Maximum Drawdown and Bankroll Reserve

## Drawdown vs Ruin Risk of ruin is the ultimate disaster — bankroll → 0. But there is a lesser disaster that stops most bettors before reaching zero: a drawdown large enough to cause psychological or financial abandonment of the strategy. ## The Expected Maximum Drawdown For a given staking strategy, the expected maximum drawdown over N bets is approximately: E[Max Drawdown] ≈ 2 × σ_per_bet × √N × (some constant depending on distribution) A simplified version: E[Max Drawdown] ≈ 2 × stake × √N at 50% win probability. For 500 bets at £25 stake: E[Max Drawdown] ≈ 2 × £25 × √500 ≈ 2 × £25 × 22.4 ≈ £1,120 This means you should expect to experience a drawdown of roughly £1,120 at some point during 500 bets, even with genuine positive edge. ## The Bankroll Reserve Principle Your operational bankroll (available for betting) should be separate from a reserve that is never staked. The reserve absorbs the expected maximum drawdown while the operational bankroll continues running. Conservative split: 70% operational, 30% reserve. At total bankroll £2,000: £1,400 operational, £600 reserve. If operational bankroll drops to £800: top up to £1,400 from reserve. This prevents forced stake reduction from temporary variance. ## The Reserve Replenishment Rule After topping up from reserve, do not restore the reserve until the operational bankroll has recovered to its previous peak. The reserve should only be consumed by variance, not replenished through further downside. ## The Reserve as Psychological Insurance Knowing you have a reserve eliminates one category of fear during downswings — the fear that this run will bankrupt you. This psychological benefit makes the reserve worthwhile even if you never need to use it.