Understand the odds. Use the maths. Bet smarter.

Choose where to start

If you are new to the site, these three starting points cover the main ways to use Betting Maths.

Learn the key betting maths concepts

Start with these guides if you want to understand how odds are priced, how bookmaker margin works, how free bets are calculated, how each-way terms work, how staking methods differ, and why betting systems should be treated carefully.

Betting jargon explained

Betting can be full of confusing terms: acca, overround, lay bet, liability, vig, juice, dutching, hedging, free bet, matched betting, stake not returned, Rule 4, non-runner, back/lay, each-way, value betting, underround and more.

Our betting glossary explains common betting terms in plain English and links important maths terms to the right calculator.

Free bet example

Many bookmaker free bets are stake not returned. That means a £50 free bet at odds of 6.00 usually pays £250 profit if it wins, not a £300 return.

The Free Bet Calculator works out lay stake, liability, conversion rate and possible profit from a free bet. The What Is a Free Bet? guide explains the terms in plain English.

Each-way and Rule 4 example

A £10 each-way bet usually costs £20 because it has a win part and a place part. If non-runners affect the market, Rule 4 deductions can also reduce winnings.

Read Each-Way Betting Terms Explained, What Are Extra Places?, and What Is Rule 4? for the plain-English explanations.

Start with a simple bookmaker margin example

A football match might have odds of 2.10 for the home win, 3.40 for the draw and 3.60 for the away win. Converted into implied probability, those prices add up to 104.81%.

That means the market has a 4.81% overround. This is one simple example of how betting maths helps explain bookmaker margin.

Arbitrage example

Arbitrage can exist in theory when all possible outcomes in a market add up to less than 100% implied probability.

These two outcomes add up to 95.24%, which is an underround. The Arbitrage Calculator can show the stake split and estimated profit.

Back/lay example

A back/lay calculation is useful when you back a selection first and then lay the same selection on an exchange. For example, backing £100 at 3.00 and laying at 2.00 with 2% commission creates a balanced hedge.

The Back/Lay Calculator works out the lay stake, lay liability and profit if the selection wins or loses. For lay-first positions, use the Hedge Bet Calculator.

Accumulator example

Accumulators multiply odds together. For example, decimal odds of 2.00, 1.80 and 2.50 combine to make accumulator odds of 9.00.

A £10 stake at combined odds of 9.00 would return £90, including £80 profit. The Accumulator Calculator works this out automatically and also shows the implied probability.

Back, lay and liability example

Lay betting is different from normal backing because your risk is based on liability. If you lay £100 at odds of 3.00, your liability is £200.

The Lay Liability Calculator helps show the real exposure behind a lay bet.