How many buy-ins do I need?

A separate growth-based comparison

Compare live cash stakes with quarter, half and full Kelly →. That tool models proportional rebalancing with its own assumptions; this bankroll model keeps a fixed stake and a lifetime ruin target.

What this estimate assumes

B = −σ² × ln(r) / (2 × μ)

B is bankroll, μ is expected net profit per block, σ is the standard deviation of one block, and r is lifetime ruin probability. Win rate and standard deviation must use the same block: an hour, 100 hands, or one tournament.

This is a Brownian-motion approximation: fixed stakes, independent results, a constant edge and variance, no withdrawals or top-ups, and play continuing indefinitely. “Ruin” means hitting zero. Actual poker has discrete bets and, especially in tournaments, large jumps; you can be unable to afford a buy-in before reaching zero.

It does not account for a changing game, uncertain win rates, living costs or moving down in stakes. A positive win rate must be an estimate of your true edge, not just a recent upswing. With a zero or negative edge, any finite bankroll eventually runs out in this model.

Source: Chin & Ingenoso, Risk Adjustment for Poker Players, §1 (diffusion model). The bankroll tool algebraically inverts that formula, then rounds up to whole buy-ins.

Starting points, with their evidence

There is no universal “normal game” preset. Stack depth, table size, rake, player style and straddles change variance. All values below describe the SD of a 100-hand block, in big blinds. A source’s measured value is not a measurement of your play.

Live NLHE cash

ASSUMED: 140; published benchmark range 120–160 BB/100. Not a measured population estimate.

Live PLO cash

ASSUMED: 175; published benchmark range 150–200+ BB/100. Deeper play can exceed it.

Online NLHE 6-max

ASSUMED: 90; published benchmark range 75–120 BB/100. These three benchmark ranges come from PrimeDope’s variance guide, not an independently audited sample.

Online GG NL50 6-max

MEASURED BY SOURCE: 78, with a middle-half range of 71–85 BB/100. Pokalab’s own reported data: regulars with 20,000+ hands, 4–6 players, no ante, after rake. GoodRun has not independently audited those hand records. Do not generalize it to live poker or every online pool.

Online PLO 6-max

ASSUMED: 140; 120–160 BB/100 is the modeled range used in SolvePoker’s simulations. Simulated inputs are not measured player SDs.

Single-player live estimates are not presets: one published estimate was revised after regrouping sessions. Neither establishes a population benchmark. Unequal-length session rates need proper normalization; taking their ordinary SD is not a common 100-hand SD estimate.

Sources checked 31 October 2026. Editing a preset changes its label to custom. Personal measurements are preferable; these inputs do not compute SD from raw hand histories.

Live hours ↔ online hands

win rate/hour = win rate/100 × hands per hour / 100

SD/hour = SD/100 × √(hands per hour / 100)

SD scales with the square root of volume; win rate scales directly. At 30 hands/hour, an assumed 140 BB/100 corresponds to about 76.68 BB for a one-hour block. Changing hands/hour estimates volume, not the table’s playing style.