International edition
June 24, 2021

By César A. Dechat (*)

How do casinos make their money? (Part Three)

In the previous two articles we have tried to produce a general theory of how casinos generate their income through the different games they offer to their customers. In search of this theory we have briefly explored the concepts of Advantage of Mathematics and Expected Value of a given position, we have tried to define what the odds are from a gambling point of view and we have done, by way of example, some calculations regarding the game of roulette using these three concepts. However, I must admit, my dear reader, that so far we have not addressed the central question which answers the question in the title of this series of articles: how do casinos make their money?


s gratitude to those of you who have had the perseverance and above all, the patience to have come this far after reading the previous two articles, which, to be honest, could have perhaps been somewhat tedious due to generic formulation (especially because of my lack of writing talent). I would like to provide you with the solution to this question and then test its justification. The answer you’re looking for can be expressed by one simple word:MATHEMATICS.

That's right, my dear reader-casino core business is pretty simple to understand:  casinos generate money from their games thanks to the mathematics operating behind them. With only a few notable exceptions, the house will always win - in the long run - thanks to the mathematical advantage that it has over players. Not without reason did our grandparents warn us as daring novice gamblers, as we tried to prolong winning streak against the House for longer then we should have: “From January to January,the money belongs to the banker,” they used to say.

While everything said so far sounds pretty obvious and trivial, it is surprising to see how often even we who work in the industry tend to misunderstand or underestimate the basic operating principles behind the different games of chance and their relationship with casino profitability, which can lead to bad decisions regarding certain scenarios that end up directly or indirectly affecting business performance.

A simple example which I think illustrates the above point, happened a couple of years ago in one of the most famous and prestigious casinos in the region, when a machine which had been recently introduced into the field of High Denomination, generated a prize of no less than US$ 267,000. After all rigor checks were made​​, and the move determined to be valid and the payment distributed, the machine was removed for "control" .

A few days later,without having been played again, the machine was indefinitely withdrawn.. Obviously, the result of this decision was bad from a commercial point of view, as it revealed at least one of the mistakes made at that time. The first failure was to use a highly volatile machine with such a high denomination that it generated economic risk, which did not meet the standards of the casino ( which ultimately led to the decision to withdraw ) . The second flaw , in my opinion , was to have been frightened by the prize awarded, to the point of shooting it down immediately, without giving any chance to recover and adjust naturally to their expected retention , and despite the fact that the odds of a payment of this magnitude would recur in the near future were short ( although, admittedly , not null ) .

Finally, we could also consider this to be a  failure from a commercial point of view, although it is debatable, and is how the casino reacted to the situation in the first place. In this sense, my view is that, despite the economic risk of a single machine having appeared to have been overcome, and having found that it worked correctly and within normal parameters, and that the payment  made was within the boundaries of theParSheetpaytable.The cost paid by the casino in terms of prestige and transparency to its customers for immediately withdrawing this floor machine the second it generated this award, far exceeded the additional risk ( the which can even be quantified financially) which would have meant to keep the machine in use for a couple more months, or at least until the impact generated by this award was sufficiently diluted.

This example demonstrates how even the most successful and prestigious companies , with highly trained and professional management, instinct and irrational impulses can sometime prevail, leading them to perform certain actions that , for one reason or another , may adversely affect earnings or the casino’s public image. Obviously , it’s one thing to assess and analyze situations like the above example from a distance and with the results already in hand, and quite another to make complex decisions with incomplete information and at critical moments , like what my colleague at the casino in question surely experienced the day after paying $ 267,000 .

From another viewpoint, we can say that the correct interpretation and understanding of the mathematical principles at work behind a particular game allows us operators to reasonably meet the expectations of our customers. In this sense, we must be aware that there is a fundamental reasoning which explains why an intelligent person , who makes rational decisions , would knowingly risk his money in a game in which your opponent, which in this case is the casino, has a particular advantage : the entertainment value you get when you do .

It is therefore clear that, on the one hand, very few people would be willing to participate in a game in which 4 or 5 percent of the unit staked is consistently lost, while on the other, hundreds of thousands of people  visit each of our casinos who are willing to participate in games that have basically the same result. Indeed, the difference between the two situations lies in the fact that, while hardly anyone would be willing to risk their money on a game that inevitably caused them to lose a fraction of it ( although small ).Most likely, a large number of people among which I include myself, would be willing to participate in a game which, with even a slight disadvantage in their favor, causes them to have  reasonable expectations of obtaining a sufficient incentive award to compensate them for the risk incurred .

In this sense we must say that new casino games owe their success or failure to the expectations they give players, and even more to their ability to meet these expectations over time. In recent years, our casinos debuted a variety of new games to attract player interest and keep their attention. Despite a relative preliminary success, many have failed dramatically in meeting players’expectations once the initial phase is over. Indeed, regardless of whether a game is fun or interesting to play at first and has many bonuses and interactive scenarios to discover, it probably won’t be successful over time, if who plays them regularly loses their  money too quickly or only has an exceptionally rare chance of winning. It is precisely in this way that the magic of the mathematics of the game kicks in again.

In the next article we will talk about a final approach to the important role which mathematics plays in our business: the analysis of different non-periodic random fluctuations that occur in either direction, for a certain expected outcome of a particular game; something known by everyone as "luck."

See you next time.

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