Calculate Winnings and Implied Probability Easily

Learn the simple maths behind odds, payouts and fair prices with Best Of Bets. Use this guide to understand returns clearly, compare bookmakers confidently and make measured, responsible decisions.

We explain odds formats, step-by-step payout calculations, implied probability, market margins and safe staking in plain English. Everything here is designed for adult bettors in Great Britain and Northern Ireland.

Betting fundamentals and hands-on how-to guides

This page is part of our Betting Fundamentals & How-To Guides series. It complements our bookmaker reviews, sports betting tips and bonus comparisons with practical, people-first education.

After reading, you will be able to calculate returns accurately, translate any odds format and spot when prices are close to your fair estimate. You will also find safer gambling advice throughout.

Understand odds formats and convert them correctly

Bookmakers display prices in fractional, decimal or American formats, but they all describe the same thing: risk and reward. Once you can convert between them, the maths becomes straightforward.

Your total return equals stake multiplied by decimal odds, and your profit equals return minus stake. With fractional odds, the fraction shows profit relative to stake, while the denominator reflects implied risk.

Fractional odds explained with quick examples

Fractional odds show profit: stake multiplied by the fraction’s numerator divided by its denominator, plus your stake back if the bet wins. For example, 5/2 returns £35 on a £10 stake (£25 profit plus £10 stake).

Shorter prices like 13/20 mean lower profit relative to stake, returning £16.50 on £10 (£6.50 profit plus £10 stake). Fractional odds are widely used in UK horse racing and football match markets.

Decimal odds and fast payout calculations

Decimal odds show the full return per £1, so the calculation is simply stake times odds. A £10 stake at 2.40 returns £24.00, for a £14.00 profit.

Decimal odds make accumulators and totals easy to manage because you multiply decimals across legs. They also make market margin checks and implied probability calculations quick.

American odds conversion for UK-based punters

Positive American odds (for example +200) show how much profit you make from a £100 base, while negative odds (for example -150) show how much you must stake to win £100 profit. They can be converted to decimal for clarity.

To convert +200 to decimal, divide by 100 and add 1, giving 3.00; to convert -150, divide 100 by 150, add 1 and get 1.6667. Many UK bettors standardise everything into decimal or fractional before calculating.

Calculate betting winnings step by step accurately

Every payout breaks down into stake, profit and total return, with the stake included only in the return figure. Always confirm whether your bet type includes special terms, such as Rule 4 in racing or push rules in US sports.

Use decimal odds for speed: Return = Stake × Decimal Odds, Profit = Return − Stake. With fractional odds, Profit = Stake × (Numerator ÷ Denominator), Return = Profit + Stake.

Singles: stake, return and profit explained

Example: £25 on 7/4 wins returns £25 × (7 ÷ 4) + £25 = £43.75 + £25 = £68.75. Profit is £43.75 because profit is the winnings excluding your original stake.

Using decimal, 7/4 converts to 2.75, so Return = £25 × 2.75 = £68.75 and Profit = £68.75 − £25 = £43.75. Both methods should match to the penny, subject to any rounding rules.

Accumulators: multiplying prices and margins

For multiples, convert each leg to decimal odds and multiply them together, then multiply by stake. A fourfold at 1.80, 2.10, 2.40 and 1.65 gives 1.80 × 2.10 × 2.40 × 1.65 = 14.98, so £10 returns £149.80.

Remember that overround compounds across legs, which is why line shopping matters. Small price improvements on each leg can make a noticeable difference to your final return.

Each-way bets, places, deductions and dead heats

An each-way bet splits your stake into win and place parts, and the place part settles at a fraction of the win odds for specified places. Example: £10 each-way at 10/1 with 1/5 odds for 4 places equals £10 win and £10 place.

If the selection places but does not win, the place return is £10 × (10 ÷ 1 × 1 ÷ 5) + £10 = £10 × 2 + £10 = £30, and the win part loses. Dead heat or Rule 4 deductions can reduce returns per standard rules, so always check the market terms.

Implied probability and finding fair prices

Implied probability translates odds into a percentage chance, which helps you judge whether a price is fair to your view. Comparing your estimated chance to the implied chance is central to disciplined betting.

Price discovery is about being realistic, not chasing certainty. A “value” price reflects a measured opinion that the odds are slightly in your favour over the long term, without guaranteeing any result.

Convert fractional, decimal and American odds

From decimal odds D, implied probability = (1 ÷ D) × 100%. From fractional odds A/B, implied probability = (B ÷ (A + B)) × 100%.

From American odds, for positive +X use 100 ÷ (X + 100) × 100%, and for negative −Y use Y ÷ (Y + 100) × 100%. Convert to a decimal to double-check your maths and avoid rounding mistakes.

From implied probability to expected value

Expected value (EV) estimates the average outcome over many similar bets. Use EV per £1 stake = (Your Probability × Net Win) − ((1 − Your Probability) × 1), where Net Win equals Decimal Odds − 1.

Example: If you estimate a 45% chance at 2.40, EV per £1 = 0.45 × 1.40 − 0.55 × 1 = 0.63 − 0.55 = +0.08. Positive EV is not a guarantee of profit, but it is a sensible target for long-run discipline.

Market overround, hold and realistic targets

Bookmakers build a margin into markets, known as the overround or hold. Sum the implied probabilities of all outcomes and subtract 100% to see the margin.

Example: a three-way football market adds to 104.5%, meaning a 4.5% margin for the book. Your aim is to shop for lower margins and better prices, while keeping your staking consistent and responsible.

Bankroll management and safer gambling tools

Set a betting budget you can comfortably afford to lose and keep it separate from essential expenses. Treat betting as entertainment and never as a source of income or a solution to financial concerns.

Use safer gambling tools provided by licensed operators to stay in control. If betting stops being enjoyable, take a break immediately.

Setting unit size, staking plans and records

Define a unit size, often 0.5%–2% of your bankroll, to keep stakes consistent. Fixed or percentage staking is easier to manage than impulsive changes based on short-term results.

Keep a record of selections, prices, closing prices and outcomes. Good records help you spot strengths and weaknesses, and they support more accurate probability estimates over time.

Time-outs, deposit limits and reality checks

Use deposit limits, reality checks and time-outs to control spend and session length. These tools are available from licensed operators and can be adjusted to suit your circumstances.

Cooling-off periods help you reset during losing spells or when emotions run high. Responsible play protects your bankroll and your wellbeing.

When betting stops being fun, stop and seek help

If you feel pressure to chase losses or find yourself betting when you did not plan to, stop immediately. Reach out to national helplines or specialist support services for confidential assistance.

Friends and family can also help you stick to a plan. Gambling is strictly for adults aged 18+ and should never harm your finances, relationships or work.

Comparing odds, boosts and welcome offers

Comparing prices is one of the most effective ways to improve returns without increasing risk. Small price edges add up, especially for accumulators and season-long betting.

We showcase offers and odds boosts from licensed operators we review and recommend. Use our banners and affiliate links to explore deals safely, and always read the full terms and conditions.

How to use our banners and tracked affiliate links

Click through our on-site banners to visit bookmakers we have independently reviewed. Our tracked links help you access the right sign-up pages, welcome packages and featured boosts.

Deals change frequently, so check back before you place a bet. If you find a stronger price or a fairer term elsewhere, prioritise the option that best suits your budget and goals.

Checking key terms, eligibility and restrictions

Before you opt in, check eligibility, opt-in steps, min odds, wagering requirements, time limits and payment method exclusions. Confirm whether bets must be placed on specific markets or at certain prices.

Welcome offers, odds boosts and insurance specials always have conditions. Make sure those conditions fit how you actually bet, not how you might bet just to chase a bonus.

Odds comparison, boosts value and price locks

Odds boosts can increase your potential return, but only compare like for like on market terms and settlement rules. Some boosts cap the maximum stake or exclude cash-out, so check the details.

Horse racing “best odds guaranteed” and price locks can be valuable where available and permitted. Always verify whether BOG applies to your race and time window before you place the bet.

Worked examples for common sports bet types

Use these quick examples to check your calculations. Adjust the numbers to your stake and odds to confirm the returns.

The settlement principles stay the same across sports, with specific competition or event rules layered on top. Always review the relevant market rules before placing your bet.

Football match odds, both teams to score, draws

Example: £20 on a draw at 12/5 returns £20 × (12 ÷ 5) + £20 = £68.00. Decimal equivalent is 3.40, so £20 × 3.40 returns £68.00 for £48.00 profit.

Both Teams To Score at 10/11 returns £20 × (10 ÷ 11) + £20 ≈ £38.18. In decimal (1.91), the same £20 returns £38.20, with tiny rounding differences depending on operator policy.

Tennis set betting and player performance props

Set betting example: £15 on 2–0 at 6/5 returns £15 × (6 ÷ 5) + £15 = £33.00. In decimal 2.20, £15 × 2.20 returns £33.00, profit £18.00.

Player aces over 9.5 at 5/6 returns £10 × (5 ÷ 6) + £10 ≈ £18.33. Decimal 1.83 gives £10 × 1.83 = £18.30, again subject to rounding rules.

Horse racing win, each-way and place markets

Win example: £25 at 9/4 returns £25 × (9 ÷ 4) + £25 = £81.25. Decimal 3.25 yields the same £81.25 return and £56.25 profit.

Each-way example: £10 each-way at 8/1 with 1/5 odds for 4 places returns £90 if the horse wins. If it places without winning, the place part returns £10 × (8 ÷ 1 × 1 ÷ 5) + £10 = £26, for a £6 overall profit.

Quick formulas, calculators and cheat sheets

Keep these formulas handy for fast checks. Running the numbers before you bet helps you compare options and avoid avoidable mistakes.

Use a basic spreadsheet or your phone’s calculator to standardise your process. Consistency builds better decisions than gut feel alone.

Handy formulas to copy into your notes app

Decimal to implied probability: 100 ÷ Decimal Odds. Fractional to implied probability: Denominator ÷ (Numerator + Denominator) × 100.

American to decimal: Positive X → (X ÷ 100) + 1; Negative −Y → (100 ÷ Y) + 1. EV per £1: (Your Probability × (Decimal − 1)) − ((1 − Your Probability) × 1).

Guide to rounding, stake factoring and margins

Bookmakers may round to two decimal places in settlement, which can cause penny-level differences. For accumulators, small rounding differences can scale with multiple legs.

When differences appear, check the operator’s settlement rules and rounding policy. Confirm whether voids, pushes or deductions apply to any leg or selection.

Using fair odds to set personal price targets

Convert your estimated probability to a fair decimal price: 1 ÷ Probability. If you estimate 42%, your fair price is 1 ÷ 0.42 ≈ 2.38.

Set a personal target slightly above fair to account for uncertainty and market costs. If you cannot find that target price, passing is a sound decision.

Frequently asked questions about bet maths

These quick answers clarify common queries from UK bettors. If a rule is unclear on your chosen market, check the operator’s terms before placing your bet.

Remember that markets and offers are for adults aged 18+ only. Always bet within your set budget.

Do bookmakers tax winnings in the United Kingdom

For recreational bettors in the UK, returns are generally paid tax-free and the bookmaker covers duties within their margin. This is not financial advice, and personal circumstances vary.

If in doubt, seek independent guidance on your situation. Always comply with local laws and operator terms.

Why does implied probability not sum to 100

When you sum the implied probabilities of a market and get more than 100%, the excess is the overround or book margin. This margin pays for operating costs and promotions and forms part of the price you receive.

Lower overrounds mean better value for bettors in aggregate. Comparing prices helps you reduce the margin you pay.

What is the difference between return and profit

Return is the total amount paid back to you on a winning bet, including the original stake. Profit is the return minus the original stake.

For example, £10 at 3.00 returns £30 and profits £20. Clear terminology helps you evaluate risk and reward accurately.

Important notices and responsible gambling

Best Of Bets promotes licensed operators and encourages responsible play for adults aged 18+ only. Gambling should be a form of entertainment, not a way to address financial issues or personal problems.

Marketing must be socially responsible and must not target or strongly appeal to under-18s. If betting stops being fun, stop and consider support from professional services.

To explore bookmaker reviews, current offers and featured tips, browse the banners and links on our site. Always read full terms, set a budget, and bet responsibly with licensed operators only.

How do I calculate my betting return and profit from decimal odds?

Multiply your stake by the decimal odds to get the total return, then subtract your stake to get the profit.

How do I work out profit and return from fractional odds?

Profit equals stake × (numerator ÷ denominator) and return equals profit + stake.

What is implied probability and how do I convert odds into a percentage?

Implied probability is the chance suggested by the price, calculated as 100 ÷ decimal odds or denominator ÷ (numerator + denominator) × 100 for fractional.

How do I calculate returns on an accumulator (multiple) bet?

Convert each leg to decimal odds, multiply all the decimals together, then multiply by your stake to get the total return.

How are each-way bets settled, and what happens if my selection only places?

Your stake is split into win and place parts, and if the selection only places the place part pays at the stated fraction of the win odds while the win part loses.

What do Rule 4 deductions, pushes and dead heats mean for my payout?

These settlement rules can reduce or adjust returns according to the market terms, so always check the operator’s rules before you bet.

What is overround (bookmaker margin) and why don’t implied probabilities add to 100%?

The overround is the bookmaker’s built-in margin, so the sum of implied probabilities exceeds 100% by the margin percentage.

What is expected value (EV) in betting and how can I use it?

EV per £1 is (your probability × (decimal odds − 1)) − ((1 − your probability) × 1), helping you target prices above your fair estimate.

Are sports betting winnings taxed in the United Kingdom?

For recreational bettors in the UK, winnings are generally paid tax-free and bookmaker duties are covered within the margin.

How can I compare odds, boosts and welcome offers safely on Best Of Bets?

Visit BestOfBets.com to follow our banners and tracked links to licensed UK operators, read full terms, and only opt in to offers that fit your staking and markets (18+).