Three Formulas Cover Everything

Odds calculators seem essential until you realise the entire tool is three formulas: one for returns, one for conversion, one for implied probability. Learn them by hand and you'll calculate faster than any app — and more importantly, you'll understand what the numbers mean while you're comparing prices across bookmakers. This guide walks through all three with worked examples, plus the expected-value formula that turns calculation into decision-making.

Animated graphic showing the three core betting formulas
The three formulas: return = stake × odds, implied probability = 1 ÷ odds, EV = probability × profit − loss. — Photo credit: PagBets.org

Formula 1: Returns and Profit

Decimal odds make returns trivial: return = stake × odds, and profit = stake × (odds − 1). A $30 bet at 2.50 returns $75 total — $30 stake plus $45 profit. The profit formula is the one that matters for comparisons: the same $30 at 2.40 returns $42 profit, so the 0.10 odds difference costs you $3 of profit. Run that comparison before every bet and the calculator has already paid for itself.

Animated graphic converting 2.50 decimal into fractional and American odds
One price, three formats: 2.50 decimal = 3/2 fractional = +150 American. — Photo credit: PagBets.org
Odds$10 stake returnsProfit
1.50$15.00$5.00
2.00$20.00$10.00
2.50$25.00$15.00
5.00$50.00$40.00

Formula 2: Converting Formats

Conversion is mechanical once memorised. Decimal → fractional: subtract 1 and simplify — 2.50 becomes 1.50, which is 3/2. Decimal → American: above 2.00, multiply by 100 and subtract 100 (2.50 → +150); below 2.00, −100 ÷ (odds − 1) (1.67 → −150). Fractional → decimal: divide and add 1 (6/4 → 1.5 + 1 = 2.50). In practice, set every bookmaker account to decimal odds and conversion disappears — the comparison across sites becomes one subtraction.

Chart showing returns at different stakes and odds combinations
Returns at a glance: how stakes and odds combine into total payouts. — Photo credit: PagBets.org
Practical shortcut: decimal everywhere. It's the default at most international bookmakers, the maths is one multiplication, and every other format converts from it in seconds.

Formula 3: Implied Probability

Implied probability converts a price into the chance it represents: probability = 1 ÷ decimal odds, times 100 for a percentage. Odds of 2.00 imply 50%; 1.50 implies 66.7%; 4.00 implies 25%. The critical application is the margin check: add the implied probabilities of all outcomes in a market and the total always exceeds 100% — a two-outcome market priced at 1.95/1.95 implies 51.3% + 51.3% = 102.6%, so the bookmaker's margin is 2.6%. Lower margins mean better prices; the calculation takes ten seconds and is the fastest quality check in betting.

  • 1 ÷ odds = implied probability (2.00 → 50%)
  • Sum all outcomes' probabilities — the excess over 100% is the margin
  • Margins near 4% are sharp for football; above 8% is expensive
  • Compare margins across bookmakers before comparing individual prices

The Master Formula: Expected Value

Expected value turns calculation into decision: EV = (win probability × profit per win) − (loss probability × stake). A $100 bet at 2.50 with your estimated 45% true chance: (0.45 × $150) − (0.55 × $100) = +$12.50 — positive EV, a bet worth making. Negative EV, skip it. The formula requires an honest probability estimate, which is the entire skill of betting — our value betting guide teaches the estimation process in depth.

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Frequently Asked Questions

How do I calculate my betting returns?
With decimal odds, multiply: return = stake × odds. A $25 bet at 2.50 returns $62.50 total, of which $37.50 is profit. Profit = stake × (odds − 1). That one multiplication covers every decimal-odds bet you'll ever place.
How do I convert odds between formats?
Decimal to fractional: subtract 1 and simplify (2.50 → 1.50 → 3/2). Decimal to American: above 2.00, multiply by 100 and subtract 100 (2.50 → +150); below 2.00, use −100 ÷ (odds − 1) (1.67 → −150). Fractional to decimal: divide and add 1 (3/2 → 2.50).
How do I calculate implied probability?
Divide 1 by the decimal odds, then multiply by 100. Odds of 2.00 imply 50%, odds of 1.50 imply 66.7%, odds of 4.00 imply 25%. Add all outcomes' implied probabilities in a market and you'll exceed 100% — the excess is the bookmaker's margin.
How do I calculate expected value?
EV = (win probability × profit per win) − (loss probability × stake). For a $100 bet at 2.50 with a true 45% win chance: (0.45 × $150) − (0.55 × $100) = +$12.50. Positive EV bets make money on average; negative EV bets lose it. Our value betting guide builds on this.
Do I need an odds calculator app?
No — the three formulas above cover everything an app does for single bets, and knowing them by hand makes you faster at spotting value while comparing bookmakers. For complex accumulators and system bets, a calculator app is genuinely useful.