# American odds

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American odds express a price as the amount you win on a $100 stake (positive numbers) or the amount you must stake to win $100 (negative numbers).

```
from probability p: if p > 0.5, A = -(p / (1 - p)) x 100; if p < 0.5, A = +((1 - p) / p) x 100
```

American odds are the standard format at US sportsbooks. A plus sign marks an underdog and tells you the profit on a $100 bet: +200 wins $200. A minus sign marks a favorite and tells you how much to bet to win $100: -150 means a $150 stake wins $100. Even money is +100, which some books also write as -100. The format is easy for whole-dollar stakes and awkward for anything else, which is why traders often convert to probabilities or decimal odds.

## How it works

To convert American odds to implied probability, use q = |A| / (|A| + 100) for negative odds and q = 100 / (A + 100) for positive odds. To convert to decimal, use 1 + 100 / |A| for negative odds and 1 + A / 100 for positive odds. Going the other way, from a probability p, use the formula above: a probability over 50% gives a negative number, under 50% a positive one, and exactly 50% gives +100.

## Worked example

American odds converted

| American | Implied probability | Decimal | Profit on $100 stake |
| --- | --- | --- | --- |
| -250 | 71.43% | 1.400 | $40.00 |
| -150 | 60.00% | 1.667 | $66.67 |
| -110 | 52.38% | 1.909 | $90.91 |
| +120 | 45.45% | 2.200 | $120.00 |
| +200 | 33.33% | 3.000 | $200.00 |
| +450 | 18.18% | 5.500 | $450.00 |


For -250: 250 / 350 = 71.43%, and $100 x 100 / 250 = $40 profit. For +450: 100 / 550 = 18.18%. The [odds converter](https://novigapi.com/odds-converter) converts between American, decimal, fractional and probability, and the [implied probability calculator](https://novigapi.com/implied-probability-calculator) handles whole markets.

## On Novig

Novig shows prices as percentages, not American odds. A 60% price converts to -(0.60 / 0.40) x 100 = -150, and a 40% price to +((0.60) / 0.40) x 100 = +150. Two Novig-specific adjustments matter. The price you can buy at is the ask, 1 minus the best bid on the other side, not the bid you see on your own side. And on live game markets the taker fee of 0.06 x P x (1 - P) per contract makes your effective odds slightly worse: buying at 40% in-game costs $0.4144 per $1 of payout, which is +141.3 instead of +150. The [Novig odds converter](https://novigapi.com/novig-odds-converter) shows both figures.

## Common mistakes

- Assuming -110 and +110 are opposites of the same price. -110 implies 52.38%; +110 implies 47.62%.
- Averaging American odds. Average probabilities or decimal odds instead; American numbers jump from -100 to +100.
- Reading -100 and +100 as different. Both are even money.

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