Speaking of gamblingwe often hear: “The house always wins”. Yet, we have all had experiences that seem to contradict it: we certainly know someone That he won at least once a scratch card or a ticket. But then why do we say it? Well, because the bench has mathematical certainty that, if he gets enough people playing or if he gets them playing long enough, he will be able to have a margin of profit pre-established. Simply put, the house knows that it will always win in the long term. And there’s no trick behind it, it’s simply math. Each game, whether it is a roulette, a slot machine or a scratch card, is designed for ensure a house advantage. This advantage is known as house edge (house edge) and represents the percentage of each bet that the house expects to keep as profit in the long term.
What are fair and unfair games
A game is considered not fair when the winnings offered to participants and the chances of winning are balanced in such a way that, in the long term, the bench results advantaged compared to the participants. In short, from a mathematical and probabilistic point of view, The players’ winnings never exceed the bank’s winnings.
In a game fairInstead, neither side has an advantage on the others. But let’s look at it better with an example.
Let’s imagine we want to make people bet 5 people on the tossing a coin. We involve Andrea, Beatrice, Carlo, Daniela, Elena and tell them that in order to participate they must bet €1 for each launchand that, if they win they will receive €2.
So, at each launch each of them can:
- Lose €1 if you bet on the side that doesn’t come out;
- Win €1 if you bet on the face that comes up. This is because if he wins the bet he receives €2, but he had to put one in to be able to play, so he actually only won €1.
For each toss, the probability of heads is 1 in 2 (50%) and the probability of tails is again 1 in 2 (still 50%). All this can be summarized more formally as follows:
(Losses × probability of losing) + (wins × probability of winning) =
(-1 × ½) + (1 × ½) = 0
The game is fair because, on average, there will be neither gains nor losses for the house in the long run. If we try to simulate what would happen if we played many times, for example up to 3000, we will get this situation: Daniela was very lucky, Beatrice incredibly unlucky and the dealer, on average, earned nothing. In this case, the house edge is zero.
But what would happen if instead of receiving €2 for your winnings you received only 1.9? Such a small change would be enough to completely change the balance of the game!
In unfair games the house is certain to gain
If instead of receiving €2 to victory they received €1.9at each launch each of them could:
- Lose €1 if you bet on the side that doesn’t come out;
- Win 90 cents if you bet on the face that comes up.
So now this happens:
(Losses × probability of losing) + (winnings × probability of winning) = (-1 × ½) + (0.9 × ½) = -0.05 = -5%
It may seem like an insignificant change to us, but in this way the the dealer is certain to have a margin of 5% on all the money that is bet!
In fact, the situation changes drastically:
Although there are ups and downs, the overall result is that all players tend to lose moneybecause the rules of the game do not allow long-term losses to be compensated for. As lucky as Daniela was, at the end of the games she will have less money in her pocket than at the beginning. The mathematics of gambling, in fact, is based on a theorem called “law of large numbers”. This principle states that the more you bet, the closer you get to the “average player”what loses exactly the 5% (the house edge) of all the money played.
Gambling games are not fair: the house always wins
Obviously, not all gambling games are the same: each game has its own characteristics profit margin and also from your own volatilitythat is, by how much wins and losses can swing us. High volatility games deliver rare but high winningswith less predictable results, while those with low volatility guarantee more frequent wins and losses but of limited amounts.
What they all have in common, however, is that they are always unfair games. We can therefore be sure that by playing any game for a long time, we will lose money.
How many? Depends on the game: alla roulette French, for example, we lose The 2.7%at sports betting we lose about the 9% (varies by agency), we can lose at slot machines up to 35%. In some cases, we can also find this information outside the theaters. In the case of slot rooms, for example, you often see the writing “RTP“, acronym for “Return to player”, which indicates the percentage of money played that, on average and in the long term, will return to the player in the form of winnings. If it were, therefore, written RTP=90%it would mean that the player will recover on average 90% of the money bet, while the 10% it will be one certain loss.
In every game of chance, therefore, luck matters up to a certain point. If we play for a long time, it is mathematically certain that we will lose money.
