Risk of ruin
Risk of ruin is the probability that a trading account falls to a level at which it can no longer continue, such as zero, a margin threshold or a prop firm drawdown floor, before reaching a goal or within a horizon. It depends on the edge, the payoff profile and, above all, on how many units of risk separate the account from that floor.
Senzoukria · Glossary · Updated September 2026
At a glance
- Classic formula
- ((1 − p) ÷ p)ᵏ for equal wins and losses, p > 0.5, k units
- Units k
- Distance to the floor ÷ risk per trade
- Key driver
- k: halving the risk per trade doubles k
- Unequal payoffs
- Require simulation rather than the closed formula
The gambler's ruin formula
In the simplest model, each trade wins or loses one unit with probabilities p and 1 − p, and the account starts k units above the floor with no upper target. When p is above one half, the probability of ever touching the floor is ((1 − p) ÷ p)ᵏ. When p is one half or less, ruin is certain in this model. The exponent is what makes size so powerful: the same edge with twice as many units of distance squares the survival odds.
| Win rate | Units to the floor | Risk of ruin |
|---|---|---|
| 55% | 10 | 13.4% |
| 55% | 20 | 1.8% |
| 52% | 20 | 20.2% |
| 60% | 10 | 1.7% |
Ruin is wherever the account stops
For a prop firm account, ruin is not zero but the drawdown floor. A 2,000 dollar allowance traded with 200 dollars of risk per trade is only 10 units deep; with a 55% win rate and equal wins and losses, the formula gives about 13% before any daily loss rule is considered. A trailing drawdown makes the floor follow the peak, so the distance in units can shrink after a winning run, which the simple formula does not capture.
Real trading adds unequal payoffs, variable size, correlated losses and costs. Closed formulas exist for some extensions, but the practical approach is simulation on the trader's own results.
In Senzoukria
The prop firm simulation estimates ruin empirically from backtest or journal trades. The panel 'Odds an account hits the max DD' replays the whole run many times with recurring account purchases and block-shuffled sessions, so that losing streaks survive the shuffle, and reports the share of accounts that die on the drawdown, counted separately from other causes. The Drawdown zones panel shows how often each level of the allowance is reached. The Gauntlet adds the distribution of maximum drawdown over 10,000 reshuffles of the trade order. These estimates reuse the observed results; they do not assume an edge the trades did not show.
Related
- Drawdown zones
- Trailing drawdown
- Monte Carlo simulation
- Monte Carlo on prop accounts
- Fixed fractional position sizing
In the same section
- Risk-reward ratio
- Rho
- Rithmic
- Revenge trading
- Rithmic plants
- Resting vs executed
- Roll implied spread
- Resting order
This page in other languages
Frequently asked questions
- How can I lower my risk of ruin without changing the strategy?
- By reducing the risk per trade relative to the distance to the floor, which increases the number of units. In the formula the effect is exponential: moving from 10 to 20 units at a 55% win rate cuts the risk of ruin from about 13% to under 2%.
- Is a zero risk of ruin possible?
- Not with a finite account and a strategy that can lose several trades in a row. The goal is to make the probability small enough for the purpose, knowing that estimates rest on a win rate and payoff that are themselves uncertain.