The formula
For a positive-edge game, the standard exponential approximation is:
RoR = e^(-2 × edge × bankroll / (σ² × bet))
Where edge is your fractional edge per bet, bankroll is your starting roll, σ is per-unit standard deviation, and bet is unit bet size. The formula assumes constant bet size and constant edge — a simplification that holds well enough for tournament-style or fixed-spread play.
What RoR numbers actually mean
- RoR = 1% — Industry standard for professional play. Means you have a 99% chance of doubling your bankroll before busting.
- RoR = 5% — Aggressive. Acceptable for short-term goals like a single trip.
- RoR = 13.5% — Full Kelly. Maximizes growth but risks total ruin once in seven careers.
- RoR = 50% — You're roughly betting your entire bankroll. Don't.
Bankroll multiples — the rule of thumb
A common shortcut: aim for ≥ 1000× the unit bet for 1% RoR at typical AP edges. With a $5 unit bet, that's a $5,000 bankroll. Half-Kelly play targets the same 13.5% RoR as full-Kelly per unit but at a different bet sizing. The calculator above lets you check your exact number rather than relying on the rule of thumb.
Why the formula breaks for negative edge
If you don't have an edge, the math says your RoR approaches 100% — given enough time you will bust. The formula above explicitly returns 1 for non-positive edge. If you're playing a -EV game, your only bankroll question is how long until you bust, not whether.