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Calculate expected value of your casino bonus easily (with examples!)

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Math matters. When you are looking at a sportsbook, casino or poker bonus to claim, they have conditions attached. By looking at these conditions you can quickly and easily calculate the expected value of your bonus, in order to be able to rank it against other bonuses. Bonuses on website online kladionice, for example, all list the percentage and the cash value, but to find the expected value you have to dig just a bit deeper. Let’s teach you how to do that.

Three variables

To calculate the expected value of a bonus, you need 1. bonus amount, 2. wager requirement, 3. house edge. You’re actually comparing two things: the amount of money you get and the amount of money you’ll lose while playing, and are then comparing the two to see what you have left, if anything. This is the basic principle of calculating expected value of a bonus and it applies to all bonuses.

Let’s use the Bet365 casino bonus as an example.

They are offering a 100% bonus up to €100, with a rollover requirement of 15x deposit plus bonus, so 15 x 200 = €3000. You’re obviously getting €100 for free, so let’s see how much you’d lose while wagering a total of €3000 on a certain game. Bet365 have a nice little slot game in their lobby, Bermuda Triangle, and it has RTP of 96.73%, which means the house edge is 3.27%. Of course, this is the theoretical payout over an infinite number of spins and the actual RTP will vary wildly in one playing session, but we need to use the data we can get.

If you’re wagering €3000 on something with a house edge of 3.27%, you’re expected to lose 3000 x 0.0327 = €98.10. That means the expected value of your bonus is 100 – 98.10 = €1.90. That’s not much, but if you’d choose a slot game with RTP of 98.00%, or a house edge of only 2%, then you’re expected to lose €60 while meeting the rollover requirements so the expected value of your bonus is 100 – 60 = €40.

Or, if you’re playing one of our favorite slots, Ooh Aah Dracula, that has RTP of 99.00% and even lets you purchase a bonus feature for cash as opposed to waiting for it, you’re only expected to lose €30 while meeting the rollover conditions and would be left with nice €70. Bet365 don’t have this particular Barcrest slot, so we’re just using it as a mathematical example of how much more money you’d be left with if you chose a higher-payout game.

Now, an interesting wrinkle here is that Bet365 allows the bonus to be played through on baccarat with a 25% contribution, on roulette with 20% contribution, and even on blackjack with a 10% contribution – but this is actually making things worse. European roulette has a house edge of only 2.70%, which is great, but you’d have to wager 5x more on roulette than you would on slots for the purposes of this bonus, and you’d end up with a calculation that goes like this. You get €100 for free, but have to wager €15,000 on a game with a 2.70% house edge, and you’re expected to lose €405 while doing that – so the expected value of your bonus is actually negative – minus €305.

Using this same principle, you can quickly calculate the expected value of any bonus you can get, regardless of it being a casino, poker, sportsbook or bingo bonus. The only thing that matters is calculating how much money you’ll lose while meeting the rollover requirements. That’s it. When you have that, simply see if the number is larger or smaller than the bonus you’re getting.

Advanced calculation

Any advanced calculation of expected value will not only include the house edge as such, but will also include the chance of you winning, and will sometimes even take into account your bet size. For example, if you’re claiming a sportsbook bonus and have to play through your bonus on odds 1.70 and the bookmaker already has a house edge of 8% embedded in the odds, then the bookmaker will offer odds of 1.83 on two sided bets where real odds should be 2.00-2.00. That means you have a 50% chance of winning that bet but will be losing quite a bit on the vigorish.

When it comes to slot machines, they have different degrees of variance and different hit rates (percentage of spins that produce a win), and of course the overall risk is much lower if you pick a slot game that doesn’t have a high variance, as you might just catch the high-variance slot machine at the wrong time and get no wins. What you need are slots that pay regularly, small amounts, so you can claim your bonus without going too deep into negative. Lower variance also lets you play with courage, with a larger bet per spin.

We can’t possibly give an example for this, we’re not experts in probability theory! If you are, just bear in mind the hit rate counts and you want it to be high in order to decrease variance and therefore decrease the chance of bankruptcy. Further reading: Wikipedia article on Expected Value

Conclusion

Do calculate the expected value of your bonus each and every time you want to claim one. Pick the highest-payout game in the casino and calculate the expected value if you played through your bonus on that game alone. After doing this a few times you’ll feel as if you have control over the casino and over what is essentially a random game of chance, just because you took the available data and made sense of them. Soon you’ll discover not all bonuses were created equal, and some are just not to be touched with a ten foot pole while some are a gambler’s dream.

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