The expected value (EV) is an anticipated value for a given investment at some point in the future. In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur, and summing all of those values.
To make it clearer, let’s look at this part of the story with an example. Let’s take roulette, classic European, with one zero. Something like this:
For each gambling game, two concepts are defined: House Edge (HE) and Return To Player (RTP). Essentially it’s the same thing, but from different sides.
- House Advantage / House Edge (Casino Advantage) is the percentage of each bet that remains with the casino.
- Return To Player is the percentage of each bet that remains with the player.
Both concepts and expected value (EV) are calculated in the “long term” from the point of view of probability theory. This means that if the RTP of a slot machine is 95%, then the player is guaranteed to get 95% of their money back, but only if they play for a very long time.
This is not a problem for the casino; it has many players who all play a lot together. This means that there are a lot of bets happening every day. Some of them will be winning, some will be losing, but on average, over the course of a month of life, the casino will receive its 5% income from bets on this machine.
Slot games expected value (EV).
There are core elements that must be considered while claiming a bonus in order to foresee potential outcome or expected value (EV). Wagering requirements, game RTP (sometimes max. bet amount and maximum win cap). A bonus wagering requirements (i.e. x40) largely determines expected value outcome.
Lets take 100% Match Bonus of €100, which would require a total of €4000 wagering/playthrough, and which can be used mainly on slot games (applicable games) with the house edge of approx. 5.00% (average casino margin on slot games). The formula will look like:
EV of bonus = (€100) – (5%) x (€4000)
EV of bonus = (€100) – (€200)
Total EV of bonus = – €100
So, it takes approx. €100 extra in trying to wager/playthrough the bonus and which makes this bonus epected value (EV) negative.
Hint: in order to make this bonus expected value neutral or make some gain, you have to seek and play low volatility slot games with an avg. RTP 97% and above. This tactics can be utilized only on applicable games and lowest possible bet amount. However, many casinos have a long list of bonus excluded games, which would prevent to play high RTP and various bonus feature games.
Important: please note, aforementioned outcomes might vary due to game data complexity, such as game volatility, hit rate, stake amount, specific game RTP etc., hence only theoretical values can be considered.
The main thing to remember is that the mathematical expectation does not guarantee that we will get exactly the result on the first try. Maybe we won’t even get the tenth. But if we continue these attempts long enough, then we will definitely get closer to the desired result.
Roulette games expected value (EV).
Let’s see why this happens from a mathematical point of view. There is a roulette with 37 sectors. If you bet $1 on one of them and win, you will receive $35 for it (these are the rules of roulette). Your bet is added to them and in total you are left with 36 dollars. And the chances of guessing were 1/37. This difference between the chance of winning and the payout is where the casino’s income lies. Yes, the same rule applies in sports betting, but I don’t know how exactly the probability of a team winning is calculated.
Let’s calculate the exact numbers for roulette. For those who didn’t miss the chance to study probability theory, I’ll say right away that HE is just a mathematical expectation, no magic.
So, the formula for calculation:
HE = p_lose * bet – p_win * payoff,
where p_win is the probability of winning, p_lose is the probability of losing, payoff is the payout in case of winning, bet is the bet.
As you can see, everything is quite simple and can be reduced to the usual construction of a win/loss table and basic probability theory.
What bet size to take is absolutely unimportant, the main thing is to take the corresponding payment, so let bet = 1 dollar.
Then
HE = 36/37 * 1 – 1/37 * 35 = 36/37 – 35/37 = 1/37 = 0.027.
The percentage turns out to be 2.7%, which consistently goes into the casino’s pocket.
What if we only bet on red/black? Let’s check.
Let me remind you that there are 18 red sectors, 18 black sectors and one special sector – zero. It turns out that if you bet on red, then 18 cells are “on our side” and 19 are playing against us. The payout when betting on color is one to one.
HE = 19/37 * 1 – 18/37 * 1 = 1/37 = 0.027.
Coincidence? Definitely not. Whatever tactics you follow, it is impossible to get HE < 2.7% when playing European roulette.
I hope the general idea of the expected value (EV) here is clear – they always pay less than what it would cost for the risk taken.
The numbers differ for different games, some more, some less. For example, on underground house edge slot machines it can be 40% (and a “twisted” random number generator on top), and on licensed slot machines from a popular casino it can be equal to a couple of percent.
