Slot math: The science behind the game (part 1)

If you ever worked in the gaming industry, I’m sure you are familiar with several people asking you the million-dollar question: “Can you tell me what’s the secret to win?” To which I usually respond: “My secret is that I don’t gamble.” However, we know that is not exactly what they want to hear. In this article, I will finally answer that question by explaining the science behind a slot machine and the components that make them work.

A slot machine is nothing more than a computer that is programmed to control all the functionality that is presented to the players by means of graphics and animation displayed through one or several monitors, depending on the specifications of the cabinet. Inside every cabinet there is a computer with a logic board that is designed by a machine manufacturer or it can also be a conventional computer such as those found in a desktop or laptop computer, which are then programmed like any computer, with software and firmware to make them work. The main program executed by the game is the operating system. For slot machines, there are many types of operating systems, some of them highly specific to perform the tasks of handling a slot game, but others are as common and well-known as those you use on your computer, such Windows or Linux.

The operating system is a very important component, but even most important is the application program, from now on, the game program. This program has all the functions that allow the computer to be a slot machine. It controls events such as the insertion of bills, the game button panel, screen animations or the movement of mechanical reels in the case of games with physical reels. This program is also in charge of tasks that are not as relevant to the player, but are key elements for the management of the casino floor operation: managing internal accounting, historical record of events and managing communication protocols that allow this information to be sent electronically and in real time to an Online Monitoring Control system or Casino Management system.

CAN A SLOT MACHINE BE TAMPERED WITH?

Technically, yes. However, it is extremely hard and almost impossible after all the safeguards in place to avoid such scenarios. Gaming is a highly regulated industry and even though there have been hacks, it is really not possible to alter the way slot machines function. The only way to tamper with a slot machine is to tamper with its game program. That would require direct manipulation of the inside of the machine and a respectable amount of technical knowledge. Not to mention that this would be very difficult in a casino environment surrounded by surveillance. I’m sure many of you have seen or heard several arguments made by people who actually believe that they can alter the outcome of the slot machines with the power of their minds or some other way of external intervention, and just so we are clear, that is not the case.

LET’S TALK ABOUT RANDOMNESS

Many of you would think that there is nothing random about a computer, and you are correct. Computers do what their programs tell them to do and nothing else, so how can they generate a game play whose result is random? Where do they get the combinations of symbols and outcomes that are shown to the players? One of the highly regulated functions of the game program is to implement a continuous source of numbers. They are not created only by chance, but by using a mathematical formula that allows them to produce the combinations of symbols that are presented to the player as the result of the games played.

This source of numbers is called a Pseudo-Random Number Generator or RNG. The RNG is used to generate numbers in a sequence that appears random, but is difficult to predict. Its main function is to produce a sequence in which it is not possible to find in an obvious way what the next number will be. If we add the fact that the RNG constantly generates numbers every 50 milliseconds (even when the reels may not be spinning), we are faced with the human impossibility of predicting the next number in the sequence. In this way, a slot machine’s computer has a way of generating plays “at random” using a pseudo-random mathematical formula.

SO WHERE DOES THE MATH COME IN?

Gambling has a solid statistical and mathematical foundation, from the beginning of times. In the design of games of chance, “nothing is left to chance”, and the rules of play are always clear and irrefutable, so there is no way to deviate from this design. The most basic concept when designing slot games is the concept of probabilities. In our daily lives, we are faced with scenarios in which we must make decisions based on the probability of the occurrence of events. We don’t go around calculating those probabilities, but we use ideas like “it’s possible that”, “it’s almost certain that” or “I don’t think this will happen.” Probability is mostly defined as our perception about the occurrence of an event based on our knowledge… or our deepest desire that things happen one way or another.

One of the things that will be very valuable from this article is the understanding that the probability of an event occurring is completely out of our control. This is especially true in gambling. The probability that you will win a game of chance does not depend on your emotional state or your perception of how a game works. The odds of a game of chance have been established mathematically at the time the rules of the game were created, and nothing can make you more or less likely to win than any other player.

WHAT ARE THE PROBABILITIES OF WINNING ON A SLOT MACHINE?

We previously defined that randomness means the lack of pattern or predictability in future events, which in gaming it indicates that the symbol selection has no order and does not follow any patterns. To illustrate this, we can say that when we throw two dice, the outcome of any particular roll is completely unpredictable. Technically, a random selection is a method of selecting items from a population where the probability of choosing a specific item is the proportion of those items within that sample population.

Let’s discuss a more complicated scenario: a bowl containing 10 red marbles and 90 blue marbles. The red marble has the probability of being selected as 1 in every 10. However, with random selection mechanisms established by the RNG functionality, it is not always going to be 1 red and 9 blue marbles that are selected, and the number of those possible outcomes is what is called a Game Cycle.

A game cycle is the total number of possible combinations on a slot machine, or total number of possible card combinations on a video poker machine, for example:

• The cycle of a coin flip is Two (2)
• The cycle of a 6-sided dice is Six (6)
• The cycle of a pair of dice is Thirty-Six (6×6=36)

The probabilities of winning or losing are also referred to as Odds, for example:

• The odds of getting heads on a single coin flip is 50%
• But then what happens after 4-coin flips, on the 5th flip, what are the odds of getting heads? The answer is still 50%. The odds of probabilities of an event occurring randomly are completely independent of the outcomes of previous events. The same applies to slot machines.

To calculate and know the probabilities of winning in the game we need to know:

• The total number of combinations or outcomes possible
• Each of the possible outcomes has the same probability of occurring
• The number of winning outcomes

Let’s build a simple slot game: the winning combination is 3 Cherry Symbols:

Probability is the frequency in which an event occurs, from 0% meaning it never occurs to 100% meaning it always occurs. This gives us a tool to determine how often an event will occur, but does not allow us to predict when exactly that event will occur. This is an estimate of the chance of winning divided by the total number of chances available:

• There are 100 Cherry Symbols total (5x4x5)
• There are 1,000 total symbol combinations (10x10x10)
• The probability of getting 3 Cherry Symbols is 10%, 100/1000 or 1 in 10

Now, if you are wondering if the probability of getting a jackpot is 1 in 10 million, is it possible to get back to back jackpots. The answer is yes, but the mathematical calculation of those probabilities is way more complicated, as you can imagine.