A skill, not an invitation
Slot machines and other games of chance have a built-in house edge, and no strategy, system or timing changes the odds. Most players lose money over time, and nobody should gamble money they cannot afford to lose. Gambling is illegal or age-restricted in many places, and rules differ by country. This article explains notation only, as a numeracy skill, and does not suggest placing any wager.
Odds appear in newspapers, sports coverage and general conversation, written in different styles depending on region. Each style encodes the same information, and each can be turned into a percentage chance with a short calculation.
Fractional odds
Fractional odds, common in the United Kingdom and Ireland, are written like 5/2 or “5 to 2”. They state profit relative to stake: 5/2 means a 2-unit stake would return 5 units of profit, plus the stake back.
Read as chances, fractional odds quoted this way are odds against. For a/b:
probability = b ÷ (a + b)
- 5/2: 2 ÷ 7 = 0.2857, about 28.6%
- 4/1: 1 ÷ 5 = 20%
- 1/1 (even money): 1 ÷ 2 = 50%
- 1/2: 2 ÷ 3 = 0.6667, about 66.7%
A fraction smaller than 1, like 1/2, means the outcome is considered more likely than not.
Decimal odds
Decimal odds, common across much of continental Europe, Canada and Australia, are written like 3.50. They represent the total return for each 1 unit of stake, including the stake itself. A figure of 3.50 means 3.50 back for 1 staked, so profit of 2.50.
The implied probability is simply 1 divided by the decimal figure:
- 3.50: 1 ÷ 3.50 = 0.2857, about 28.6%
- 2.00: 50%
- 5.00: 20%
- 1.50: 1 ÷ 1.5 = 0.6667, about 66.7%
To get from decimal to fractional, subtract 1. So 3.50 becomes 2.50, which is 5/2. Both 5/2 and 3.50 describe the same thing, and the table below shows this.
American odds
American odds, also called moneyline odds, use a plus or minus sign with a number, relative to 100.
- Positive numbers (such as +250) show the profit on a 100-unit stake. +250 means 250 profit on 100.
- Negative numbers (such as −200) show the stake needed to make 100 profit. −200 means staking 200 to make 100.
Implied probability:
- For positive odds: 100 ÷ (odds + 100). For +250: 100 ÷ 350 = 0.2857, about 28.6%.
- For negative odds: odds ÷ (odds + 100), using the number without its sign. For −200: 200 ÷ 300 = 0.6667, about 66.7%.
Even money is +100 (some sources show −100), and both give 50%.
Side-by-side table
| Fractional | Decimal | American | Implied chance |
|---|---|---|---|
| 1/1 | 2.00 | +100 | 50% |
| 4/1 | 5.00 | +400 | 20% |
| 5/2 | 3.50 | +250 | about 28.6% |
| 3/2 | 2.50 | +150 | 40% |
| 1/2 | 1.50 | −200 | about 66.7% |
You can check one row. For 3/2: probability is 2 ÷ 5 = 40%. Decimal is 3/2 + 1 = 2.50, and 1 ÷ 2.5 = 40%. American is +150, and 100 ÷ 250 = 40%. All consistent.
Why implied percentages often add up to more than 100%
If you convert the quoted odds for every possible outcome of an event into percentages, the total commonly exceeds 100%. Because probabilities of all outcomes should sum to exactly 100%, the excess is the margin that the organizer builds into the prices. This is the same idea as the built-in house edge in other games: the payouts are set below what the true chances would justify. In a fair world the numbers would add to 100%.
A quick numeracy exercise helps here. A coin-flip with two outcomes each quoted at 1.90 in decimal has implied chances of about 52.6% each (1 ÷ 1.9 = 0.5263). Together that is about 105.3%, so the excess of about 5.3 points is the margin. The numbers here are hypothetical.
Common mistakes
- Reading 5/2 as 5 out of 2 or as 2.5 percent. It is a 28.6% implied chance.
- Forgetting that decimal odds already include the stake.
- Mixing up the signs in American odds. A minus sign signals the favorite, a plus sign the underdog.
- Treating an implied probability as a prediction. It is a way of reading a price, and prices include a margin.
What the numbers do not tell you
Converting odds to percentages is useful for understanding the information in a quote. It does not reveal a hidden advantage, and it does not make an outcome more likely. The quoted number includes the operator’s margin, and over many plays, the expected result for the customer is negative. Over short periods, results vary widely, and that variation is not a signal that anything is due. If you want to practice conversions further, see our walkthrough of odds conversion.
If you gamble, treat it as paid entertainment, set limits first, and never chase losses. If gambling is affecting your life, a national problem-gambling helpline or local health service can offer confidential help.