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The Sum of the Implied Probabilities Is Never One Hundred

Published 9/15/2026 · 4 min read · Everyday calculators

Camille Laurent

Camille LaurentFinance writer at OneKitly

Tax · Personal finance

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In short

The three notations say the same thing in different clothes. American -110 means staking 110 to win 100; decimal 1.909 means a stake of 1 returns 1.909 including the stake; fractional 0.909/1 means winning 0.909 for every 1 risked. Converting between them is arithmetic and the converter shows all three at once. The number that matters is the fourth column: one divided by the decimal odds gives the implied probability, 52.4 % for -110. Do that for both sides of a two-way market and add them up. A fair market would total exactly 100 %, since one of the two must happen. Two sides at -110 total 104.8 %. Those 4.8 points are the margin — the bookmaker's built-in edge, called the vig or the overround — and they are the reason a bettor who picks correctly half the time still loses money. A tighter market, -150 against +130, carries 3.5 points, and the only way to see either figure is to convert and add.

Two sides both priced at -110 imply 52.4 % each. That adds to 104.8 %, and the 4.8 points that should not exist are the margin — visible the moment you convert the odds.

Why the notations exist at all

Each was designed to make one question easy at the cost of the others. Decimal answers what comes back, stake included, which is why it dominates in Europe and why it is the easiest to reason with. Fractional answers what is won on top of the stake, which is the older British form and reads naturally at long prices. American answers two different questions depending on sign — a negative number is what you must stake to win a hundred, a positive one is what you win on a hundred staked — which is why the same market flips between the two forms around an even chance. None of them shows the probability, and that is not an oversight: it is the number the customer would use to compare markets.

What the margin costs a bettor who is right half the time

At -110 on both sides, staking 110 to win 100, a bettor who wins exactly half of a hundred bets wins fifty times a hundred and loses fifty times a hundred and ten: five thousand won against five thousand five hundred lost. The margin does not take a cut of the winnings, it moves the break-even point — and at these prices break-even is 52.4 % rather than 50 %. That is the number to hold onto: beating a market is not picking winners more often than losers, it is picking them more often than the implied probability, and the implied probability is set above the truth on purpose.

Decimal
The same odds in three notations, and what they imply
AmericanDecimalFractionalImplied probability
-2001.5000.500/166.7 %
-1101.9090.909/152.4 %
+1502.5001.500/140.0 %
+3004.0003.000/125.0 %
Both sides at -1101.909 each104.8 % — margin 4.8 points
Betting Odds ConverterConvert between American, decimal, fractional odds and implied probability, with the bookmaker's vig.Try the tool

Frequently asked questions

Is the implied probability the real probability?
No — it is the price, and the price includes the margin. To recover an estimate of the market's actual view, divide each implied probability by their sum: at -110 both sides, 52.4 divided by 104.8 gives exactly 50 %. That normalised figure is what the market thinks, and the gap between it and the raw implied probability is what the market charges.
Why do some markets carry a bigger margin than others?
Broadly, the harder the outcome is to price and the fewer people are betting on it, the wider the margin. Two-way markets on major events are the tightest; markets with many possible outcomes stack a margin on each one, so the sum can exceed 100 % by a great deal more than five points. Adding up the implied probabilities of every outcome is the fastest comparison you can make between two offers on the same event.
Is this a betting strategy?
No, and it should not be read as one. It is a conversion and a piece of arithmetic that makes a cost visible, which is worth knowing whether or not you bet. The margin means the average participant loses over time by construction, and no notation, conversion or system changes that — betting is entertainment priced accordingly, and treating it as anything else is where the harm starts.

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Nothing here is betting advice. The margin means the average participant loses over time; if gambling is causing you difficulty, national helplines exist in every country covered by this site.

Sources

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