Risk of ruin

Risk of ruin asks how likely it is that a sequence of results drains your balance to zero, or to a level where you can't continue. It depends on three things: your real probability of winning, the payout, and the share of your balance you stake on each trade.

Two conclusions follow from the maths:

• With a negative expected value, the risk of ruin over an unlimited number of trades approaches 100% whatever your stake size. Smaller stakes only make it take longer.
• With a genuine positive edge, risk of ruin depends heavily on stake size. Large stakes can ruin a profitable trader through an ordinary losing streak; small stakes make ruin very unlikely.

This is why “bet big to grow fast” is so dangerous. The larger the share of your balance on each trade, the fewer consecutive losses it takes to finish you. With a fixed stake of 25% of your starting balance, four losses in a row wipe it out; at 2%, the same four losses cost 8%.

You can't calculate risk of ruin precisely without knowing your true win rate, but you can always reason about it through stake size. See why martingale fails and drawdown and recovery.