Kelly Criterion Bet Sizing

Optimal bet sizing and why you're probably getting it wrong

The Kelly criterion is the mathematical answer to the question: "given a known edge, what fraction of my bankroll should I risk on this bet to maximise long-run growth?" The answer is a specific number, and almost every poker player operates at either a fraction of it (too cautious) or a multiple of it (moving toward ruin). The tool calculates both the optimal stake and the expected bankroll growth rate, which is the part most people skip.

The model

For a simple bet with win probability p, loss probability q = 1 - p, and payout odds b (net profit per unit staked if you win):

f* = (b*p - q) / b = p - q/b

where f* is the fraction of your bankroll to bet. This is the full Kelly stake. The expected log-growth rate per bet at this stake is:

G = p * ln(1 + b*f*) + q * ln(1 - f*)

Any bet larger than f* produces negative expected log-growth in the long run, meaning the bankroll is expected to eventually go to zero regardless of the edge. Betting less than f* is suboptimal for growth but safe from ruin.

Poker application

Translating poker into Kelly requires estimating your edge. For cash games, a reasonable approximation uses win rate and standard deviation. The fractional Kelly stake for a cash game session is approximately:

f* = wr / sd^2

where wr and sd are both in bb/100. For a 5bb/100 winner with sd = 100bb/100: f* = 5 / 10,000 = 0.0005, or 0.05% of your bankroll per hand. Over 100 hands (one typical session): maximum session exposure = 0.05% * 100 = 5% of your bankroll. That translates to approximately 100bb as the Kelly-correct single-table stake when your bankroll is around 2,000bb, or 20 buy-ins.

Worked example: tournament ROI

Player with 10% ROI playing $200 buy-in MTTs. Bankroll: $10,000.

For a single tournament, treat it as a bet with b = 1.10 (expected return $1.10 per $1.00 invested), p = ITM rate (say 15% for a typical field), and adjust for the payout structure. The simplified Kelly fraction: f* = edge / odds = 0.10 / 1.0 = 10% of bankroll per tournament. 10% of $10,000 is $1,000. The $200 buy-in represents 2% of bankroll, well within Kelly. Running five simultaneous $200 tournaments (10% of bankroll combined) sits right at the Kelly threshold. Running ten simultaneous events starts to push into over-Kelly territory.

What each output means

Full Kelly fraction is the theoretically growth-maximising stake as a percentage of your current bankroll. Half Kelly and quarter Kelly are the practical variants most professionals use: they give up some growth rate in exchange for dramatically reduced volatility and ruin risk. Expected bankroll growth rate shows the geometric mean return per trial at each Kelly fraction, making the growth-safety trade-off explicit. The Kelly curve visualisation is the most important output: it shows log-growth on the Y axis against bet fraction on the X axis, with the peak at f* and the decline toward zero growth (and eventual negative growth) past 2f*.

Where the model breaks

Kelly assumes your edge estimate is exact. In poker, it absolutely is not. A player who believes they run 10% ROI but actually runs 5% will compute twice the correct Kelly fraction and substantially increase their ruin risk. The practical response is to use fractional Kelly as a default: half-Kelly cuts the ruin risk dramatically while preserving most of the growth benefit.

The model also assumes you can bet exactly the Kelly fraction each time. At low stakes this is often impossible due to minimum buy-in requirements. A player with $500 wanting to play NL10 ($10 max buy-in) is forced into a 2% bankroll allocation regardless of what Kelly prescribes.

Multi-tabling creates a specific Kelly problem: if you're playing six tables simultaneously, the combined exposure is six times your per-table stake. Six NL50 tables at $50 each represents $300 at risk at once. Kelly for the aggregate session is a function of combined variance, not single-table variance. The multi-table field in the calculator handles this by dividing the Kelly stake proportionally across concurrent tables.

For the bankroll floor that Kelly implies, see the bankroll calculator. For how Kelly-sized exposures interact with downswing depth, the variance calculator gives you the distribution around the expected outcome.