Three fields and one equation. The model implemented is the discrete gambler ruin problem, the only one for which we found two independent academic sources with unambiguous variable definitions. Its four limits are shown above the result rather than below it, because a model limits should be read before its number.
What risk of ruin is and where the idea came from
Risk of ruin answers a different question from the one that occupies most traders. The question is not whether you win over the long run but whether you survive long enough for your edge to show. You can hold a genuine edge and still go broke before it materialises, because a passing losing streak consumed the capital. The idea originates in a classical problem in probability theory known as the gambler ruin, carried over to trading because the structure is identical: successive bets, finite capital and an absolute floor.
The two variables the formula rests on
The formula rests on two variables and no more. The first is the loss-to-win odds ratio, the probability of losing divided by the probability of winning. The second is the number of capital units, the ruin threshold divided by the risk per trade, rounded down. The probability is the first raised to the power of the second. That the units appear as an exponent rather than a coefficient is what makes their effect enormous: a small rise in risk per trade shrinks the exponent and the probability leaps.
Worked example: 55% win rate at 2% risk
Take a 55% win rate, 2% risk and a 100% ruin threshold. The probability of winning is 0.55 and of losing 0.45, so the loss-to-win ratio is 0.818182. Capital units are 100 divided by 2, that is fifty units. The probability is 0.818182 raised to the power of 50, which equals 0.0000439, displayed as 0.0044% at four decimals. A very small number, and a direct consequence of the capital absorbing fifty consecutive losses before reaching the threshold.
Worked example: raising risk alone
Now hold the win rate at 55% and move the risk alone. At 2% the probability is 0.0044%. At 5% the units become twenty and the probability 1.8072%, roughly 411 times higher. At 10% the units become ten and the probability 13.4431%, more than three thousand times the first figure. The win rate did not change at all across the three cases. The sensitivity table above shows this relation at whatever win rate you entered.
Worked example: a razor-thin edge
A razor-thin edge deserves a look. Take a 51% win rate, one percentage point above break even, with the lowest practical risk of 1%. The loss-to-win ratio is 0.960784 and capital units are one hundred. The probability is 1.8306%. So an edge of one point, combined with the most conservative sizing available, still returns a ruin probability near two percent over an unlimited horizon. A small edge needs very small risk to survive.
What happens with no edge
With no edge the picture collapses entirely. At a win rate of 50% or below the model returns a probability of one, that is 100%. This is not an opinion or a cautionary exaggeration: Karl Sigman notes at Columbia University state that if p is at most 0.50 the probability of reaching unlimited fortune is zero, and Grinstead and Snell state that if q is greater than or equal to p the probability of eventual ruin is one. The two sources are independent and agree on the formula and on the infinite-horizon behaviour.
The model’s four limits
The model has four limits, and each moves the number in a known direction. The first is that it assumes reward equal to risk; a higher reward-to-risk ratio pushes the real probability below this figure. The second is that it assumes a fixed bet size rather than a percentage of a moving balance; risking a percentage of a shrinking balance postpones ruin indefinitely in theory. The third is that it assumes independent trades; correlation between outcomes raises the probability. The fourth is an unlimited horizon; over a finite number of trades the probability is lower.
Why we do not show fields the formula ignores
Every competitor we surveyed accepts a reward-to-risk field, and this calculator does not. The reason is that we found no published closed-form formula in any acceptable source that consumes it. Every page reproducing such a formula was a tool site or a trading blog. That left two options and both are unacceptable: display a field the formula ignores, which is deceptive, or invent a formula that uses it, which directly breaks the no-invention rule. We chose to state what we do not know rather than fill the gap.
What this number does and does not do
What this number does is measure a property of the model at your inputs. What it does not do is forecast what will happen to your account or recommend a risk percentage. Read it beside the drawdown and recovery calculator rather than alone, because drawdowns are common and ruin is rare: a ruin probability of 0.0044% does not mean the road is clear, since the forty percent drawdown we saw in that calculator remains entirely possible at the very same inputs.
Frequently asked questions
Why is there no reward-to-risk field in this calculator?
Because we found no published closed-form formula that accepts one in any verifiable reference source. The only formula supported by two independent academic sources is the gambler’s ruin model, which assumes a win equals a loss in size. Every page we found offering a formula that takes a different reward ratio was a tool site or a blog, and our rule is that a formula source is never one of those. Showing a field the formula does not consume is misleading, and inventing a formula so that it does would be worse.
Why does the probability show 100% when I enter a 50% win rate?
Because both sources state it directly. The Columbia notes write that when p ≤ 0.50 the complementary probability is zero, meaning ruin is essentially certain, and Grinstead & Snell write that when q ≥ p the probability of eventual ruin is one. The condition is the unlimited horizon: with no probabilistic edge and an unbounded number of trades, capital reaches zero eventually. That is a property of the mathematical model, not a forecast of what happens to you within a year.
What is a capital unit and how is it computed?
It is the number of consecutive losses your capital absorbs before reaching the ruin threshold, computed by dividing the ruin threshold by the risk per trade and rounding down. At 2% risk with a 100% threshold that gives 50 units. This figure is the exponent in the formula, which is why changing it matters so much: raising risk from 2% to 5% drops the units from 50 to 20 and multiplies the probability by roughly 411.
Where do I get an accurate win rate?
From your actual trade record, over a large enough sample. A win rate measured over ten or twenty trades means nothing statistically, since random variation alone can produce it. The result here is extremely sensitive to this number: the difference between 51% and 55% moves the probability from about 1.83% to near zero at 1% risk. Entering an optimistic estimate returns a reassuring figure with nothing behind it.
Why does the result sometimes read ‘Below 0.0001%’ instead of a number?
Because for some inputs the probability becomes too small to display at four decimals, and printing ‘0.0000%’ would read as an absolute zero when it is not. At a 70% win rate with 2% risk the probability is roughly 4 × 10⁻¹⁹ — extremely small, but not zero. A zero probability does not exist in this model as long as the loss probability is above zero.
Does a low probability mean my approach is safe?
No. The figure is a property of the mathematical model under the inputs you gave, not a verdict on your approach. The model assumes four things that do not hold in trading: reward equal to risk, a fixed risk amount, full independence between trades, and an unlimited number of trades. Any departure from those assumptions changes the result, and this calculator recommends no risk percentage and calls no figure acceptable or safe.