Risk of ruin

The probability of losing an entire bankroll, given an edge, a stake size and a starting balance. It is a real number that can be calculated, and it is almost never zero.

Ruin is driven by the ratio of stake to bankroll far more than by the size of the edge. A large edge staked recklessly has a higher chance of ruin than a small edge staked carefully, which is counter-intuitive and is the whole reason the calculation exists.

Ruin is not only zero. Most people stop long before the balance reaches nothing, at whatever drawdown breaks their nerve — so the practical threshold is psychological and is always closer than the mathematical one.

That is also the expensive part. An edge is treated as insurance against a bad run. It is not; it is a tilt in the distribution, and the distribution still contains long losing sequences at every realistic strike rate.

What to do with it. Choose the stake size from the drawdown you can actually sit through, not from the edge you believe you have.