Sports betting maths
Every bet has a price. We show you how to read it.
A standard -110 line keeps 4.55% of every stake on average. Put four such legs in a parlay and the bookmaker's edge compounds to 16.98%; ten legs, 37.20%. Our calculators turn odds into probabilities, strip out the margin and show what a bet is worth before you place it.
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What a parlay really costs
| Legs | Parlay pays (decimal) | Fair payout | Chance to win | Bookmaker's edge |
|---|---|---|---|---|
| 2 | 3.64 | 4 | 1 in 4 | 8.88% |
| 4 | 13.28 | 16 | 1 in 16 | 16.98% |
| 6 | 48.41 | 64 | 1 in 64 | 24.36% |
| 10 | 643.08 | 1,024 | 1 in 1,024 | 37.20% |
Odds converter
Decimal, fractional and American odds, and the probability they imply.
Margin and fair odds
How much the bookmaker keeps on a market, and the odds without it.
Kelly criterion
How much of a bankroll to stake when you have a real edge.
Expected value
Your probability against the odds: what the bet is worth per unit.
Hedge calculator
The stake that locks in the same result whatever happens.
Arbitrage calculator
Stakes across two or three bookmakers for the same return on every outcome.
How bookmakers make money
A bookmaker prices every outcome a little shorter than its true chance. Add up the probabilities implied by the odds on all outcomes of a market and you get more than 100%: the excess is the overround, and it becomes the bookmaker's margin, the share of all stakes it keeps on average. The bettor pays that margin on every bet, whatever the result of any single one, so the average bettor loses. Knowing the size of the margin, and how it compounds in parlays, is the first thing the maths can tell you.
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Latest guides
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Dutching three selections: the same profit whichever wins, and a total loss if none does
Dutching splits stakes by implied probability to equalize returns, though the bookmaker margin still reduces overall value.
Overbetting: why twice the Kelly stake grows nothing
Staking beyond the Kelly optimum reduces expected growth because losses impact the bankroll more heavily than wins.
Free bets: why you keep most of one at long odds and under half at short odds
Long odds preserve more value from a non-returnable free bet than short odds due to how winnings exclude the stake.
Each-way bets: how the place terms turn into money
An each-way bet splits your stake into win and place parts, with the place fraction determining the separate payout.
Price a bet before you place it
Turn any odds into a probability, strip out the margin and see what a parlay really costs.
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