JILI77 Kelly Criterion: Size a Stake From Edge and Odds

The Kelly criterion answers the question every bettor faces after finding a price: how much should this bet use? This page gives you the formula, a worked stake with every figure shown, and the reason most bettors use a fraction of the result. For where staking sits in the wider process, read how sports betting works from price to payout.

The Kelly criterion formula

The Kelly criterion gives the fraction of your bankroll to stake:

f = (b x p minus q) / b

• b is the decimal price minus 1, the profit per 1 staked.
• p is your estimated chance of winning, as a decimal.
• q is the chance of losing, which is 1 minus p.

The formula needs your own estimate of p. The price alone cannot tell you the edge. Decimal odds and the implied probability they carry gives you the book’s figure to compare against.

A worked stake

You are offered a price of 2.10 and you estimate the true chance at 50 percent. Your bankroll is 2,000.

1. b = 2.10 minus 1 = 1.10.
2. p = 0.50, so q = 0.50.
3. b x p = 1.10 x 0.50 = 0.55.
4. Numerator = 0.55 minus 0.50 = 0.05.
5. f = 0.05 / 1.10 = 0.04545, or 4.55 percent of bankroll.
6. Stake = 2,000 x 0.04545 = 90.91.

The book’s implied probability at 2.10 is 1 / 2.10 = 47.62 percent. Your 50 percent beats it by 2.38 points, and that gap is the edge.

Expected value betting

Expected value betting means staking only when the price pays more than your chance justifies. Expected value per 1 staked is p x price minus 1.

At your 50 percent and a price of 2.10: 0.50 x 2.10 minus 1 = 0.05. You expect to gain 5 percent of each stake over many bets. If your chance is 47.62 percent, the result is 0 and Kelly returns a stake of 0.

If your chance is only 45 percent, expected value is 0.45 x 2.10 minus 1 = minus 0.055. Kelly goes negative, which means no bet.

Value betting

Value betting is the habit behind the formula: place a bet only when your estimated chance is higher than the implied probability of the price. A price with value is not a price that wins; it is a price that wins more often than it is charged for.

Fractional Kelly

Fractional Kelly stakes a share of the full figure, such as half or a quarter. Using the example above:

Full Kelly assumes your estimate is exact. It is not, and a chance that is really 48 percent instead of 50 turns a stake sized for a large edge into one sized for a small edge. A fraction absorbs that error and shrinks the swings in your bankroll.

Flat betting as the baseline

Flat betting stakes the same amount every time, such as 1 percent of the starting bankroll. At 2,000 that is 20 per bet.

It is simpler than Kelly and never grows a stake on a bad estimate. It also ignores edge size, so a strong edge earns the same stake as a thin one. Many bettors use flat betting as a floor and cap any Kelly figure at a multiple of it.

Keep it inside your limits

No formula makes a bet profitable when the edge is imaginary. Before you apply any of this, run this check:

1. Write down the bankroll you can afford to lose entirely.
2. Set a cap on the stake as a share of it, for example 5 percent.
3. Read responsible betting limits and how to set them before your first stake.
4. Stop when the limit is reached, whatever the formula says.