Required bankroll formula
The bankroll needed to survive a session with confidence level z is: B = expected_loss + z ร ฯ_session, where ฯ_session = bet_size ร โn ร ฯ_per_bet. For 95% survival, z = 1.645. This assumes normally distributed outcomes (valid for large n by CLT).
- 95% survival for 1,000 bets at $10 bets with 1.06% HE: โ $600
- More bets = more variance = larger required bankroll
- High-variance games require much larger bankrolls for same survival probability
The 1% rule of thumb
A common rule: each bet should be at most 1% of total bankroll. This extends your session and reduces ruin probability. For $1,000 bankroll, maximum bet = $10. This is conservative โ professional players may use Kelly criterion for +EV situations.
- Kelly criterion maximizes long-run growth for +EV games only
- For house-edge games (all negative EV), Kelly says: bet 0 (do not play)
- Set a loss limit and stick to it โ a fixed loss limit prevents catastrophic sessions