Casinos, unsurprisingly, are businesses and their intention is to make money. However, unique to casinos, their customers are also looking to make money, but at their direct expense. Since gambling houses have been successful businesses for as long as gambling has been around, one must ask; how casinos convince their customers to give up their money, and how do they keep them coming back?
The answer is that they offer prizes that are low enough in value not to create a loss, but high enough in value to entice people to play. This is a delicate balancing act and casinos use something called the ‘expected value’ of a bet to make sure they win. The ‘expected value’ of a bet is calculated by multiplying the odds of success by the amount that is stood to be won and subtracting that from the buy in—the average amount that the casino can expect to make on every bet.
Let’s work through an example using roulette. A roulette table has 36 red or black numbers and one or two green zeroes. This means that each number has a 1/37 or 1/38 chance of coming up. The payout for guessing a correct number is 35 times the amount you bet, which we will call n . The expected value for the casino therefore (in the case with only one green zero) is n – (35/37)n which comes to (2/37)n. Since all bets have to be positive numbers, the value will be a positive number. So, for every £37 that a gambler puts in, they will expect to get £35 back, netting a £2 profit for the casino.
The same holds true for bets placed on black/red, odd/even, high/low. Since zero is excluded from each of these, there is a 18/37 chance of the gambler winning each bet, with a reward of double the initial bet, leading to an expected value of n – (36/37)n or (1/37)n for the casino. These are better odds for the gambler; they are expected to lose half as much on average, but it is still a loss, which makes the casino happy. This basic principle applies to any scenario that involves calculated risk, even those that aren’t obvious such as insurance.
So, the casino makes a profit on average, but it cannot guarantee a profit on any individual bet. Increasing the number of bets that are made increases the chance that the gambler will lose money in the long run, as they have a 51.3% chance of losing on a single round of roulette if they bet on red, but a 52.5% chance to lose money after five bets, and 53.3% chance to lose after nine.
| Number of rounds played | Odds of gaining money | Odds of going even | Odds of losing money | Difference in odds between win and loss |
| 1 | 48.667% | 0% | 51.334% | 2.667% |
| 2 | 23.667% | 49.963% | 26.370% | 2.703% |
| 3 | 47.973% | 0% | 52.027% | 4.054% |
| 4 | 29.251% | 37.445% | 33.304% | 4.053% |
| 5 | 47.467% | 0% | 52.533% | 5.065% |
| 6 | 31.877% | 31.182% | 36.941% | 5.064% |
With thousands of bets placed on a single roulette table every day, the casino can virtually guarantee a profit. Their only challenge after that is getting enough people to make enough bets to allow for this, but if the history of gambling has taught us anything, it’s that that won’t be too much of a problem.
