Expected Value

September 14, 2023

Lots of people spend & lose without knowing the real value of their casino bonus. Let me reiterate that you can not beat Casino for long term due to the built-in house edge. However, when the bonus comes in play, the rule of the game changes.

Yes you can turn a bonus cash into real money.

The basic terms we need to understand for this is Odds, House Edge and RTP

Odds are statistical likelihood of a predicted outcome.

For example betting on heads or tails has a ration of 50-50 or 1:1 chance of winning or losing. Simple.

House Edge

On most casino games there is House Edge to makes you lose in the long run. Obviously this doesn’t count as cheating as it is absolutely fair for a business to aim for a profitable structure to cover their costs with reasonable profit.

Since the house edge is in favor of the casino, you always want to find games with as low house edge as possible.

House Edge averages

To give you an idea, typically casino games have the following house edge percentages:

Blackjack 0,5 to 3%
Roulette 5 to 6%
Keno 25 to 30%
Slots 15 to 22%

Despite slots being worst of these 3 example they are still undisputed kings of online casino. And they account for a massive amount of all gaming revenue.

For simple games like slots, the House Edge is the opposite of RTP.

RTP (Return to Players)

RTP describes the pay back to players. As starburst is a very popular slot at the moment we will use is as an example.

Starburst has a RTP of 96,1% meaning that over time this slow will keep about 3,9% of the money deposited and return about 96,1% to the players.

House Edge (HE %)

As seen above you should not aim for a long term profit. And instead aim for a positive Expected value before betting. We are not here to gamble even tho this a gambling strategy guide, we are here to calculate the expected value. Our aim is therefor not to beat the casino, it’s to find out where we have a positive edge on our expected value. We will call it EV, short for Expected Value.

EV (Expected Value)

In short this is a concept in probability describing the average outcome of a bonus. As long as you only take advantage of positive EV you will surely beat the casino in the long run. There is no question to if this works or not, you simply can’t beat the math.

First we need to calculate the EV of the casino game

Simply for calculating your Casino game EV you need 2 variables:

1. House Edge
2. Total Wager amount you bet

Let’s pretend you play Blackjack with a 3% house edge, and you wager 100€ in total, you will theoretically lose 3€ Obviously this number could be a lot bigger or smaller. Relying on probability when wagering a small amount for profit is highly risky.

But when the wager amount (to be precise the number of playing games) becomes large such as 10,000€ (10€ x 1,000 times play), the loss will get a lot closer to 3%.
Therefor high roller bonuses are potentially much more profitable in the long run compared to smaller bonuses.

Finally we get to the Bonus EV

For this calculation we need 3 variables:

1. Bonus amount
2. Wager requirement
3. House edge

The math is simple: Bonus amount – (Wager requirement) x House edge = EV

To make it easier for you to see the whole picture we provide you with 2 example below one with negative EV and one with positive EV

Lets continue on the blackjack example above that had a 3% house edge. We will use 100€ on these bonus examples.

Example 1:

Let’s say you apply for a 100% match deposit bonus with a wager requirement of 40x.

Bonus amount = 100€
Wager requirement = 40 x 100€ = 4000€
House edge = 3%

100€ – (4000€) x 3% = -20€

The expected value in the end is -20€ making this a negative EV.

Example 2:

Let’s say you apply for a 500% match deposit bonus with a wager requirement of 20x.

Bonus amount = 500€
Wager requirement = 20 x 500€ = 10000€
House edge = 3%

500€ – (10000) x 3% = 200€

The expected value for this example is a positive 200€ EV.

Calculating bonus spins

We will use Spinsons current offer of 999 bonus spins as an example and use them on Starburst. To be eligible for all bonus spins we need to deposit 300€.

As I couldn’t find any info on their site what each spin are worth I’m going to assume it’s the standard value of 0,1€.

999 bonus spins x 0,1€ = 99€

The wager requirement for the bonus spins are 35x and with the information above about RTP we can see that the RTP for Starburst is 96,1% meaning that the House Edge is 3,9%.

If you really wanna go into the nitty-gritty you need to calculate the average return for each bonus spins to get our your expected bonus value.

I wouldn’t go further than this and just accept bonus spins as a “bonus”, As trying to calculate the expected value on each bonus spins has too many factors in play. Calculating the average return for each bonus spins (Number of bonus spins) x (average return from each spin) is not enough as it leaves out all the other possible outcomes such as re-spins, wilds, re-trigger and much more.

Bonus amount = 99€
Wager requirement = 35 x 99€ = 3465€
House edge = 3,9%

99€ – (3465) x 3,9% = -36,135€

I hope you enjoyed this read and if you have any questions or insight on this subject please leave a comment.