Understanding Casino Odds: Probability, Payouts and Expected Value
Every casino bet has two numbers attached: the probability that it wins and the payout it offers when it does. The house edge lives in the gap between them. Once you can convert odds into probabilities and calculate expected value, you can evaluate any bet in a casino or at a bookmaker in under a minute. This guide belongs to our casino tips and strategy section.
Odds Formats and How to Convert Them
| Format | Example | Meaning | Implied probability |
|---|---|---|---|
| Casino “to 1” | 35 to 1 | Win A$35 profit per A$1, plus your stake back | 1 / (35 + 1) = 2.78% |
| Decimal (used by Australian bookmakers) | 3.00 | Total return per A$1, including stake | 1 / 3.00 = 33.3% |
| Fractional | 2/1 | A$2 profit per A$1 | 1 / (2 + 1) = 33.3% |
| American | +200 / -150 | Profit per US$100 / stake to win US$100 | 100 / 300 = 33.3% / 150 / 250 = 60% |
Quick conversions: decimal = fractional + 1. “35 to 1” in a casino equals decimal 36.00. Implied probability is always 1 divided by decimal odds.
True Odds vs Payout Odds
True odds reflect the actual probability. Payout odds are what the casino pays. In a mathematically fair game they would be equal. In a casino the payout is always slightly lower.
| Bet | Probability of winning | True odds | Pays | House edge |
|---|---|---|---|---|
| European roulette, single number | 1/37 = 2.70% | 36 to 1 | 35 to 1 | 2.70% |
| American roulette, single number | 1/38 = 2.63% | 37 to 1 | 35 to 1 | 5.26% |
| European roulette, red | 18/37 = 48.65% | 19 to 18 | 1 to 1 | 2.70% |
| Craps, Any Seven | 6/36 = 16.67% | 5 to 1 | 4 to 1 | 16.67% |
| Sic Bo, Small (4 to 10, triples lose) | 105/216 = 48.61% | about 1.06 to 1 | 1 to 1 | 2.78% |
| Baccarat, Tie | about 9.52% | about 9.5 to 1 | 8 to 1 | 14.36% |
Expected Value: The Formula
EV = (probability of winning x profit if you win) – (probability of losing x stake)
Craps Any Seven, A$10 bet: (1/6 x A$40) – (5/6 x A$10) = A$6.67 – A$8.33 = -A$1.67, or -16.67% of the stake.
European roulette red, A$10 bet: (18/37 x A$10) – (19/37 x A$10) = -A$0.27, or -2.70%.
Negative EV means the bet loses money on average. Every standard casino bet has negative EV for the player; the size of the negative number is what you compare. Our house edge guide lists the figures for most games.
Counting Outcomes: Dice and Cards
Many casino probabilities come from counting combinations.
- Two dice (craps): 36 combinations. A total of 7 has six (1-6, 2-5, 3-4 and reverses), so 6/36. A total of 2 has one, so 1/36.
- Three dice (sic bo): 216 combinations. A specific triple (e.g. three 4s) is 1/216. Any triple is 6/216 = 2.78%.
- Blackjack natural: roughly 4.8% of hands from a six-deck shoe. That is why the 3:2 versus 6:5 payout matters: switching to 6:5 adds roughly 1.4 percentage points to the house edge. See blackjack odds.
Pokie Odds Are Hidden, RTP Is Not
Pokies do not publish the probability of each combination. What they publish is the RTP (return to player), the long-run percentage returned, and often a hit frequency or volatility rating. The RTP is the useful number: house edge = 100% – RTP. The payout percentage guide explains how to find the version a casino runs, and the RTP explainer covers the detail.
Sports Odds and the Bookmaker’s Margin
Bookmakers build their edge into the odds. Add the implied probabilities of all outcomes in a market; anything over 100% is the overround.
| Market | Odds | Implied probabilities | Total |
|---|---|---|---|
| Head-to-head, two teams | 1.90 / 1.90 | 52.63% + 52.63% | 105.26% |
| Soccer, home / draw / away | 2.50 / 3.30 / 2.90 | 40.00% + 30.30% + 34.48% | 104.78% |
In the first market the bookmaker’s expected margin on balanced action is about 5%. Comparing that with a 1.06% Banker bet or a 2.70% roulette bet shows that sports betting is not automatically cheaper than casino play. The difference is that skill in estimating probabilities can matter in sport; in casino games the probabilities are fixed. More in sports betting vs casino games.
Probability of Streaks
For independent bets, multiply probabilities. The chance of five losses in a row on red is (19/37)^5 = 3.57%. The chance of winning three in a row is (18/37)^3 = 11.5%. These numbers matter when evaluating staking plans; see betting systems. They do not mean that a streak, once started, changes the next result; that error is the gambler’s fallacy.
Three Common Odds Mistakes
- Confusing “pays 2 to 1” with “pays 2 for 1”. 2 to 1 returns A$3 on a A$1 bet (A$2 profit plus stake). 2 for 1 returns A$2 in total, which is only A$1 profit. Some game show and keno paytables use the “for” format.
- Reading a big multiplier as good value. A 500x maximum prize says nothing about the edge. A 1-in-1,000 chance paying 500x has a return of 50%.
- Adding probabilities that overlap. Betting red and the first dozen does not give 48.65% + 32.43% coverage, because 6 numbers are counted twice. Count the distinct winning pockets instead: 24 of 37, or 64.86%.
A 60-Second Check for Any Bet
- Find the probability of winning (count outcomes, or read the rules).
- Convert the payout to decimal odds (to-1 payout + 1).
- Multiply: probability x decimal odds = return per A$1.
- Subtract from 1: that is the house edge. Example: 18/37 x 2.00 = 0.973, so the edge is 2.7%.
Frequently Asked Questions
Divide 1 by the decimal odds. Odds of 4.00 imply a 25% probability; odds of 1.50 imply 66.7%.
True odds reflect the real chance of winning. Payout odds are what the casino pays. The casino pays slightly less than true odds, and that gap is the house edge.
Among common bets, high-payout propositions such as craps Any Seven (16.67% edge) and baccarat Tie at 8 to 1 (14.36%) are among the most expensive.
Not automatically. A typical two-way market with odds of 1.90 on each side carries about a 5% margin, higher than several casino table bets.
Multiply the win probability by the profit, subtract the loss probability multiplied by the stake. A negative result is the average amount you lose per bet.
Knowing the odds does not change them. Gambling is for adults 18+; if it is causing harm, contact Gambling Help Online on 1800 858 858.