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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4.55%the bookmaker's edge on a single bet at -110 on both sides
16.98%the edge on a four-leg parlay of -110 legs
10%the Kelly stake with a 55% chance at even money, and zero with no edge at all
3.73%locked in by the arbitrage example: 2.10 and 2.05 on the two sides at different bookmakers

What a parlay really costs

Every leg priced at -110 (1.91) on a genuine 50/50 outcome. The edge compounds with each leg.
LegsParlay pays (decimal)Fair payoutChance to winBookmaker's edge
23.6441 in 48.88%
413.28161 in 1616.98%
648.41641 in 6424.36%
10643.081,0241 in 1,02437.20%

Price your own parlay

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.

We take no bets and give no tips. If betting is causing you problems, free help is available.

Price a bet before you place it

Turn any odds into a probability, strip out the margin and see what a parlay really costs.

Open the calculators

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