How to convert betting odds into implied probability

Decimal odds are a multiplier

Decimal odds are the international standard. Multiply the stake by the odds and the result is everything the bookmaker pays back.

Stake 100 at 2.50 and 250 comes back. The original 100 sits inside that number, so the profit is 150.

Longer odds pay more and land less often. Odds of 1.20 win often and pay little. Odds of 10.00 pay a lot and rarely win.

The same odds in three formats

Britain uses fractional odds. 3/2 means winning three for every two risked. Fractional odds show the profit only, so the stake comes back on top of it.

The United States uses a plus or minus sign. These are also called moneyline odds. Plus shows the profit from a stake of 100, so +150 pays 150 profit. Minus shows the stake needed to win 100, so -125 means risking 125.

A minus sign only means the outcome is the more likely one.

Two more formats appear on Asian sites. Hong Kong odds are decimal odds minus one. Indonesian odds are American odds divided by 100. Odds of 1.80 become 0.80 in Hong Kong and -1.25 in Indonesian.

Every conversion formula in both directions

Into decimal odds:

• Fractional to decimal: divide the top by the bottom, then add 1. So 3/2 becomes 2.50.
• American to decimal: for plus odds, divide by 100 and add 1. For minus odds, divide 100 by the number and add 1. So +150 becomes 2.50, and -125 becomes 1.80.
• Percentage to decimal: divide 100 by the percentage. So 40 percent becomes 2.50.

Out of decimal odds:

• Decimal to American: at 2.00 and above, take away 1 and multiply by 100. Below 2.00, divide -100 by the decimal minus 1. So 2.50 becomes +150, and 1.80 becomes -125.
• Decimal to fractional: take away 1 and write the result as a fraction. 2.50 minus 1 is 1.5, which is 3/2.
• Decimal to implied probability: divide 100 by the odds. So 2.50 gives 40 percent.

The percentage-to-decimal line runs backwards, from an estimate of the real chance to the odds that match it. That is where the Kelly criterion guide starts.

Implied probability is a break-even win rate

The percentage inside a price is called the implied probability. It is easier to use as a target.

Say 100 bets are placed at 2.50. Winning 40 of them breaks even. Winning 45 shows a profit. Winning 35 shows a loss.

That is what 40 percent means here. It is a pass mark to beat over many bets, not a forecast about one match.

Short odds set a high mark. At 1.50 the mark is two out of three. Long odds set a low one. At 5.00 it is one in five.

-110 and the number behind it

In American markets most bets are priced at -110 on both sides. It looks like an even contest.

At -110 the stake is 110 to win 100. In decimal that is 1.9091, which most sites round to 1.91. A stake of 100 returns 190.91 and profits 90.91.

The break-even mark is 52.38 percent.

-110 is not a coin flip. It is a coin flip that has to land 52.4 percent of the time to break even.

Rounded decimal odds and exact American odds give slightly different percentages. Dividing 100 by 1.91 gives 52.36, while the exact 1.9091 gives 52.38. The converter and the chart below both work from the exact value.

Some bookmakers price the same bets at -105. American bettors call this the nickel line, or reduced juice. The mark drops to 51.22 percent, and that small gap is worth a lot over a season.

Returns and profit come from different sums

Multiply the stake by the odds and the answer is the total return, with the stake inside it.

Multiply by the odds minus one and the answer is the profit on its own.

A stake of 50 at 2.50 returns 125 and profits 75. The same 50 at -110 returns 95.45 and profits 45.45.

Odds conversion chart

Decimal odds in the chart are rounded to two places. Every percentage comes from the exact American odds, so dividing 100 by the rounded decimal can differ by a few hundredths.

Where the bookmaker fee sits in the odds

Take both sides of a market and turn each price into implied probability. Add the two together.

Inside one bookmaker's own market the total is always above 100. Two sides at -110 give 52.38 percent each, which is 104.76 together.

Those 4.76 percent above 100 are the bookmaker fee. In Europe it is called the margin. In the United States it is the vig, the juice or the hold. The words mean the same thing.

The fee is already inside the odds, the way a shop's markup is inside the price on the shelf. An even contest still loses money at -110, because the fee is paid on every bet.

Two prices taken from two different bookmakers can total under 100. That is an arbitrage, and it is what surebet scanners search for.

Comparing bookmakers by their total percentage

Adding up the implied probabilities is the fastest way to see which bookmaker is cheaper.

A bookmaker charging 2 percent beats one charging 7 percent over a season. On screen the two sets of odds look almost the same.

No other number in the odds matters as much to someone who bets often. Account limits and withdrawal speed can matter more, and neither of them is visible in the price.

No-vig odds: the price without the fee

Take a market priced 1.50 and 2.50. Those are 66.67 and 40 percent, so 106.67 together.

Divide each one by that total. The fair chances are 62.5 and 37.5 percent, which turn back into odds of 1.60 and 2.67. These are called no-vig odds, or de-vigged odds.

The method spreads the fee evenly across both sides, so it cannot show which side is carrying more of it. On two-way markets that assumption is close enough to be useful. On long odds the fee is usually loaded differently, so treat the answer as an estimate.

Putting the second price into the converter

The converter at the top of this page takes the opposite price as well as the first one.

With both sides entered it stacks the two implied probabilities on a single bar and totals them. Anything past 100 percent is drawn as hatched overflow, which is the fee made visible.

Under the bar it shows the no-vig odds for both sides.

If the two prices total under 100, the display switches to the arbitrage profit instead. Two prices from one bookmaker will never do that. Two prices from different bookmakers sometimes will: 2.10 and 2.00 come to 97.62 percent, which is a profit of 2.44 percent whichever side wins.

Decimal is the format to compare in

Change the odds format in account settings to decimal.

Comparing decimal odds takes no thought, because the bigger number always pays more. Comparing 15/8 with 17/9 takes a calculator. In decimal they are 2.875 and 2.889.

Decimal odds also turn into implied probability with one division, and that percentage decides whether a bet is worth making.

The percentage is the bookmaker's opinion

Converting odds is arithmetic. The answer is always right, and it settles nothing.

The implied probability inside a price is the bookmaker's opinion with the fee added on top. It is not the real chance of anything.

A bet makes money only when the real chance is better than that percentage. Working out the real chance is the hard part, and no converter does it.