Your game & roll
Your assumed edge. Remember it’s itself a range — check it on the confidence calculator.
~100 is typical for online 6-max No-Limit Hold’em.
How many 100-big-blind buy-ins you have for this stake.
Your risk of ruin
Chance of losing this entire bankroll
22.3%
before your long-term edge plays out — assuming you never move down.
- For under 5% risk, hold60 buy-ins
- For under 1% risk, hold92 buy-ins
- Common guidance · live cash20–40 buy-ins
- Common guidance · online cash100+ buy-ins
- Common guidance · tournaments50–100 buy-ins
Dangerously thin. A perfectly ordinary downswing has a serious chance of wiping you out before your edge can show up.
How this is calculated
Using the standard diffusion (gambler’s-ruin) approximation, the long-run risk of losing a bankroll B big blinds is RoR = e^(−2 · WR · B / SD²), with win rate and standard deviation both in bb/100 and one buy-in counted as 100 big blinds. Inverting it gives the bankroll needed to keep ruin under a target probability.
Two honest caveats. First, it assumes a fixed, known win rate — but your real edge is uncertain, and the calculation breaks entirely if your true rate is below zero. Second, it assumes you never move down in stakes; in practice, dropping down when your roll shrinks cuts your real risk far below this figure. Treat it as the pessimistic, never- adjust ceiling.
Bankroll is a variance problem, not a balance
The size of bankroll you need has almost nothing to do with how much money you’d like to have, and almost everything to do with how wild your swings are relative to your edge. A big edge in a low-variance game needs a smaller roll; a thin edge in a swingy game needs a deep one. That’s the whole story the formula above tells — your win rate pulls the risk down, your standard deviation pushes it up.
The familiar rules of thumb — roughly 20–40 buy-ins for live cash, 100+ for online cash, and 50–100 for tournaments — are just this maths pre-chewed for typical win rates and standard deviations. They’re a fine starting point, but your numbers are your own.
This assumes your win rate is real and known. It usually isn’t — early samples flatter you, and a roll sized off an inflated win rate is thinner than it looks. Pressure-test the edge first on the win-rate confidence calculator and see the swings it implies on the variance simulator.
Know your real swings before you size your roll.
StackWise tracks your actual win rate and standard deviation as your sample grows — honest inputs for an honest bankroll. Free to start, no account.
Sources & method
Risk of ruin uses the standard diffusion approximation RoR = e^(−2·WR·B/SD²) (win rate and SD in bb/100, one buy-in = 100 bb). Bankroll guidelines and the formula from ThePokerBank, Primedope, and BlackRain79.