Kelly Criterion Calculator

What the Numbers Mean

The Kelly fraction is the maximum percentage of your bankroll you should risk per buy-in to maximize long-term growth. At the defaults of 5 bb/100 win rate and 80 bb/100 standard deviation, full Kelly works out to 7.8% of your bankroll per buy-in, or 12.8 buy-ins. Half-Kelly doubles that to 25.6 buy-ins. Full Kelly's 12.8 sits well under the 20 to 30 buy-in rule of thumb most players follow, and half-Kelly lands inside it. The conventional wisdom already builds in a safety margin beyond what pure math requires.

The stake table translates Kelly into dollar-denominated levels. If a stake shows "optimal," your bankroll supports it at half-Kelly sizing. "Over-rolled" means you could move up. "Too high" means the math says your bankroll cannot sustain that stake's variance at your measured edge. None of these labels account for rake differences across stakes. Your effective win rate changes when you move up, and a 1 bb/100 rake increase can double the bankroll Kelly requires. Run your actual post-rake numbers through the rake calculator before treating this output as a green light.

Why Half Kelly

Full Kelly assumes you know your edge exactly, and nobody does. A 50,000-hand sample at 80 bb/100 standard deviation gives your win rate a standard error of 3.6 bb/100. Your true rate could easily be half of what your tracker shows. If your real edge is half the measured edge, full Kelly has you playing a stake twice as high as your bankroll supports, and your risk of ruin jumps from near-zero to double digits. Half-Kelly gives up only 25% of the theoretical growth rate but cuts variance in half, providing a large buffer against that estimation error. The fraction you use should scale with your confidence in the edge estimate. With 500,000+ hands at a single stake, half-Kelly is defensible. With 50,000-200,000 hands, a quarter to a third of Kelly better reflects how wide your confidence interval still is. Below 50,000 hands, Kelly-based stake selection is premature; use a flat 30-40 buy-in rule instead. Stakers running a stable of players should be even more conservative per player, since their confidence in any individual's edge is inherently lower than the player's own. Chen and Ankenman cover this in Chapter 25 of The Mathematics of Poker, treating a stable as a portfolio, with Kelly applied to the aggregate of all players rather than to each one in isolation.

What This Calculator Does Not Do

Kelly sizing is a single-stake, steady-state model. It does not account for rake changes as you move between stakes, variance from game selection (your edge differs across tables and time slots), or shot-taking strategies where you temporarily play above Kelly at reduced volume. For a model that simulates the actual trajectory of your bankroll across hands, including ruin probability and drawdown depth, use the bankroll simulator.