# What is the odds payout on each side?

Computes the payout and profit of a stake on each side of a two-way betting line (a moneyline), the implied probability of each side, and the bookmaker’s margin.

- Page: https://www.acalculator.org/game/betting-odds-calculator
- JSON spec: https://www.acalculator.org/game/betting-odds-calculator.json
- Version: 56e73725f9d3

## Default answer

Example with the default inputs (Odds format American, Odds on side 1 -150, Odds on side 2 +130, Stake $100.00): A $100.00 bet pays $166.67 if side 1 (-150) wins and $230.00 if side 2 (+130) wins.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| format | Odds format | The format of both odds: American, decimal, or fractional. |
| odds1 | Odds on side 1 | The odds offered on side 1 of the two-way line, in the chosen format. |
| odds2 | Odds on side 2 | The odds offered on side 2 of the two-way line, in the chosen format. |
| stake | Stake | The amount bet on one side. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| payout1 | Payout on side 1 | What the stake returns if side 1 wins: stake × decimal odds, stake included. |
| profit1 | Profit on side 1 | Payout on side 1 minus the stake. |
| payout2 | Payout on side 2 | What the stake returns if side 2 wins: stake × decimal odds, stake included. |
| profit2 | Profit on side 2 | Payout on side 2 minus the stake. |
| prob1 | Implied probability, side 1 | The win chance side 1’s odds imply: 1 ÷ decimal odds. |
| prob2 | Implied probability, side 2 | The win chance side 2’s odds imply: 1 ÷ decimal odds. |
| overround | Overround | How far the two implied probabilities add up past 100%. |
| hold | Bookmaker’s margin (hold) | The share of all money staked that the bookmaker keeps when bets on both sides pay out the same: 1 − 1 ÷ (sum of implied probabilities). |

## Method

Payout = stake × d and profit = stake × (d − 1) on each side; implied probability p = 100 ÷ d; overround = p₁ + p₂ − 100; hold = 100 − 10,000 ÷ (p₁ + p₂) percent.

## Assumptions

- The same stake goes on each side, shown side by side; each is a separate single bet.
- The line has exactly two outcomes (no draw). For three or more outcomes, use the no-vig calculator.
- Results are mathematics, not betting advice.

## Worked examples

1. format = american, odds1 = -150, odds2 = +130, stake = $100.00 gives payout1 = $166.67, profit1 = $66.67, payout2 = $230.00, profit2 = $130.00, prob1 = 60%, prob2 = 43.478261%, overround = 3.478261%, hold = 3.361345%. Source: hand calculation in content.mdx: d = 5/3 and 23/10; 3/5 + 10/23 = 119/115; hold 1 − 115/119 = 4/119.
2. format = american, odds1 = -110, odds2 = -110, stake = $110.00 gives payout1 = $210.00, profit2 = $100.00, prob1 = 52.380952%, overround = 4.761905%, hold = 4.545455%. Source: hand calculation in content.mdx: 22/21 − 1 = 1/21 = 4.76%; hold 1 − 21/22 = 1/22 = 4.55%.
3. format = decimal, odds1 = 2, odds2 = 2, stake = $50.00 gives payout1 = $100.00, payout2 = $100.00, overround = 0%, hold = 0%. Source: hand calculation in content.mdx: a fair even-money line has no margin.

## FAQ

### How do I read a moneyline such as −150 / +130?

The minus side is the favourite: you stake 150 to win 100. The plus side is the underdog: a 100 stake wins 130. A 100 stake pays 166.67 in total on the favourite and 230 on the underdog.

### What is the bookmaker’s margin or hold?

It is the share of the money staked that the bookmaker keeps when the bets on both sides pay out the same amount. For −110 on both sides it is 1/22, about 4.55%.

### What is the difference between the overround and the hold?

The overround is how far the implied probabilities add up past 100% (4.76% for −110 / −110). The hold is the same margin measured as a share of the money staked (4.55%). The hold is always a little smaller.

### Why do the two implied probabilities add up to more than 100%?

Because the odds on each side are shorter than fair odds. The extra over 100% is the bookmaker’s margin. A fair line, such as decimal 2.0 on both sides, adds up to exactly 100%.

### What if the implied probabilities add up to less than 100%?

Then the overround and hold are negative. This happens when the two odds come from different bookmakers and leave room for an arbitrage. The arbitrage calculator shows the stakes for that case.

## Sources

- Wikipedia, Fixed-odds betting (odds formats and overround): https://en.wikipedia.org/wiki/Fixed-odds_betting
- Grinstead and Snell, Introduction to Probability, 2nd ed., American Mathematical Society, section 1.2, odds and probabilities (page 28): https://math.dartmouth.edu/~prob/prob/prob.pdf
- National Council on Problem Gambling, help and treatment (1-800-MY-RESET): https://www.ncpgambling.org/help-treatment/