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 are expected to lose during the mandatory period of meeting the rollover conditions.
If the game you’re playing – some online slot – has 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 a loss of 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.
For example, if you played a game with RTP 97.30%, you’d be expected to 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, which is why the casino restricts the games you can play using Bonus funds.
What about the live dealer games?
We know some casinos allow live dealer games to contribute towards rollover, but usually with only a 10% or 20% contribution in rare cases.
Is that a value proposition? Let’s do some math.
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.
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’re expected to lose a whopping £2,025.
Even if you were allowed to play Blackjack with an RTP of 99.47%, you’d still be expected to lose £795.
In most cases, it’s simply not possible to have a positive expected value if you’re wagering on live dealer games that contribute 10%.
If the contribution is 20%, the calculation suddenly 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.
How to Calculate Casino Bonus Expected Value (EV)
Firstly, look at the terms and conditions of the bonus to see what games are allowed. In most cases, you’ll 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.
Chances are, one of these games will be allowed by your casino, and you might prefer that game 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 have to wager only the bonus amount or the bonus plus deposit.
When you have the total wager amount and the RTP, put them together to see how much you’re expected to lose.
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’re expected to lose £525.
Finally, look at how much bonus money you’re getting and compare that to the amount you’re expected 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?
You can count on a casino to be quite skilled in offering bonuses. They usually make sure they are the ones that benefit in the end.
Therefore, if we know about EVs, so does the casino, except their method of calculating EVs is probably even more refined. It will involve statistics of how they fared with the previous deposit bonus they offered.
That being said, 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 for that matter, is one where you’re not expected to lose a lot but still have a decent chance of winning and winning 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 alright. 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.
You do want to give yourself a chance to win, and the chance is present for as long as the EV isn’t so poor as to hurt your chances more than it should.
The trick here is to eliminate those bonuses that have an awful EV.
Those are the ones you don’t want to partake in, so use the EV calculations to identify them.
How to make use of a reasonable bonus with a good EV
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 that you know can deliver a big win. Meaning even the 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, your bonus money is put to good use, and the chances of you 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 that has an awful EV. You’d have to win big to break even with that kind of a bonus.
Practice 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!