Risk of ruin

A method can have a real edge and still destroy the account running it. That sentence sounds like a paradox and is a calculation, and this lesson runs it.

What four numbers set the probability?

Your win rate and payoff ratio describe the method - together they make the edge, the average outcome per unit risked. Your risk fraction sets the unit's size. The ruin threshold defines what counts as dead: total loss, or more usefully the drawdown at which lesson 6's curve says the climb has become unrealistic. Fifty percent is a common working definition, and the calculator takes whichever you give it.

From those four, the mathematics of a random walk with drift produces one number: the probability that the account ever touches the threshold. Not this month, not per trade - ever, if the method's statistics hold.

Why can a winning method still ruin an account?

Because sequences do not respect averages. A method that wins 45% of trades will, often enough, lose ten or twelve in a row - and whether the account survives such a run is entirely a question of how large each unit was. The risk fraction converts the same sequence into a shallow drawdown or a breach of the threshold. Divide the ruin threshold by the fraction: that quotient, the number of consecutive-loss-equivalents the account can absorb, is the buffer the probability is computed over, and it moves in your control.

The edge matters too, and asymmetrically: at zero or negative edge, ruin is certain with enough trades, at any fraction. The calculation cannot rescue a method that loses; it prices the survival of one that wins.

What is the probability good for?

Judging a fraction before the market judges it for you. The worked example prices one configuration; move the risk fraction down and watch the probability collapse - the buffer grows, and the probability falls with a power of it. That sensitivity, far stronger than the sensitivity to win rate, is the quantitative case behind every small-fixed-fraction rule you have ever seen stated without justification.

What this means for you

Put your honest numbers into the calculator - your measured win rate and payoff once module 5 has you measuring, your lesson 1 fraction, and the drawdown you meant it when you called intolerable. The output is the probability you are implicitly accepting every time you trade the configuration. If the number surprises you, the fraction is the input to move: it is the one the probability responds to most, and the one entirely in your hands.