whole bets steps over. The probability depends on 2m ÷ s2, not on edge alone.
Most of the lifetime drawdown risk arrives early, while the bankroll is closest to the level and the drift has not had time to work. That is the argument for sizing down at the start of a strategy rather than after the first bad run.
| Staking | Event | Within 500 bets | Ever | Method |
|---|---|---|---|---|
| Fixed fraction, 5% | fall to $12,500 | 11.55% | 12.27% | first passage on log wealth |
| Fixed fraction, 5% | lose everything | 0.00% | 0.00% | unreachable by construction |
| Fixed unit, 20 units | fall 10 units to $12,500 | not defined | 13.23% | gambler's ruin, exact |
| Fixed unit, 20 units | lose everything | not defined | 1.78% | gambler's ruin, exact |
Read the last row first, then the first. The classic fixed-unit ruin number, 1.78%, is the figure most risk-of-ruin calculators return, and it is the answer to a question you are not asking if you size as a percentage: it describes betting a constant dollar amount until the account is literally empty, with a stop-at-double rule. At even money the classic formula is exact. The number that describes what you would actually experience is the first row.
How the same account, under both stakings
Half-Kelly at even money, 55% win probability, 5% of bankroll a bet, over 500 bets. The same account, computed four ways.
| Staking | Event | Within 500 bets | Ever | Method |
|---|---|---|---|---|
| Fixed fraction, 5% | fall to $12,500 | 11.55% | 12.27% | first passage on log wealth |
| Fixed fraction, 5% | lose everything | 0.00% | 0.00% | unreachable by construction |
| Fixed unit, 20 units | fall 10 units | not defined | 13.23% | gambler's ruin, exact |
| Fixed unit, 20 units | lose everything | not defined | 1.78% | gambler's ruin, exact |
Why is my risk of ruin 0% under fractional staking?
Because fixed-fractional staking bets a percentage of what remains, so the balance is asymptotic to zero and never technically reaches it: the classic ruin number, betting a constant dollar amount until the account is literally empty, is exactly 0% under this staking. That is not the good news it sounds like. A stated drawdown level, such as the 50% event above, still carries real risk: 12.27% eventually, 11.55% within 500 bets, at the defaults printed from the calculator above.
Why does this disagree with the calculator that gave me a different number?
Most risk-of-ruin calculators return the classic fixed-unit, bet-to-broke number: at even money that is exactly 1.78% at the defaults above, and this page also computes it, visible in the table, for comparison. At prices other than even money the plus-or-minus-one-unit formula it relies on does not apply. At -110 (decimal 1.91), for example, this page solves the Lundberg exponent instead, the theta solving E[exp(-theta X)] = 1, giving a fixed-unit-to-zero probability of 25.87% at a 53% win probability, 2% a bet. The Lundberg exponent is the correct generalization at non-even prices, and it reduces back to the classic gambler's ruin answer whenever the price is even, as shown above.
How the drawdown risk builds up over time
Most of the lifetime risk of the 50% drawdown, at the defaults, arrives early, while the bankroll is closest to the level and the drift has had no time to work.
| Bets elapsed | Chance of the drawdown by then | Share of the eventual risk |
|---|---|---|
| 50 | 1.54% | 13% |
| 100 | 4.80% | 39% |
| 250 | 9.54% | 78% |
| 500 | 11.55% | 94% |
| 1,250 | 12.23% | 100% |
| 2,500 | 12.26% | 100% |
| 5,000 | 12.27% | 100% |
What this does not model
- The diffusion result treats log wealth as continuous, which is accurate over hundreds of bets and conservative over a handful: a continuous path touches a level that a bankroll moving in whole bets can step over, so the short-horizon figure reads high.
- Bets are assumed independent, identically priced, and settled one at a time: simultaneous positions raise the effective fraction and therefore the risk, sometimes by a lot.
- The edge is assumed known and constant; it is worth running the numbers again at the pessimistic end of the interval your record supports, which the significance calculator will give you.
- No fees, no slippage, no bet limits, and no behaviour: the model has no opinion about what you do after the drawdown, which is the variable that usually decides the outcome.
Set the drawdown level at the loss that would genuinely make you quit, not at zero, set the tolerance at the odds you would accept of that happening, and let the tool tell you the stake. Then check the run of losses that gets you there on the losing streak calculator, and translate the fraction into an actual order with the position size calculator.
The next question after this one
Kelly criterion calculatorCalculatorRuin risk is a function of stake size. This is the size the edge supports, and the fraction of it you can afford to use.Open nextOther questions
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What Pro adds here
Correlated-book drawdown modelling, path simulation against an imported ledger, and live drawdown alerts are Pro features. The launch list sends one email at launch.