How casino’s make money 💰

Just like the local video arcade or bowling alley, a casino is a business which needs to make money in order to stay open. But how exactly does a casino do this? In this article we will examine the fundamental principles of how a casino works - looking at the house edge, RTP and variance.

House Edge
The inclusion of a house edge, sometimes referred to as the house advantage, is how casinos make their money. The concept of a house edge is actually very simple and is all based around mathematics and probability.

Lets take European Roulette as an example. In this game there are 18 black numbers, 18 red numbers and one green 0. The payout for betting on 'black' is 1:1, meaning that if you bet £10 and won, you would receive £20 back (£10 profit + the return of your £10 stake).

However, the probability (or odds) of winning your bet isn't quite 50/50. To win your bet you need a black number to come up - there are 18 black numbers and 19 numbers that aren't black (18 red + 1 green), making the probability of a black number being spun 18/37.

So out of the 37 possible outcomes you would win 18 of them (+£180) but lose 19 of them (-£190) leaving a net loss, or cost, of £10.

We can now use this idea to calculate the expected outcome of single zero roulette:

Expected Outcome = Change of Winning - Chance of Losing = 18/37 - 19/37 = - 1/37 = -0.027, or -2.7%

As you can see, the expected outcome is negative - meaning the player is expected to lose over time and giving the house and edge of 2.7%.

Using the house edge you can calculate the theoretical loss (think of it as the cost of playing the game) by multiplying the amount of wagers by the house edge. So if you make 37 bets of £10, the total amount bet would be £370, and the expected loss would be £370 x 2.7% = £10.

It is important to remember that the house edge is calculated against the total bets, not the money you have at the table. So if you purchased £100 in chips at a casino and made £1,000 in single zero roulette wagers, your expected loss would be £27 (£1,000 x 2.7%) - leaving you with £73 (£100 - £27 = £73).

RTP (Return To Player)
The 'Return To Player' or 'RTP' is essentially just a different way of displaying the house edge - instead of showing the amount expected to be lost to the casino, the number is the amount expected to be returned to the player in winnings (as a percentage of their total bets).

So for European Roulette, this would be 97.3% (100% - 2.7%) - meaning that for every £100 wagered you would theoretically receive £97.30 back (at a loss of £2.70).

Variance
Up until this point we have been discussing theroetical returns. But if everytime you bet £100 on roulette you received £97.30 back, that would be quite a boring game. One that pretty much no-one would bother to play.

So why do we play? The theoretical numbers above relate to the expected long term outcome - ie: the outcome you would come to if you played for an infinite amount of time. But the short term outcome is normally quite different to the theoretical one, and this is what makes the game interesting.

For example, if you bet £100 on 'black' on a single zero roulette wheel you are either going to win +£100 or lose -£100. And if you bet £100 on the 'black' 10 times you could end up winning £1,000, losing £1,000, breaking even or anything in between.

Variance is what makes casino games exciting, and it differs significantly depending on what game you choose to play. A table game such as Blackjack or Baccarat has a relatively low variance, whereas the lottery has huge variance. The higher a games variance, the more chance you will have of losing your bankroll whilst playing, but the wins have the potential to be much bigger.

There is also a difference in variance between different bets in the same game - such as betting red/black in roulette vs betting single numbers or betting £100 once vs betting £1 one hundred times. Different versions of the same slot game can also have vastly different levels of variance.

When at the casino, your tolerance for risk should help you decide what games to play. If you're not a risk taker, then playing blackjack or betting red/black on a roulette wheel will reduce your chance of losing all of your chips, but it will also limit your winnings. Conversely, playing slots or betting single numbers in roulette will increase the chance of going bust but also gives you the opportunity to win big.