Casino games are games of chance with a built-in house edge. No strategy, system or timing changes the odds in the player’s favor over time, and most players lose money over time. Nobody should gamble money they cannot afford to lose. Converting odds helps you read the numbers honestly; it does not make a bet more favorable.
The same chance, written several ways
A single chance can be expressed in many forms. Take one roll of a die landing on a specific number:
- Fraction: 1/6
- Decimal: about 0.1667
- Percentage: about 16.67%
- “1 in 6”
- Odds against: 5 to 1
All of these describe the same thing. Confusion starts when a source uses one form and the reader assumes another, especially with the last one.
Probability versus odds
Probability compares the favorable outcomes to all outcomes: 1 out of 6.
Odds against compare the unfavorable outcomes to the favorable ones: 5 unfavorable to 1 favorable, written “5 to 1 against.”
That is the single most important distinction. A probability of 1/6 and odds of 5 to 1 are the same chance but are not the same number.
Converting step by step
Fraction, decimal and percentage
- Fraction to decimal: divide the top by the bottom. 3/8 = 0.375.
- Decimal to percentage: multiply by 100. 0.375 = 37.5%.
- Percentage to decimal: divide by 100. 12.5% = 0.125.
- Decimal to fraction: write it over a power of ten and simplify. 0.125 = 125/1000 = 1/8.
Probability to odds against
If the probability is p, the odds against are (1 − p) to p. Using fractions, this is usually easier: if the probability is a/(a + b) the odds against are b to a.
- Probability 1/4 (25%): there are 3 unfavorable outcomes for every 1 favorable, so odds against are 3 to 1.
- Probability 1/13 (an ace from a full deck, 4 of 52): odds against are 12 to 1.
- Probability 1/37 (one number on a single-zero wheel): odds against are 36 to 1.
- Probability 1/38 (one number on a double-zero wheel): odds against are 37 to 1.
Odds against to probability
If the odds against are a to b, the probability is b ÷ (a + b).
- 3 to 1 against: 1 ÷ 4 = 25%.
- 5 to 2 against: 2 ÷ 7, about 28.57%.
- 1 to 2 against (often described as “2 to 1 on”): 2 ÷ 3, about 66.67%.
- 1 to 1 (even): 1 ÷ 2 = 50%.
“1 in N”
A probability of p is “1 in N” where N = 1 ÷ p. Two dice totaling seven can happen in 6 of 36 ways, which is 1/6, or 1 in 6. That is the same as odds of 5 to 1 against. The 36 equally likely ordered results of two dice are discussed in the guide to two-dice outcomes.
Quick reference table
| Probability | Decimal | Percentage | Odds against |
|---|---|---|---|
| 1/2 | 0.5 | 50% | 1 to 1 |
| 1/3 | 0.3333 | 33.33% | 2 to 1 |
| 1/4 | 0.25 | 25% | 3 to 1 |
| 1/5 | 0.2 | 20% | 4 to 1 |
| 1/6 | 0.1667 | 16.67% | 5 to 1 |
| 1/10 | 0.1 | 10% | 9 to 1 |
| 1/37 | 0.0270 | 2.70% | 36 to 1 |
The decimal and percentage columns are rounded.
Payout odds are a separate number
One reason odds conversion matters is that a game’s payout ratio is written the same way as odds, but it is a different quantity. A single-zero roulette number has odds against of 36 to 1, but the straight-up bet is paid at 35 to 1. That one-unit gap is what makes the bet cost money over time, and it is the foundation of how payout ratios are read in casino tables. Comparing the odds against with the payout is the quickest check of whether a bet is fairly priced; here it is not.
Be careful with names, too. A bet called “even money” pays 1 to 1, but the chance of winning it is less than 50% because of the zero pocket. The label describes the payout, not the probability, a point developed in the article on even-money bets.
A different “decimal” form
Some sources write “decimal odds,” such as 4.0. This is the total return per unit staked, including the stake, so 4.0 pays 3 profit for 1 staked, which is 3 to 1. The implied probability for fair pricing would be 1 ÷ 4.0 = 25%. In casino games the quoted payout and the true probability do not line up, and the difference is the edge. The wording around payout odds varies between sources, so check whether the stake is included before comparing numbers.
Rounding and sanity checks
- Percentages are usually rounded, so converting back may not return the exact original.
- All probabilities of mutually exclusive, exhaustive outcomes should sum to 100%. Eighteen red pockets, eighteen black pockets and one green on a single-zero wheel: 18/37 + 18/37 + 1/37 = 37/37.
- If your conversion gives a percentage above 100% or below 0%, something is wrong.
- Always check which direction you are converting: “odds against” put the unfavorable count first.
With these conversions, any statement of a chance can be restated in the form you find easiest. The next step is attaching money to that chance, which is the job of expected value.