Kelly Criterion Calculator
The Kelly criterion calculates the mathematically optimal stake that maximises long-run bankroll growth — provided you actually have an edge. This calculator shows what percentage of your bankroll Kelly recommends, and why professionals almost never bet full Kelly.
Kelly Criterion Calculator
What is the Kelly criterion?
The Kelly criterion is a formula published in 1956 by John L. Kelly that determines the stake which maximises the geometric growth rate of a bankroll. The formula is f* = (b·p − q) / b — where b is the net odds (decimal odds − 1), p is your estimated win probability and q = 1 − p. If f* is negative, Kelly says don't bet.
When does Kelly return a stake > 0?
Only when your probability is higher than the implied probability of the odds (1/odds). That gap is called the edge. Without an edge, Kelly says: don't bet. Example: decimal odds 2.10 imply a probability of 47.6%. If you estimate the true probability at 55%, you have a 7.4% edge — full Kelly recommends roughly 14% of bankroll.
Why do pros use Half- or Quarter-Kelly?
Full Kelly maximises expected logarithmic growth but is extremely volatile. A bad run can halve the bankroll even with a positive edge. Half-Kelly (×0.5) cuts variance to a quarter while retaining about 75% of expected growth. Quarter-Kelly is more conservative still and fits uncertain probability estimates.
What if my probability estimate is wrong?
That's the catch. Kelly is optimal when p is known exactly. In practice you estimate p — and if you systematically overestimate, full Kelly leads straight to ruin. Fractional Kelly is therefore not a comfort choice but an insurance policy against estimation error.
Can I apply Kelly to casino games?
In theory yes, in practice almost never. Most casino games have negative edge for the player — Kelly then recommends 0. Only a few edge cases (card counting blackjack with a positive count, +EV bonuses, some video poker variants) create a positive edge where Kelly applies.
How does Kelly compare to flat staking?
With flat stakes you always wager the same amount (e.g. 1% of bankroll). Kelly scales the stake with your edge: bigger edges → bigger stakes. Mathematically the bankroll grows faster with Kelly, but variance is higher. For beginners or with uncertain estimates, small flat stakes (or Quarter-Kelly) are often the more robust choice.