Expected Value and the Math behind the Casino - Investigation on Behalf of the Gamblers
Expected Value(EV) in Casino Games
When the SQUAD #GamblingGang rolls up to the casino, we are ready to go to battle and put in a shift. With expectations of profiting and dreams of winning it big, what does the math say about our opportunity and expected win/loss. We attribute luck to the outcome, but luck is really just a physical manifestation of the mathematics at work, plus your individual “skill” and intuition in action.
Every game of chance, from the money wheel to roulette or even a coin toss, is based on the math. Every time you flip a coin it will land on either heads or tails(50/50 chance). In other games, the chances and odds are more complicated, but still absolutely calculable.
While we can never say with certainty how we will do in an individual gambling session, we can definitely say we have a good idea of how we will perform over the long run / large sample size if we play a certain game for an extended time(always gotta put in a good shift) based on the numbers. This expectation is called the “expected value” by the experts and it determines just how much we will be winning or losing over playing in the long run.
Return to Player (RTP) and House Edge
Each gambling game that is played against the house comes with a certain advantage for the house. This advantage is called the house edge and it is the difference between the total percentage of money returned to the player by the game and the overall amount of bets made.
Return to player (RTP) percentages (%) are the one stat that is always displayed on electronic games and well-known in card games like blackjack or baccarat. This percentage signifies the percentage of all money wagered on the game that will be paid back through various winnings.
In a game of blackjack, players can come close to breaking even and leave the house with just a 0.5% edge, if they apply the correct strategy. Other games, such as Slot Machines, can often give the house as much as 10% or even 20% edge, which means that the long-term return of these games will be very negative for the gamer. Additionally, Slots have a volatility rating, so some will pay big with lots of losses along the way, while other will pay smaller payouts more frequently.
The expected value of the game has everything to do with the RTP of the game in question. If you are playing a game that has a 90% RTP (and a 10% house edge), you are expecting to lose 10% of your bets in the long run. I call this the rake rate, as the casino slowly dwindles your stack of chips or bankroll. If you are betting $10 per spin, you will theoretically be losing $1 in every spin. Naturally, the cadence of the game will see you win on many spins and lose on others, but the overall result will be such that you will be losing a dollar every time you spin.
Therefore, one approach to gambling smartly and efficiently is to play games that have the best possible RTP and the lowest house edge. This means deliberately playing games like poker or blackjack and applying the best possible strategies each time, to limit the house edge and maximize your winnings. This may not sound like too much fun, but it’s what the numbers say and a solid approach.
I call Craps, Blackjack and Baccarat the Holy Trinity of Table Games. My strategy is to play these games to grind out a profit and winnings, enhancing my odds due to their low house edge. I will then sprinkle my profit into “lottery tickets” or higher volatility games to hunt a HUGE WIN!!!
How is Expected Value Calculated?
The expected value and house edge of most casino games and other gambling games is usually well-known. If you don’t trust the casinos or even the regulators and you want to find out for yourself, you can calculate the winning odds and expected value of every game by using simple mathematical formulas.
The more complex your betting strategy is, the more math that is involved in calculating the expected value. However, to keep things simple and we will calculate for a single bet.
You will need to use the following formula:
Expected Value (EV) = (probability to win) * (total profit) – (probability to lose)
Let us use this in a simple example of betting red/black in the game of roulette, which we already know will come out to 2.7%, just like any other roulette bet:
Expected Value (EV) = (18:37) * (1) – (19:37)
Expected Value (EV) = 0.4864864864864865 – 0.5135135135135
Expected Value (EV) = 0.27027027027027
EV - 2.7% (the number above * 100 to convert to a %)
The same formula can be used to calculated the expected value in any other game of chance if you know the exact odds of each bet you are making. Of course, if the odds are approximate like in sports betting, your result will be approximate as well. I will touch on EV sports betting strategies in a subsequent post.
What Games to Play
Each game you can find in a traditional casino comes with a negative expected value. The only way for the casinos to make money, in the long run, is to make the games favor them ahead of the players. It is similar to the Vig in sports betting, the operators need a way to grind their fee.
However, the games are not all the same, and despite what players might believe, there is every difference between choosing different games on the casino floor. You can find the full list of RTPs for different games in the Auscasinos RTP guide, but here are the RTPs of a few most popular casino games:
Slots: Between 80% and 95%
European Roulette: 97.3% (single zero roulette, see image below)
American Roulette: 94.74% (aka double zero roulette wheel)
Blackjack: 99.5%
Video Poker: 99% (depends on version)
European Roulette
As you can see on this short list of casino games, they all come with a negative expected value. This means you can expect to lose some money every time you play these game on average. However, the closer the number is to 0, the more likely you are to win on a given session. The further it is from zero, the more probable it is that you will end up losing money.
The expected value and RTP should really be one of the first things you look at when assessing a game. A casino game that’s very fun but comes with a very bad RTP, like most slots, should be only played when you are happy to give some money back to the house and you are hunting a big WIN. The negative RTP quickly adds up over a long session and gamers are left with nearly no chance of winning on any given day, let alone the long run at these RTPs.
How Expected Value Manifests in IRL
If you think about a very simple game of heads or tails, you should start to understand how gambling and odds works. In a neutral setting, heads or tails has an expected value of 0 as there are two betting options and a payout of exactly 1:1 (the chance to win is exactly 50%).
Now, go ahead and toss a coin 10 times. Chances are you will not get exactly 5 heads and 5 tails. In some sets of 10 tosses, you may even end up getting all 10 heads or 10 tails. This phenomenon is known, in gambling, as variance / variability and it depends on the standard deviation statistics. The standard deviation is very high in games with many possible outcomes and lower in games with few possible outcomes. The closer a game is to 0 expected value, the lower the deviation will be.
In games like slots that sometimes give the house a huge edge, the standard deviation will also be quite high. This means players will have sessions where they will keep losing and lose at a faster rate than one would expect based on the RTP. On the flipside, they could also have big winning sessions and hit big wins early in their session.
The key takeaway is that a little luck can actually carry you and keep you positive for a long time in games with a low house edge. However, when you play games that give the casino a significant advantage, any winnings streak you do find will be short-lived. This is why after a large win on the slots, if you keep playing then you are almost guaranteed to give it back.
Do It on LAN, we are here to help make you a better and more informed GAMBLER!
Finally, trust and security is crucial. Therefore, we only play on regulated and authorized iGaming sites in compliance with local regulations.
Stay Safe, Gamble Responsibly and Keep it Highbrow…
