Core terms
Risk of ruin
The probability that an account reaches a chosen loss threshold, such as a 30% drawdown from its peak, within a set number of trades, given an outcome distribution and the risk taken per trade.
Risk of ruin has four inputs: the outcome distribution per trade in R after costs, risk per trade, the ruin threshold and the horizon. "Ruin" does not need to mean zero; in trading it is usually a drawdown chosen in advance, the point at which a trader stops or an account rule applies.
A positive expectancy does not remove it. In a simulation in the Foundations course (1,000 runs of 200 trades from an assumed +0.25R-per-trade distribution, ruin at a 30% drawdown; Illustrative), 0.1% of runs reached the threshold at 1% risk per trade and 39.7% at 3%. In the textbook gambler's-ruin model (Feller, 1968), halving the risk per trade doubles the number of losses needed to reach the threshold, and the probability falls roughly with the square rather than by half.
What traders should verify
State all four inputs next to any risk-of-ruin figure. Estimate it by resampling your own logged trades in R at several risk levels, and read the result as optimistic, because a log cannot contain losses that have not happened yet.
Do not conflate
Trader usage; there is no official definition. The figure depends on the threshold and horizon chosen and on an assumed distribution; simulations usually assume independent trades and unchanged behaviour after losses, which real trading often violates.
Primary source
Trader usage: there is no official definition, and platforms and tools may calculate it differently.