Understanding Risk of Ruin

## The Ultimate Bankroll Management Question Risk of ruin (RoR) is the probability that your bankroll reaches zero before your edge can compound into profit. It is the single most important number in bankroll management — and most bettors have never calculated it. ## The Formula For a simplified binary model (win/loss at fixed odds): RoR = ((1 - edge/variance) / (1 + edge/variance)) ^ (Bankroll / Stake) Where edge = expected value per unit staked. ## An Intuitive Understanding Risk of ruin depends on three variables: 1. **Edge:** Higher edge → lower RoR 2. **Stake size:** Larger stakes relative to bankroll → higher RoR 3. **Bankroll size:** Larger bankroll → lower RoR If you have positive edge and bet 1% of bankroll per bet, ruin is nearly impossible. If you bet 10% of bankroll per bet, ruin is likely even with moderate edge. ## Calculating RoR for Your Operation At edge = 3%, stake = 1% of bankroll, and conservative variance assumption: RoR ≈ e^(-2 × 0.03 × 100) = e^(-6) ≈ 0.25% At stake = 3% of bankroll (same edge): RoR ≈ e^(-2 × 0.03 × 33) = e^(-2) ≈ 13.5% Same edge, 3× larger relative stake: RoR increases from 0.25% to 13.5%. ## The Professional Threshold A professional operation targets RoR below 1%. This means: - At 3% edge: stake at most 1.5% of bankroll - At 2% edge: stake at most 1% of bankroll - At 5% edge: stake at most 2.5% of bankroll Below these thresholds, your edge will almost certainly compound before ruin. Above them, significant ruin probability persists.