How much to bet with Kelly at +150: the stake, step by step

At +150 a win pays 1.5 times the stake, so b = 1.5. With an estimated 45% chance of winning, the Kelly stake is (1.5 × 0.45 − 0.55) ÷ 1.5 = 8.33% of bankroll. At 40% the stake is zero, because 40% is the break-even rate at +150. The result is only as good as the 45%.

Enter your own price and probability in the Kelly criterion calculator to check each step below.

The formula in one line

The Kelly stake is f = (b × p − q) ÷ b, where p is your estimated chance of winning, q = 1 − p, and b is the net payout per unit staked. It can be rewritten as f = p − q ÷ b, which is easier to do in your head: your win chance minus the loss chance divided by the payout. A negative answer means no bet.

Step 1: turn the American price into b

For a positive price, b = price ÷ 100, so +150 gives 1.5. For a negative price, b = 100 ÷ the price without its sign, so -150 gives 0.667. This is the profit on one unit, not the total return, which would add the stake back.

Step 2: write down a probability

This is the only input that is yours. Kelly has no opinion about how you got it. The break-even probability at +150 is 100 ÷ 250 = 40%, so any estimate at or below 40% returns a stake of zero.

The stake at +150 for different probabilities

• 40%: 0.0% of bankroll (the price is exactly fair)
• 42%: 3.3%
• 45%: 8.3%
• 50%: 16.7%
• 55%: 25.0%

The table shows the sensitivity of the method. Moving the estimate from 42% to 50% multiplies the stake by five. An eight-point difference in a probability is well inside the uncertainty of many models, which is why the next two articles cover estimation error and several bets at once.

The same sum at a negative price

At -150, b = 0.667 and the break-even rate is 60%. With an estimate of 62%, f = 0.62 − 0.38 ÷ 0.667 = 0.62 − 0.57 = 0.05, or 5% of bankroll. Two points above break-even gave a 5% stake here, while at +150 a two-point edge over 40% gave only 3.3%. Kelly scales with the edge relative to the price, not with the edge alone.

Why people stake less than the number

Full Kelly maximises the long-run growth rate if the probability is exactly right and bets settle one after another. Neither condition holds in practice, and the growth curve is lopsided: staking half of Kelly gives up about a quarter of the growth, while staking double Kelly gives up all of it. The fractions most people use, a half or a quarter, are covered in the fractional Kelly article.

Use it. Put the price, your probability and your bankroll into the Kelly criterion calculator to see the full, half and quarter stakes side by side.