Betting calculators and plain-English guides
Understand the odds. Use the maths. Bet smarter.
Betting Maths helps you understand odds, stakes, overround, arbitrage, dutching, hedging, free bets, matched betting, back/lay betting, accumulators, each-way bets, extra places, Kelly staking, Rule 4 deductions, lay liability, exchange commission, bookmaker margin and common betting jargon with simple calculators and practical examples.
What is Betting Maths?
Betting Maths is a free betting education and calculator site. It explains how odds, implied probability, overround, arbitrage, dutching, hedging, free bets, matched betting, back/lay betting, accumulators, each-way bets, extra places, Kelly staking, Rule 4 deductions, lay liability, exchange commission and bookmaker margins work in plain English.
The aim is not to provide betting tips or guaranteed profit systems. The aim is to help you understand the numbers behind betting markets so you can read odds, calculate outcomes and understand risk more clearly.
Choose where to start
If you are new to the site, these three starting points cover the main ways to use Betting Maths.
Use the calculators
Find tools for odds, overround, arbitrage, free bets, matched betting, accumulators, each-way bets, dutching, hedging, back/lay betting, Kelly staking and lay liability.
Guide hubLearn the concepts
Read plain-English guides to implied probability, bookmaker margin, free bets, matched betting, lay liability, exchange commission, Kelly staking, each-way terms, Rule 4, dutching and hedging.
GlossaryLook up betting terms
Search common betting jargon including acca, lay bet, liability, commission, vig, juice, free bet, each-way, Rule 4, value, underround and more.
Popular betting calculators
Odds Converter
Convert decimal, fractional and American odds, and calculate implied probability.
Open calculator →Overround Calculator
Work out the total book percentage and bookmaker margin built into a betting market.
Open calculator →Arbitrage Calculator
Check whether odds create an underround and calculate stake splits across all outcomes.
Open calculator →Dutching Calculator
Split a total stake across two or more selections for a balanced return.
Open calculator →Hedge Bet Calculator
Calculate back-first and lay-first hedge stakes, lay liability, commission and possible profit or loss.
Open calculator →Back/Lay Calculator
Calculate lay stake, lay liability and profit across standard back bets and free bet examples.
Open calculator →Free Bet Calculator
Calculate free bet lay stake, liability, conversion rate and possible profit.
Open calculator →Matched Betting Calculator
Estimate qualifying bet result, free bet profit, lay stakes and overall matched betting result.
Open calculator →Lay Liability Calculator
Calculate lay liability, exchange commission and profit or loss from a lay bet.
Open calculator →Kelly Criterion Calculator
Estimate stake size from bankroll, decimal odds, your estimated probability and fractional Kelly.
Open calculator →Accumulator Calculator
Multiply odds across multiple selections and calculate acca returns, profit and implied probability.
Open calculator →Each-Way Calculator
Calculate total stake, place odds, win return, place return and each-way profit or loss.
Open calculator →Each-Way Extra Places Calculator
Compare standard each-way place terms with enhanced extra places offers.
Open calculator →Rule 4 Calculator
Estimate horse racing Rule 4 deductions, adjusted profit and adjusted return.
Open calculator →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 exchange betting works, how each-way terms work, how staking methods differ, and why betting systems should be treated carefully.
What Is Implied Probability?
Learn how odds convert into percentage chance and why implied probability matters across betting maths.
Core guideBookmaker Margin Explained
Understand bookmaker margin, overround, book percentage and why markets usually add up to more than 100%.
Core guideWhat Is Lay Liability?
Learn how lay liability works and why exchange bets can risk more than the lay stake.
GuideWhat Is the Kelly Criterion?
Understand Kelly staking, fractional Kelly and why estimated probability matters.
GuideWhat Is Exchange Commission?
Learn how commission affects lay bets, hedging, free bets and matched betting.
GuideWhat Is a Free Bet?
Learn how free bets, stake not returned, lay stakes and offer value work.
GuideWhat Is Matched Betting?
Understand qualifying bets, free bets, back bets, lay bets and exchange liability.
GuideStake Returned vs Stake Not Returned
Learn the difference between cash-style returns and stake-not-returned free bets.
GuideWhat Is Rule 4 in Horse Racing?
Learn how non-runners can reduce winnings and how Rule 4 deductions are estimated.
GuideWhat Are Extra Places?
Understand enhanced each-way place offers and how they compare with standard terms.
GuideEach-Way Betting Terms Explained
Learn win part, place part, place terms, extra places, non-runners and Rule 4.
GuideWhat Is Overround in Betting?
Learn how book percentage and bookmaker margin are calculated from market odds.
GuideHow Bookmakers Make Money
Understand overround, odds movement, weight of money and liability management.
GuideHow to Hedge a Bet
Understand back and lay hedging, lay liability, commission and greening up.
GuideHedging vs Cash Out
Compare bookmaker cash out offers with manual hedging calculations.
GuideWhat Is Dutching in Betting?
Learn how dutching splits stakes across multiple selections.
GuideDutching vs Arbitrage
Learn the difference between splitting stakes and covering all outcomes for a theoretical profit.
GuideCan You Always Beat the Bookie?
Learn why guaranteed betting systems are risky and what maths can actually show.
Betting jargon explained
Betting can be full of confusing terms: acca, overround, lay bet, liability, commission, 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.
| Free bet stake | Back odds | Lay odds | Commission | Estimated profit |
|---|---|---|---|---|
| £50 | 6.00 | 5.50 | 2% | About £44.71 |
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.
Lay liability and commission example
Lay betting is different from normal backing because the amount at risk is based on liability. If you lay £100 at odds of 3.00, your liability is £200.
| Lay stake | Lay odds | Liability | Commission | If selection loses |
|---|---|---|---|---|
| £100 | 3.00 | £200 | 2% | £98 net exchange win |
Read What Is Lay Liability? and What Is Exchange Commission? to understand the difference between amount at risk and commission on winnings.
Kelly staking example
The Kelly Criterion estimates stake size using bankroll, odds and your estimated probability. For example, decimal odds of 3.00 imply 33.33%, but if you estimate the true chance is 40%, Kelly staking may suggest a positive stake.
| Bankroll | Decimal odds | Your estimate | Full Kelly stake |
|---|---|---|---|
| £1,000 | 3.00 | 40% | £100 |
The Kelly Criterion Calculator lets you test full Kelly and fractional Kelly stake sizes. The What Is the Kelly Criterion? guide explains the formula and risks.
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.
| Example | What matters | Useful tool |
|---|---|---|
| £10 each-way at 9.00 | Total stake, place odds and place terms | Each-Way Calculator |
| Extra 5 places instead of standard 3 | Whether the finishing position is inside the enhanced place terms | Each-Way Extra Places Calculator |
| 20p Rule 4 deduction | Deduction from the profit part of the winning bet | Rule 4 Calculator |
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%.
| Outcome | Decimal odds | Implied probability |
|---|---|---|
| Home win | 2.10 | 47.62% |
| Draw | 3.40 | 29.41% |
| Away win | 3.60 | 27.78% |
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.
| Outcome | Decimal odds | Implied probability |
|---|---|---|
| Outcome A | 2.10 | 47.62% |
| Outcome B | 2.10 | 47.62% |
These two outcomes add up to 95.24%, which is an underround. The Arbitrage Calculator can show the stake split and estimated profit.
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.
| Selection | Decimal odds |
|---|---|
| Selection 1 | 2.00 |
| Selection 2 | 1.80 |
| Selection 3 | 2.50 |
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.