Casino Expected Value (EV) Ultimate Guide – How to Value Bonuses and Games Properly

What does EV in Gambling Mean?

EV stands for Expected Value.

It is a number that indicates how much money you’ll win or lose if you play a particular casino game with real or Bonus money. Known factors are used to make the calculation, including the game’s RTP or the amount you must wager to meet the bonus conditions.

EV is predominantly used as a sanity check when looking at casino bonuses.

In short, if the EV is positive, then you’re mathematically expected to win money. If it’s negative, then you’ll probably lose.

Casino Bonus Expected Value

Have you ever wondered what the actual value of your casino bonus is?

Bonus Expected Value (EV) is a metric that a cunning gambler will use to determine whether a bonus is worth claiming. It is the amount you will be left with after you’ve claimed the bonus cash and met the wagering conditions.

You’ll know whether the money you’re getting is free or just a way for the casino to lure you into playing, knowing you’ll lose the bonus and your qualifying deposit.

An intelligent gambler is usually the one who wins.

The Expected Value Formula – Calculate EV Yourself

Typically, if the game’s RTP is 97% and you wager £10,000, you’d expect to get a long-term return of £9,700, which is a loss of £300.

If you play the same game with more than £300 of Bonus Money, the expected value becomes positive, and you should make a profit over the long term. If there’s no Bonus or less than £300, the EV will be negative, and you’ll lose.

To calculate the exact EV of a bonus yourself, you need to know:

• how much bonus funds you’re getting
• the total amount you must wager
• the RTP of the game(s) you’ll be playing

EV = Bonus Money – Game RTP x Wager Amount

To calculate the EV of a game, perform the calculation with an arbitrary wager amount, such as £1,000.

This formula is universal, as the expected value is a term from mathematical probability. We’ve adapted it for specific use in casino deposit bonuses.

You can apply the formula to any casino game you like once you know the game’s theoretical payout.

Expected value of table game and live dealer bonuses

Most bonuses are for slots, but sometimes, the casino allows table games. When table games are included, an additional penal wagering contribution is applied, sometimes as much as 10% to 20%, which makes a considerable negative value EV.

If we take French Roulette as an example, it has a 1.35% house edge with a 98.65% RTP. Let’s say it contributes 10% towards the rollover, which means that for every £1 you bet, only 0.10 qualifies for the wagering requirement.

The increased rollover amount hurts your prospects a lot. If you have £500 in bonus and have to wager £150,000 instead of £15,000 on a 98.65% game, you expect to lose a whopping £2,025.

Even if you were allowed to play Blackjack with an RTP of 99.47% using the same contribution, you’d expect to lose £795.

In most cases, having a positive expected value is impossible if you’re wagering on live dealer games that contribute 10%.

If the contribution is 20%, the calculation becomes profitable – give it a go and calculate it yourself – this is why you see it so rarely.

Feel free to check my Live Dealer Bonus page to see if there’s something with a positive EV or at least a neutral one.

What about the Expected Value of Free Spins?

Some bonuses hand out free spins on the side, which everyone ignores when calculating the EV.

You shouldn’t ignore the free spins. You need to know the cash value of each spin, and you can calculate the EV.

And let me tell you, the EV of free spins can be positive!

Let’s assume you’re getting 200 free spins at 10p each. That’s £20 right there.

If you’re playing a slot game with an RTP of 96%, you’d expect to return £20 x 0.96 = £19.20. Since you haven’t invested anything, that’s a +£19.20 EV!

The free spins won’t be wager-free in most cases, so you’ll have to meet the playthrough conditions, usually 35x or so.

In this example, if you won £19.20, you’d have to wager a total of £19.20 x 35 = £672 in the casino before you can withdraw.

If you played a 96.00% RTP slot, you’d expect to get back £645.12 for a loss of -£26.88 and an overall loss of £7.68.

However, if you were allowed to play a slot with a 98.00% RTP, the EV would be +£5.76!

This shows that free spins can be profitable and can also increase the value of the casino deposit bonus.

So, are casino bonuses profitable?

If you’ve been calculating EV for lots of casino bonuses, you’re now aware that EV is usually negative. That’s because the casinos design the bonuses with a negative EV in mind, so they end up making money from the pool of players that they issued bonuses to.

That doesn’t mean you can’t make money!

While the group will lose, your short playing session will still depend on whether you experience a brief burst of luck. The RTP won’t kick into even things out on such a small scale.

The bonus, from your perspective, gives you more game rounds, so you have more chances to get lucky and win a lot.

In a sense, any EV calculation for a casino bonus is inherently wrong, as that’s not what you’ll experience while playing.

You’ll either win big or lose it all. Calculating the EV allows us to check if the casino has given us a fair playground and compare bonuses to see which ones are the best.

Tips for increasing the EV of a casino bonus

• Play a game with high RTP – this turns the EV in your favour
• Play a high-variance game that is known to pay big
• Claim the free spins
• Don’t think about the math of the bonus

Casino Bonus Strategy

Now that you know about EV, let’s create a casino bonus strategy. A good strategy always follows the same rules.

Pick a bonus with good underlying terms and conditions that make the EV more or less okay. It’s great if the bonus has some free spins on the side, as that’s where you squeeze the extra value.

Play high-variance games that pay big when a player gets lucky, and ignore the low-variance games designed to keep you from losing too much.

You’ll play the latter when it’s time to meet the playthrough requirements.

So, high variance when you play with the bonus, low variance when you’re meeting the wagering conditions. That’s all you need to know.

Focus on high-RTP games, in both cases, to bring your EV numbers up.

Strategies for claiming deposit bonuses differ; every experienced online casino player will have a system he swears by.

But one thing’s for sure: you do not want to play games that don’t provide a chance to win big.

In other words, don’t take a deposit bonus to play Red and Black on roulette. Because all you can ever win is 1 unit. And that means you most certainly won’t win big.

What you want to do with a deposit bonus is to have a few hundred attempts at a game you know can deliver a big win. It means that low-variance online slots are out of the question.

The low-variance games that don’t lose money are good after you have already hit big when you want to meet the bonus conditions without additional risk.

Ideally, you’d get a deposit bonus to play Crazy Time or a similar entertainment show game with a good RTP, which can deliver massive wins. Or, go for an online slot with an advantageous free spins feature.

That way, you’re putting your bonus money to good use, and the chances of winning are reduced (compared to that Red/Black thing), but if you are lucky, you will have a lot of cash in your pocket when your bonus run is over.

Of course, this wouldn’t be possible if you went for a bonus with an awful EV. You’d have to win big to break even with that kind of a bonus.

Wagering Requirements Calculator

Wagering requirements for clearing bonuses have several elements you need to consider. For this example, we’ll use a wagering requirement of 40x.

The total amount you need to wager to clear the bonus is:

 Wagering Requirement = ( Bonus + Deposit ) x Wagering Requirement x Game Contribution Factor

If the bonus you got is £100 and you had to deposit £100 to get it, the wagering requirement is 40x, and you’re playing a game that contributes 100%, which is a factor of 1.00, you get this:

£200 x 40 x 1 = £8,000

In this example, you must wager a total of £8,000 to clear the wagering requirements for a £100 bonus.

Bonus only or bonus plus deposit? The wagering requirement usually applies to a bonus plus deposit, but always make sure to read the terms and conditions—you might just find a bonus for which the wagering only applies to the bonus amount!

Rollover – Deposit bonuses usually have a rollover requirement of 40x to 45x, while no deposit bonuses and free spins typically have rollover requirements of 50x or more.

Game contribution – As a general rule, slots contribute 100% or a factor of 1.00 to the wagering requirements, so every £1 you wager will contribute £1. Live games don’t contribute at all or contribute 10%, or 0.10. You’re lucky to get 20%, or 0.20 with table games.

Maximum bet – There’s always a cap on how much you can bet to clear the wagering requirements because it’s beneficial to wager more. For example, the cap might be £5, so if you wagered £7, only £5 would contribute to the wagering requirements, or you’ve broken the Bonus terms, and the casino may reject anything you’ve won. Read the T&Cs carefully!

Expected Value of Casino Games

The expected value of casino games is equivalent to their theoretical return to player (RTP) value. They’re the same thing.

If you’re playing Crazy Time, the RTP of the game as a whole is 95.41%, and that’s the EV of the game, too.

You can see all the casino games RTPs in my RTP Payouts article and the Live Dealer Game Show RTPs article.

I must note two things here.

1. RTPs are, for the most part, theoretical values that you’ll never experience during your playing time. The profitability in the short run will vary wildly, which is the foundation of gambling.
2. Different bets on the same game may have different RTPs, so pay attention when playing Crazy Time, blackjack, craps, sic bo and the like. It’s always good practice to see if different bets have different RTPs.

In some games, such as roulette, the expected value is the same regardless of your bet.

For some games, it gets complicated.

For some, you can’t know.

In Crazy Time, the EV spans from 94.41% to 96.08%, depending on your bet type. You can use Crazy Time stats trackers to come up with your answer on which bet is most profitable to bet on. In this game, the EV is influenced by how much money gets won in each of the four bonus rounds.

Sic Bo is a perfect example of a game with different RTP (or EV) values for different bet types, and players are often blissfully unaware. Super Sic Bo by Evolution has an EV of 97.22% for Small/Big and Odd/Even bets, which is superb, but the EV for a bet on numbers 5 and 16 is only 58.33%. Also, this particular game has win multipliers, so it’s possible that a bet on 7 and 14, with a base EV of 90.28%, is worth much more because it can potentially land a multiplier that goes up to 29:1.

Whenever the game hides the critical piece of the puzzle, such as the frequency of the multiplier, you can’t calculate an EV yourself. You can only trust the numbers stated by the developer.

The key takeaway is that different bets on the same game may, and often do, have different EVs. Sometimes, you can’t know exactly what the EV is, so you have to trust the developer or form your own opinion based on past results.

Positive EV Casino Games

Casinos do not offer games with a positive expected value, as they would lose in the long run.

The term +EV is common in sports betting, where it is theoretically possible to place a bet whose chances to win are higher than the odds suggest. In sports betting, you can place a bet on odds that are better than they should be – if you have more accurate information than the bookmaker.

For example, you might get a price of evens (2.00) but think the home team has a better than 50% chance to win the game. If you are correct in your assumption, a bet on the home team would be a +EV bet.

In Texas Hold’em Poker, it is also very possible to make profitable moves. The game is all about betting more and, therefore, maximising profit when the situation has a positive EV.

As far as casino games are concerned, you likely won’t encounter any positive EV situations except for one game.

Positive EV Blackjack

Blackjack is all about exploiting the favourable situation and being allowed to bet more when you know you have a higher chance to win than the dealer, which means your hand has a positive EV.

This situation is when you Double Down.

That’s your positive EV play.

Expected Value of a Casino Deposit Bonus

The usual terms for a casino deposit bonus go something like this.

You get a certain amount, say £500, and can only play slots and other games. Live dealer games and slots with high RTP do not count towards the rollover. And then you have to wager 30x the bonus amount.

The general idea is to calculate how much you expect to lose during the mandatory period of meeting the rollover conditions.

If the game you’re playing is an online slot with an RTP of 96.20%, and you have to wager 30x £500 on it, you’ll get back 96.20% of £15,000, which is £14,430. That’s 3.80% or £570.

If you have £500 in bonus funds, the Expected Value of your bonus is -£70, at least if you play that 96.20% RTP game.

If you played a game with an RTP of 97.30%, you’d probably get back £14,595 for a loss of £405 or an overall EV profit of £95.

The choice of the game you’re playing matters, so the casino restricts the games you can play using bonus funds.

Pro Tips for Calculating Casino Bonus Expected Value (EV)

Firstly, look at the terms and conditions of the bonus to see what games are allowed. You’ll most likely be looking for the highest RTP online slot among those offered.

As you can see in my RTP table of live games, many games offer excellent RTP and aren’t necessarily on your radar. Such as Baccarat, Andar Bahar, 3 Card Brag, Football Studio Dice, Sic Bo, and Spin A Win. Have a look for yourself.

Your casino will likely allow one of these games, and you might prefer it to an online slot.

When you’ve decided on which game to play, you’ve got your RTP.

Next, look at the rollover conditions and see how much money you have to wager. Pay attention to whether the requirements say you must wager only the bonus amount or the plus deposit.

When you have the total wager amount and the RTP, add them together to determine your expected loss.

For example, if your RTP is 96.50% and the total wager amount is £15,000, the calculation is:

0.965 x 15000 = 14475

Which means you expect to lose £525.

Finally, compare how much bonus money you get to the amount you expect to lose.

In the above example, if you got £500, that’s an excellent bonus. Bonuses don’t usually have a positive EV, so a minimal expected loss is the best you can hope for.

What is a Good Casino Bonus EV?

Casinos are quite adept at offering bonuses that strike a fine balance between being tempting enough for the player and beneficial for the casino on a large scale.

Casinos design good bonuses using big data, statistics of how they fared with previous bonuses they offered and a lot of math.

You can safely assume no deposit bonus in the world will have a positive expected value. The best you can hope for is a minimal negative expected value.

A good Expected Value, or a good bonus, is one in which you do not expect to lose a lot but still have a decent chance of winning, and you have a chance to win big.

If you’re getting a £500 bonus and see that the expected value is a loss of £50, that’s excellent. If the expected loss is up to £100, that’s more or less ok. You can work with that.

If you see a bonus like that, it’s a good one that gives you a fighting chance. You get some free money upfront, and your skills and luck will determine if you’ll have anything left at the end of the run.

The trick here is to eliminate those bonuses that have an awful EV. You don’t want to take those, so use the EV calculations to identify them.

Sports Betting +EV

I will briefly mention sports betting because the positive expected value, or +EV, is huge.

It’s the idea that bets can have a positive expected value because you know something the bookmakers don’t, or the odds are wrong and don’t reflect the actual probability.

Sports betting is all about identifying such situations – finding +EV bets.

The formula for expected value = (fair win probability) x (profit if win) – (fair loss probability) x (stake).

Conclusion

Practise calculating bonus expected value on your own and identify casino games that are good candidates for wagering bonus money.

The ideal bonus run is a combination of a bonus that has a good EV and a clever choice of a game (or multiple games) that you’ll be playing.

Winning money with a deposit bonus is indeed a matter of luck and skill, and it all starts by calculating the expected bonus value.

Which I hope you now know how to do!