Risk of Ruin: What Busts Accounts

Risk of ruin is the chance that your equity eventually falls to a level you define as ruin. It moves with a few inputs. It rises as you risk a larger fraction per trade, because bigger bets reach ruin faster. It falls as your edge and win rate improve, because you lose less often and less far. And it falls as you hold more units of capital between your starting point and ruin, because there is more cushion to absorb a bad run. Of these, the fraction risked per trade is the one you control most directly and the one that moves the number most.

It is a common and dangerous belief that a profitable strategy cannot blow up. It can. A positive edge tilts the long-run average in your favour, but it does not stop a bad run from reaching ruin first if each bet is large. Expectancy describes where you end up after many trades; risk of ruin describes whether you survive the path to get there. The two are different questions. You can have a genuinely positive edge and still carry a real probability of busting, purely because the bets are sized too big to outlast a normal losing sequence.

A simple model makes the bet-size effect concrete. In an even-money game where you risk one unit to win one with win probability p above one half, the probability of eventually losing a bankroll of U units is the ratio of the loss probability to the win probability, raised to the power U. With a fifty-five percent win rate and twenty units of bankroll, meaning each bet risks one twentieth, this is about two percent. Cut the bankroll to ten units, meaning each bet risks one tenth, and it jumps to about thirteen percent. Real trading has variable win and loss sizes, so this exact formula does not apply, but the lesson it shows, that halving your bet size can cut ruin risk many times over, holds far more generally.