Risk of Ruin

What risk of ruin is

An account does not just earn the average. It travels through a path of wins and losses, and a long enough run of losses can end the account before the average has a chance to show. Risk of ruin is the chance that happens. "Ruin" is whatever level you cannot continue from: zero, a margin level, a prop-firm limit or a loss you will not accept.

The answer is not about the average trade. A strategy can have a positive expected value and still have a large risk of ruin if it is bet too big.

The simple model and its formula

The cleanest case is the one-unit game. Every bet wins one unit with probability p or loses one unit with probability q = 1 - p. You start with N units and keep betting forever. The probability of ever reaching zero is:

This is exact for that game, and it only applies under these conditions: each bet is the same size, each pays 1 to 1, the bets are independent, p is fixed and known, and there is no upper limit. It is a model, not a description of a real account. Real trades have different sizes, payoffs that are not 1 to 1, costs and dependence. Use it for the shape of the answer, not as a prediction.

If p is less than or equal to one half, the formula gives a ratio q/p of 1 or more, and ruin is certain given enough time. A coin flip with no edge ends in ruin, if you keep going.

A computed table

Here is the formula worked out for three win probabilities and three account sizes in units. Calculated by us on 27 Oct 2026, exact for the simple one-unit game.

Look at two things. First, going from p = 0.51 to p = 0.55 helps, and the gain is large. Second, the number of units matters even more. At p = 0.52, moving from 10 units to 50 units takes the risk from 44.9% to 1.8%. Doubling the account in units, or equivalently halving the size of each bet, squares the risk (0.4491 becomes 0.2017). That is why bet size matters more than win rate.

Fixed fractional sizing

Instead of betting a fixed dollar amount, a trader may risk a fixed fraction of the account on each trade, such as 1 percent. The account then holds roughly 100 "units" of risk, where a unit is one trade's risk. The simple model gives a rough picture: with p = 0.52 and 100 units, 0.03%. With 10 percent per trade there are only 10 units, and it is 44.9%.

It is only a rough picture. A fraction of the account shrinks after losses, so the account does not reach exactly zero, and the "ruin level" has to be defined, such as a 50 percent loss. The direction holds: smaller bets mean more units, and more units make ruin fall steeply. See the risk of ruin calculator to try your own numbers.

Why martingale ends in ruin

A martingale ladder is a different game. After each loss it doubles, and one win ends the cycle with a small profit. Suppose the ladder has k steps and the account can afford exactly k. A cycle fails only if all k trades lose, which for a fair coin has probability 0.5^k. Over c cycles the chance that at least one of them fails is:

This is exact for independent 50-50 trades, a ladder of k steps and a failed cycle that costs the whole account. Calculated by us on 27 Oct 2026.

A 7-step ladder fails once in 128 cycles, which sounds remote. Over 100 cycles the chance is 54.4%, and over 500 cycles it is 98.0%. Even a 10-step ladder, which fails once in 1,024 cycles, reaches 38.6% after 500. As the number of cycles grows, the chance climbs toward 1. The small chance per cycle is not a safety margin, it is a fixed rate that accumulates. That is the sense in which martingale makes ruin close to certain if it is run long enough. A bot that wins small amounts reliably is also a bot that is walking toward the cycle that ends the account. Real markets are not fair coins, and a real edge or a real bias can change the numbers, but the structure does not change.

How it hits other bots

• Grid bots hold more positions as price moves away from the middle. Their ruin comes from a sustained trend, and the number of units in the account decides how far a trend can go before the margin ends.
• DCA bots face ruin through a falling price with no recovery. Average cost drops, but capital runs out, and an instrument can fall to zero.
• EAs that raise lot size after losses behave like a martingale in part, and their ruin risk is harder to see in a backtest. Look at the biggest position they can open.

How to check before running a bot

• Find the largest loss one trade or one ladder can cause, as a share of the account. That is your unit.
• Count how many of those units the account holds, and put the number into the formula along with an honest estimate of the edge.
• Use a pessimistic p. A small error in p changes the answer a lot, as the p = 0.51 row shows.
• Run a Monte Carlo simulation on your own trade list, which handles uneven wins and losses better than the one-unit formula.
• For ladders, read martingale and check the number of steps the account can afford.

What it does not tell you

The formula assumes the win probability is known. It never is. It assumes bets are independent, and markets can cluster losses. It assumes no costs, and costs lower the effective p. A low risk of ruin number does not remove the possibility, and it says nothing about drawdown short of ruin, which can still be more than you can accept.