How the kelly criterion calculator works
The Kelly criterion gives the stake, as a fraction of your bankroll, that maximises the long-run growth of the bankroll for a bet with a known edge. It is aggressive at full strength, so most people bet a fraction of it.
- Let b be the decimal odds minus one, p your win probability and q equal to 1 minus p.
- The Kelly fraction is (b × p − q) divided by b. A negative result means no bet.
- Multiply by your chosen fraction of Kelly, then by the bankroll, for the stake.
Worked example
£1,000 bankroll, a price of 2.50 and a 45% chance, at half Kelly.
- b = 1.5, p = 0.45, q = 0.55.
- Full Kelly = (1.5 × 0.45 − 0.55) ÷ 1.5 = 8.3% of the bankroll.
- Half Kelly stake: £41.67.
The stake is exactly as reliable as the probability. Overestimating your edge by a few points turns a growth-optimal stake into an over-bet.
Questions
- Why bet less than full Kelly?
- Full Kelly assumes your probability is exactly right and tolerates deep drawdowns. Half or quarter Kelly gives up a little growth for far less variance and protects against an overstated edge.
- What does a negative Kelly mean?
- That the price is below what your probability deserves. The correct stake is zero.
- Should the bankroll be my whole balance?
- It should be the money set aside for betting that you would replenish only from winnings. Applied to money you could not afford to part with, the formula stops being Kelly.
