American odds explained: what + and − prices mean

The two halves of the format

Above +100, the number is profit on a hundred-dollar stake. A bet at +200 wins $200 for every $100 risked and returns $300 in total. A bet at +550 wins $550 and returns $650. The stake comes back on top in both cases, which is the detail that trips people who read the number as the payout rather than as the profit, and it is worth fixing early because every later figure on this page depends on it.

Below −100, the number is the stake required to win a hundred dollars. A bet at −150 risks $150 to win $100, returning $250. A bet at −400 risks $400 to win $100, returning $500.

+100 sits between them and means the same thing either way: risk $100, win $100. Nothing is quoted between −100 and +100, because that region would describe a price that pays less than it costs.

The sign also carries information. Minus marks the side the market considers more likely, plus the side it considers less likely, and the size of the number says how strongly. That is the part people read correctly straight away.

The part that causes trouble is that the magnitude runs in opposite directions on either side of the crossing. A bigger plus number means less likely. A bigger minus number means more likely, and the two halves of the scale therefore read backwards from each other.

Converting to probability

Every price implies a win rate, and it is the rate at which the bet breaks even. For a plus price, divide 100 by the price plus 100: +200 gives 100 divided by 300, or 33.33%. For a minus price, divide its size by its size plus 100: −150 gives 150 divided by 250, or 60%.

These implied figures are the most useful thing American odds carry, and they are the reason any serious treatment of American odds explained gets to probability quickly. A price is an opinion about how often something happens, expressed in an awkward unit. Converting it back makes it arguable: if the market implies 60% and you think 50%, you now have a specific disagreement instead of a feeling.

One caution: the implied probability includes the sportsbook’s margin, so it is always slightly worse than the market’s honest estimate.

Both sides of a spread implying 52.38% adds to 104.76%, which no set of probabilities can, and removing the margin needs every price in the market rather than the one you happen to be looking at. That is what the vig calculator does.

Why decimal is the working format

American odds are what US sportsbooks display, and they are poor to calculate with. Decimal odds include the stake in the figure, so 1.909091 means a dollar returns a dollar ninety-one. That single property makes them multiply cleanly, which is what makes parlay arithmetic possible, and invert cleanly, which is what makes probability arithmetic possible.

Converting is mechanical. A plus price divided by 100 plus 1 gives the decimal, so +200 becomes 3.00. For a minus price, 100 divided by its size plus 1, so −150 becomes 1.6667. Fractions convert the same way once you read them as profit against stake, and Hong Kong odds are only decimal odds with the stake taken out again. Nothing is lost at any step and nothing is approximated, which is why the odds calculator can hand the same price back in four notations and every one of them agrees about the payout.

Fractional odds survive in horse racing and British markets, quoting profit against stake: 10/11 means eleven risked to win ten. Hong Kong odds are decimal odds with the stake removed, so 1.909091 becomes 0.909091. All four describe the same bet, and which one you see is a matter of where you are and not what you are buying.

The practical habit worth forming is to read the American price for the direction and convert for the arithmetic. −110 tells you instantly that this is the favoured side of a near-even market. 52.38% tells you what it costs, and that is the number that decides whether the bet is worth making.

Two habits make the format easier to live with. The first is to stop reading the number as a quantity and start reading it as a rate: +200 is not “two hundred” but “one in three”, and −150 is not “a hundred and fifty” but “three in five”. That reframing removes most of the confusion the sign creates, because probabilities run in one direction no matter which side of the crossing they came from.

The second is to notice how compressed the short prices are. Between −110 and −130 lies less than five percentage points of implied probability, and between +200 and +300 lies more than eight. American odds spread the unlikely end of the scale across a huge numeric range and squeeze the likely end into a narrow one, which is why small movements on heavy favourites matter more than they look and large movements on longshots matter less.

That compression is also why line shopping is worth more on short prices than on long ones. Moving from −115 to −105 is a bigger change in what you are paying than moving from +400 to +420, even though the second looks like the larger number. Converting both to probability makes the comparison obvious in a way the posted prices never do.