Risk of Ruin: The One Number Win Rate and Risk-Reward Don't Tell You

Two traders run the identical system: same win rate, same risk-reward ratio, same setups, same edge on paper. One of them is several times more likely to blow up their account than the other. Nothing about their trading skill explains the gap — the difference is a number neither of them was treating as part of the edge at all: how much of the account each trade actually risks.

Win rate and risk-reward ratio tell you whether a system makes money over a large number of trades. They say nothing about whether the account survives long enough to find out. That second question has its own name — risk of ruin — and its own math, and the math runs almost entirely on the one input that position sizing treats as a decision you make trade by trade, not a fixed trait of the strategy.

The same edge, two very different outcomes

Both traders have a real, positive edge — a 55% win rate at 1:1 is comfortably above the 50% breakeven that ratio requires, the same calculation covered in risk-reward ratio. Edge isn't the problem for either of them. What differs is how many independent trials that edge gets to express itself before a run of bad luck can end the account outright, and that number is set entirely by position size.

Where the risk-of-ruin number actually comes from

The classic version of this calculation comes from gambler's-ruin probability theory, applied to a trader with a fixed edge betting a fixed share of capital each time. For a system with a win rate and an even-money (1:1) payoff, the edge is just win rate minus loss rate — call it A. Divide the account into risk-sized units — if you risk 1% per trade, that's 100 units standing between you and zero; at 10% per trade, it's only 10. Risk of ruin works out to:

RoR = ((1 − A) / (1 + A)) ^ units

The edge sets the base of that exponent. The number of units — which is just 1 divided by your risk-per-trade percentage — sets how many times it gets raised. That's the whole mechanism: the same base number, multiplied against itself more or fewer times depending on how big each bet is.

Cutting risk per trade in half, from 10% to 5%, doesn't cut the odds of ruin in half — it cuts them by roughly a factor of seven. Cutting it in half again, to 2.5%, doesn't just shave a bit more off — it takes the number from a real possibility to something you'd need to run for lifetimes to see. That's what an exponent does: small, linear-looking changes in the input produce enormous, nonlinear changes in the output. Risk per trade is the input doing that work here, and it's the one most traders set once out of habit and never revisit.

What the exponent actually looks like in a drawdown

Numbers on their own can be easy to wave off. Here's the same mechanism as a worked sequence: a stretch of 8 losses in a row, followed by a recovery, run through two traders using the identical sequence of wins and losses — only the risk per trade differs.

Neither trader actually goes to zero in this particular 20-trade run — an 8-loss stretch is a rough patch, not a guarantee of ruin, and that's exactly the point the risk-of-ruin number is built to capture. The 5%-risk trader is sitting at 66% of starting capital after the stretch, one more bad run of that length away from a hole that takes a much larger winning streak to climb out of. The 1%-risk trader dipped to 92% and barely noticed. Run that same 5% exposure across enough losing stretches over a trading career, and the 13.4% figure from the table above is what's waiting on the other side of enough bad luck. Run the 1% exposure across the same career, and it almost never is.

Deciding your risk per trade before you need to

The number that actually protects an account isn't a better win rate or a wider risk-reward ratio — plenty of real edges sit well above breakeven and still get wiped out by position size. It's deciding, in advance, how much of the account a single trade is allowed to cost, and holding that number through the exact stretch that makes you want to change it.

Win rate and risk-reward ratio are the numbers traders quote because they describe the edge, and the edge is the interesting part. Risk of ruin is less interesting and more decisive — it's the number that decides whether the edge gets enough trades to prove itself before the account runs out of room. Checking that the stop and target behind your ratio actually come from the chart, rather than from a number that felt comfortable, is the first half of getting this right. Setting your risk per trade before the next rough stretch, and leaving it there through it, is the second.