Every casino game ultimately comes down to odds. One game might look very different from another, but if they have the same odds, you’ll experience similar wins and losses over the long term.
In the short term, luck plays a big factor. One player might hit a slots jackpot, another might go on a losing streak. But over time, the odds take over. That’s the Law of Large Numbers we talked about in our first lesson, “What is Probability?”
You’ve probably heard the expression, “The house always wins.” What that means is that the odds of every casino game are in the casino’s favor.
How much they’re in the casino’s favor is called the house edge. The specific probabilities and payouts of the game determine how big of an edge that is. When we talk about a game’s “odds,” we’re talking about all of those features.
Multiple Meanings of “Odds”
Discussions about casino game odds can be confusing. One of the main reasons is that there are three slightly different yet related concepts that people use that word to mean.
What they have in common is that they all involve comparing one number to another.
Odds as Probability
The first meaning of “odds” is as a synonym for probability, especially when we’re using the “X-to-1” format to express that chance.
Going back to our last lesson, remember that the first number represents your chances of losing, and the second represents your chances of winning.
For example, if someone says your odds of winning are 7 to 1, that’s seven losses for every win or a 12.5% chance.
Odds as Payouts
The second meaning of “odds” describes the payout on a bet. Here, too, you’ll usually see that expressed as one number “to” another, e.g. 8 to 1 or 3 to 2.
In this case, the role of the numbers is reversed. The first number represents how much the casino pays on a win. The second number represents how much the player has at risk.
For instance, 7 to 1 means a potential win of $7 for every $1 you bet. If you bet $25, your potential win would be 7 x $25, or $175.
Sports betting odds: Note that sportsbooks often express payout odds differently from casinos. The “American odds” favored by US sportsbooks use 100 as the base and a + or – to indicate which side the number represents. E.g. +200 means 200 to 100 (2 to 1), while -200 means 100 to 200 (1 to 2).
Odds as House Edge
Finally, people sometimes use “odds” to talk about the house edge itself. Unlike the others, this isn’t usually numerical. Rather, you’ll see the word used that way in combination with adjectives like “good,” “bad,” “better,” or “worse.”
This is always from the perspective of the player, who naturally wants the house edge to be as small as possible. If one game has “better odds” than another, that means you’ll lose less on average over the long term.
The Relationship Between Probabilities and Payouts
There’s a reason people express probability and payouts in similar ways and use the word “odds” for both.
It’s because when there’s no house edge, the two types of odds will be equal.
For example, imagine we’re betting on the roll of a standard die:
- On a 1: I win.
- On any other number: You win.
What should the stakes be to make this a fair game? Well, there are five numbers that cause me to lose and only one number that lets me win. So, the probability odds are 5 to 1 in your favor.
If this is going to be an equal bet, that means you should lay me 5 to 1 payout odds.
For instance, if I’m risking $10 and you’re risking $50, I will win $50 once for every five times I lose $10. Likewise, you’ll lose $50 once for every five times you win $10. Over the long term, we both break even.
What Does it Mean To Say “The House Always Wins”?
Of course, in a casino, the payouts won’t exactly match the probabilities. If the games were all break-even propositions, the casino wouldn’t be able to pay its staff or the overhead on the property, let alone make any profit.
To stay in business, casinos need to make money. They do so by setting their payout odds to be slightly less than the odds of winning. The difference between the two is the house edge.
“The house always wins” doesn’t mean you can’t win money on a single visit to the casino. But it does mean that every game includes a house edge. The house always comes out ahead over time when you add up all its customers’ winnings and losses.
It also means that if you play for long enough, you will eventually fall behind. That’s why you should gamble for fun, not to try to make money.
House Edge and RTP
You can measure the house edge as a percentage. Put another way, it’s the number of cents the casino will keep on average for each dollar that players bet on the game.
The opposite of the house edge is return-to-player, or RTP for short. That’s the amount that the player will win back, on average, for each dollar they bet.
You can switch from one to the other by subtracting it from 100%:
- 100% – house edge = RTP
- 100% – RTP = house edge
For instance, 95% RTP implies 5% house edge, and vice versa.
How to Calculate RTP (or House Edge)
RTP is easy to calculate when you know the game’s payouts and probabilities.
In a nutshell:
RTP equals the chances of winning multiplied by the total amount you get back on a $1 bet. (If there is more than one way to win, you add them together.)
Unfortunately, the standard odds format makes this calculation a little trickier than it needs to be. There are a few steps to the calculation when you’re starting from the odds.
As an example, we’re going to use an imaginary game with 3 to 2 probability odds and 5 to 4 payout odds.
Remember: this means we lose three times for every two times we win. And our profit when we win is $5 for every $4 we risked.
Step 1: Convert Probability Odds to Percentage
If the probability odds are “X to Y,” then the percentage chance of winning is Y ÷ (X+Y).
In our example game, 3 to 2 probability means our win percentage is 2 ÷ 5 = 40%.
Step 2: Figure Out the Total Return on a $1 Bet
The important thing to remember here is that total return = payout + stake.
So, if you bet $1 at 2-1 and win, it’s $2 profit + $1 stake = $3 total return.
If the payout isn’t expressed “to one,” you’ll need to divide since we’re considering a $1 bet.
In our example game, 5 to 4 means a $1.20 payout (5 ÷4) on a $1 bet, making a $2.20 total return.
Step 3: Multiply the Percentage by the Payout
Remember, we defined the RTP of a game as its average payout on a $1 bet. So, now we just have to multiply that payout by the chances of getting it.
In our example game, we get a $2.20 total return when we win, which happens 40% of the time.
$2.20 x 40% = $0.88, or 88% of $1.
In other words, this game would have an 88% RTP, which means a 12% house edge. That makes it a bit of a sucker’s bet; most casino games have better than 90% RTP.
Step 4: If There Are Multiple Payouts, Add Them Together
For simplicity, our example game had only one way to win. However, if you’re looking at a game with two or more possible payouts on a single bet, all you have to do is calculate them separately and add them up.
For instance, imagine a table game with the following probabilities and payouts:
- 60% lose
- 39% win (1-1 payout)
- 1% jackpot (12-1 payout)
A 39% chance of an even money payout provides 78% RTP. However, a 1% chance of a 12-1 payout adds another 13% RTP. (Verify this for yourself using the steps above!)
The total RTP for this game would be 78% + 13% = 91%.
House Edge & RTP for Common Casino Games
Of course, the odds of winning a casino game aren’t always obvious.
It’s easy enough to count the spaces on a roulette wheel and only slightly harder to figure out all the combinations for a pair of dice like in craps.
But the math gets much harder if, for instance, you’re dealing out a hand of cards. Slot machines typically don’t give you enough information to do the calculation even if you’re a math whiz.
Fortunately, in most cases, someone else has done the math for us. Here are some of the most common types of casino games, with the house edge and RTP you can expect. We’ve ordered them from best to worst (from your perspective as a player):
|Craps (Odds Bet)||100.00%||0.00%|
|Jacks or Better Video Poker**||99.54%||0.46%|
|Baccarat (Dealer Bet)||98.95%||1.05%|
|Baccarat (Player Bet)||98.85%||1.15%|
|Craps (Don't Pass)||98.64%||1.36%|
|Typical Online Slots||96.00%||4.00%|
|Baccarat (Tie Bet)||94.51%||5.49%|
|Craps (Hard Ways)||88.9%-90.9%||9.1%-11.1%|
* Blackjack has countless minor variations in rule sets, e.g. with the number of decks, option to surrender, etc., all of which affect the RTP slightly. These are ballpark RTPs.
** Video poker machines can vary in their pay tables. This RTP is for a machine with a gross payout of 9x the bet for a full house and 6x the bet for the flush.
A Note About Skill in Casino Games
Some casino games allow you to make meaningful choices that will affect your chances of winning. Blackjack and video poker are the most common examples.
People calculating house edge for these games assume that you’re playing a mathematically perfect strategy.
So, while these games often offer “the best odds” in the casino, most players don’t play them perfectly. That means that the real house edge is usually going to be bigger in practice than what it says on paper.
Casino School: Probability
This has been Probability Lesson 2 of our four-part Casino School series. Next up is Probability Lesson 3: Game Odds Vs. Payout Odds.