Expected Value in Gambling

Expected Value refers to the average outcome of any sort of variable. In gambling, expected value can be used to calculate how much you can expect to win from a given bet (or lose, which is much more likely.)

The terms ties in closely with RTP, house edge, and other important aspects of casino strategy. Let’s take a close look at what expected value means in gambling and how we can use it to improve our skills.

Table of Contents

What is Expected Value?

It’s important to understand that this term isn’t solely used in gambling. It originates from probability theory in mathematics, and is commonly used in economics.

Expected value is the mean average of a large number of independent, variable outcomes. We’ll try to translate that a bit. Expected value is a sort of predicted outcome of a variable, based on the average probability of each outcome. Let’s explain with a quick example.

Say you’re rolling a 6-sided die a thousand times. We’ll use dice because every outcome is equally likely, and there are six of them. If you keep rolling the dice, you’ll statistically eventually get the same outcome a roughly equal number of times.

If we add all of the results together and divide them by the number of rolls, we’ll probably get somewhere around 3.5. That’s the expected value of rolling dice. Every time you roll dice, the result will be 3.5 on average.

Keep in mind that the definition of expected value may slightly vary depending on who you ask. For example, in investment economics, the expected value (EV) is an anticipated average value for an investment in the future. It uses the same principles but for different purposes.

Importantly, expected value in the context of gambling and investments shows the profit or loss you’re about to see.

In other words, expected value in gambling shows how much your stake is going to change and not just the flat total.

Test out your new knowledge at the Mr Green casino, featuring all your favorite games!

Expected Value and House Edge

Now let’s go back to casino games and how any of this relates to them. You may have noticed that all this talk of probability ties in closely to Return to Player rates, or RTP. There’s a reason for that.

First of all, you have to understand that all casino games were designed to give players a negative expected value. That’s why they say that the house always wins. On average, every bet made at a casino will lose. That’s what luck-based gambling is actually all about – hoping for results that are decidedly not average.

Return to Player is basically an inverted, percentage representation of the expected value of a bet. Again, let’s translate.

By inverted, we mean that you’re representing how much of your stake you’ll keep, not how much your stake will change. Basically, RTP is your stake minus the expected value.

This leads us to the next conclusion: that the terms expected value and house edge are almost interchangeable. They show the same thing in a slightly different way.

Specifically, expected value in gambling does take into account the size of your stake. For instance, say you’re betting $10 in a game of European roulette. As we all know, it has an RTP of 97.30%, which means the house edge is 100-97.3=2.7%.

If you keep making the same bet with the same stake over and over again, you will theoretically lose $0.27 each time. Some bets will win, others will lose, but on average, you’re losing 27 cents per spin. Like we said – the house always wins.

How to Calculate Expected Value of Any Bet

So now you know the expected value of roulette bets. What about other games?

We’ll go through some of the most popular ones later. For now, we’ll give you a simple formula for calculating the expected value of bets at any moment.

Expected Value=((probability to win) x (profit)-(proability to lose) x (stake) )/Stake

That’s fairly easy to remember. And we can confirm it using the roulette numbers from above. Let’s say you’re making an Even Money bet, which has a probability of success of 48.60%, which is 48.6/100 or 0.486. You can find the probabilities for all roulette bets in our guide.

Your stake is $10. The profit is also $10 – Even Money pays 1:1, after all.

Expected Value=( (48.6/100 x 10)-(51.3/100 x 10) )/10
Expected Value=( (0.486 x 10)-(0.513 x 10) )/10
Expected Value=(4.86-5.13 )/10
Expected Value=(-0.27)/10
Expected Value=-0.027

In other worlds, you’re expected to lose just under 3 cents with every roulette spin.

Before you ask – there’s no real way to get a positive expected value in gambling. As we said, the games were designed so that it’s always negative. The only real exception is counting cards in blackjack, which boils down to waiting until the deck offers positive expected value. That’s a story for another time, though.

Alternatively, you can use live casino bonuses to offset or decrease negative expected value. Check out these offers to boost your bankroll:

$5,000 + 30 Free Spins Welcome Bonus

A three-tier deposit offer with up to $5000. New Players only. 18+. Please gamble responsibly. Full T&Cs apply.

Keep The Game Going With Loyalty Cashback

Get 15% back on all deposits made during a single week on the following Monday. 18+ only. Please gamble responsibly. Full T&Cs apply.

Calculating House Edge

You can use the same formula to calculate house edge! Simply use the percentage probability of the outcome instead of dividing it. In the above example, you would use 48.6 instead of 0.486, and so on.

Expected Value in Popular Casino Games

There’s a simple reason why we can’t simply list the expected value for all types of games – because it depends on the size of the stake. As you may have noticed, though, the house edge is pretty much the same thing.

However, expected value can also be shown as a percentage if we just add a minus in front of the house edge. That way, it’s presented as a percentage and can be applied to any bet, regardless of the size of your wager.

Casino Game	Expected Value
European Roulette	-2.73%
American Roulette	-5.26%
Blackjack	-0.5% on average, varies with rules
Baccarat Player Bet	-1.2%
Baccarat Banker Bet	-1.05%
Caribbean Stud Poker	-5.22%
Casino Hold’em	-2.16% on average, varies with rules
Craps	From -1.36% to -14.35%

Casino Games With Highest Expected Value and Where to Play Them

Statistically speaking, blackjack is the best casino game to play in the long run. Of course, that’s assuming you’re familiar with basic blackjack strategy.

That said, every game on the casino floor technically operates at a loss for you. That’s why gambling is primarily should be seen as entertainment – you’re paying to have fun.

Which doesn’t mean we don’t want to win, of course. Picking the games and bets with the highest expected value is by far the best option for your bankroll. Of course, picking the right casino that hosts player-friendly tables is also important. You can check out our live casino reviews for a whole list of recommendations, or pick one of these highlights:

4.9/5

April 2024

The 888 brand did not become an online gambling empire for no reason. The live casino section offers tables from some of the best and brightest in the business, and all of it is wrapped up in a nice, convenient, and accessible package. Couple that with award-winning customer support and a solid reputation for fairness, and you can’t go wrong with 888casino.

4.2/5

April 2024

BetOnline.ag has been a favorite amongst US casino players for a number of years now. They have lots of blackjack tables, plus variants of other games. Give them a shot, you’ll love it.

FAQ

How do you calculate expected value in a casino?

The quickest way is to look at the game’s RTP, which must be legally displayed. Subtract the RTP from one, and you’ll get the house edge of a game. For example, a game with a 5% house edge has a -5% expected value. Alternatively, you can use the formula we described above.

What is the expected value of blackjack?

If you play using basic strategy, the expected value of blackjack is -0.5%. However, this may vary based on the table rules and the cards currently remaining in the shoe.

Why Is expected value important?

Expected value in casino games gives you a very clear picture of how much you’re winning or losing. Better yet, it predicts the exact amount you will win or lose over a long period. That’s valuable for making casino strategies and managing your spending.

Can expected value be 0?

Yes. In gambling, an expected value of 0 would be a game with no house advantage. It would be a fully fair and balanced game. However, casinos need to make money somehow, so there is no such game.