The same edge, wildly different outcomes, from bet size alone
Break-even needs 50.0%
1 means wins equal losses
Chance of losing 50% of the account
0.66%
Expectancy is +0.100R per trade, so the edge is real — but 25 consecutive losses still reach that drawdown, and a losing run that long happens on its own with probability <0.01%.
Win rate and reward ratio are held at your inputs. Only the risk per trade changes.
| Risk per trade | Losses it survives | Chance of ruin |
|---|---|---|
| 0.5% | 100 | <0.01% |
| 1% | 50 | <0.01% |
| 2% | 25 | 0.66% |
| 3% | 16 | 3.5% |
| 5% | 10 | 13% |
| 10% | 5 | 37% |
| 20% | 2 | 61% |
Each trade is treated as independent with a fixed win rate and a fixed reward ratio, and the risk is a constant fraction of the account. The result is the classic gambler's ruin probability, solved in closed form rather than simulated — for a reward ratio of 1 it reduces exactly to (q/p) raised to the number of losses you can absorb.
Real trading violates the independence assumption. Losses cluster, because the conditions that produced one usually persist for a while, and clustering makes ruin more likely than this figure suggests. Win rates also drift, and the figure you enter here is typically an estimate from too few trades.
Without a positive expectancy the calculation degenerates: ruin becomes certain given enough trades, and reducing position size only delays it. That is worth stating plainly because the usual advice — trade smaller — treats a size problem as if it could fix an edge problem.
Risk of ruin is the probability that a run of losses takes an account down to some level you would not continue from. It depends on three things: how often you win, how much a win pays relative to a loss, and what fraction of the account each trade risks. The first two get all the attention. The third moves the answer far more.
The comparison table holds the edge fixed and varies only the bet size, and the chance of ruin changes by orders of magnitude across it. That is why the same strategy can be perfectly survivable for one trader and fatal for another, and why arguments about entries are usually arguments about the least important input.
One limit is worth stating clearly. If expectancy is negative — if the win rate is below the break-even level that the reward ratio demands — then ruin is certain given enough trades, and betting smaller only postpones it. The common advice to reduce size treats a size problem as though it could fix an edge problem, and it cannot.
⚠️ Not investment advice. The model assumes independent trades with a fixed win rate and reward ratio; real losses cluster, which makes ruin more likely than shown. Win rates entered from memory or from a short record are usually too optimistic. All decisions and risks are your own.
The probability that a run of losses reduces an account to a level you would not continue trading from. It depends on the win rate, the reward-to-risk ratio, and the fraction of the account risked on each trade.
The risk per trade, by a wide margin. Holding the win rate and reward ratio fixed and varying only the bet size moves the probability of ruin by orders of magnitude. The same strategy can be survivable for one trader and fatal for another purely through position size.
No. With negative expectancy ruin is certain given enough trades, and smaller bets only postpone it. Advice to reduce size treats a sizing problem as though it could fix an edge problem, which it cannot.
In closed form rather than by simulation. The ruin probability satisfies a recursion whose solution is a geometric series, so it reduces to a root of p·z^(R+1) − z + q = 0 raised to the number of losses the account can absorb. For a reward ratio of 1 this is exactly the classic (q/p)^n result.
Because a win rate only means something relative to the reward ratio. At 2:1 you need to be right a third of the time to break even; at 1:2 you need two thirds. Without that comparison a win rate figure is unreadable.
It assumes trades are independent. In practice losses cluster, because whatever produced one usually persists for a while, and clustering makes ruin more likely than the figure shown. Win rates also drift, and the one you enter is usually estimated from too few trades.