Definition
Risk of ruin is the probability that a bettor’s bankroll falls to zero, or to a chosen stop-loss point, before the betting edge has enough time to show up. It depends on bankroll size, bet size, win probability, and payout odds.
For an even-money bet with win probability p, loss probability q = 1 - p, bankroll measured in betting units B, and p > q, the classic approximation is:
Risk of Ruin = (q / p)^B
For uneven odds, simulation or a bankroll model is usually needed because wins and losses do not move the bankroll by the same amount.
Worked Example
A bettor has a $1,000 bankroll and bets $50 per wager, so the bankroll is 20 units. They bet a -110 line where risking $110 wins $100. A $50 stake wins $45.45 profit if the bet wins.
If the bettor’s true win probability is 53%, their edge is:
0.53 × $45.45 - 0.47 × $50 = $0.59
That is a positive expected value of $0.59 per $50 bet, but the edge is small. A losing streak of 20 full-stake losses would wipe out the bankroll before the edge can compound.
Why It Matters
Risk of ruin helps a bettor size wagers so a real edge is not erased by normal variance. It is most useful when comparing flat betting, fractional Kelly staking, and bankroll limits.
