Kelly criterion bet sizing calculator
The Kelly criterion maximises the long-run growth rate of a bankroll. It is also uncomfortably aggressive, which is why most people use a fraction of it.
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%
Stake at your Kelly fraction
125.00
- Full Kelly stake
- 500.00
- Full Kelly as a share of bankroll
- 10.000 %
- Your edge
- 10.000 %
- Win rate needed to break even
- 50.000 %
- Expected log growth per bet
- 0.005 008
- You have a positive edge
- 1
Show the working
- Your estimated chance of winning = 55
- Decimal odds offered = 2
- Bankroll = 5000
- Kelly fraction = 25
- p = 55 / 100 = 0.55
- b = 2 - 1 = 1
- kelly = 1 > 0 ? (0.55 * 1 - (1 - 0.55)) / 1 : 0 = 0.1
- Full Kelly as a share of bankroll = 0.1 * 100 = 10
- Full Kelly stake = max(0.1, 0) * 5000 = 500
- Stake at your Kelly fraction = 500 * 25/100 = 125
- Your edge = (0.55 * 2 - 1) * 100 = 10
- Win rate needed to break even = 2 > 0 ? 100/2 : 0 = 50
- Expected log growth per bet = 0.1 > 0 ? 0.55 * ln(1 + 0.1*1) + (1-0.55) * ln(1 - 0.1) : 0 = 0.005 008 37
- You have a positive edge = 0.1 > 0 ? 1 : 0 = 1
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- f* = (p b - q) / b, with b the net odds, p the win probability and q = 1 - p
- growth rate = p ln(1 + f b) + q ln(1 - f)
Kelly assumes your probability estimate is correct. Overestimating your edge by a little makes full Kelly badly over-aggressive, which is why quarter Kelly is common.
A negative Kelly fraction means you have no edge and should not bet at all.