by Dr Catalin Barboianu PhD | Date of Publishing: 5 April 2023
Over the last two decades, slots became one of the most popular and the most played casino game. There are thousands of slot games on the casino market, with different designs, themes, reels, symbols, rules, payout schedules and prizes. Big slots producers develop new slot games every year, as result of the work of their designers, mathematicians, and market analysts. This diversity has of course marketing reasons, as people always like to choose among various products for those that best fit their preferences, but also their style of playing and personal criteria of gambling.
In this article, we shall see how slot design allows such diversity and what principles and inner features all these slots versions have in common.
Table of Contents
Why have slots become so popular? There are five main elements contributing to this popularity:
It is this latest element that we shall focus on in this article.
When talking about slots design, we not only refer to external physical aspects such as shapes, graphics, visuals, and sounds but also to the construction elements and principles that make the game of slots work as it does and keeps it functional in favour of the operator, while maintaining a continuous interest of players for the game.
The basic elements of the construction of a slot game are the reels, the symbols on the reels, the arrangement of the symbols on the reels, the display, the paylines, and the prize schedule. At early mechanical and electromechanical slot machines, the reels were actually physical reels with strips attached on their circumference, on which the symbols were lying in the desired arrangement for one of them on each reel to be displayed as the outcome after the spin. Each place on a reel where a symbol lies is called a stop.
At modern slot machines with virtual reels, ‘reel’ is in fact a non-physical ordered list or set of symbols with indexed stops, containing the symbols arranged in various ways. A reel holds several instances of the same symbol, whether we talk about physical or virtual reels.
While a physical reel could have a limited number of stops (usually 22), virtual reels can have stops in any number, and in modern slot games, reels come to have hundreds of stops. Just from this essential “deconstruction” of a slot machine, one can see the factors that account for the diversity of slot games – it is all about numbers associated with each construction element: First, a slot game may have from one to usually five reels. The number of stops on each reel is variable, in order from tens to hundreds. The number of symbols that every slot game use is variable as well. Each symbol appears in a number of instances on each reel. The display showing the stops after the spin is a grid with various dimensions: 1 x 3, 3 x 3, 4 x 3, 1 x 5, 3 x 5, and so on. In this grid, one or several paylines may be enabled for the winning outcomes. And, last, each game offers its own payout odds for the winning outcomes.
With so many possibilities for combining numbers associated with these constructive elements in game design, it is no wonder that there are so many versions of slots. And yet the combining possibilities for the internal design are limited and subject to technical-scientific analysis, just because every game must ensure the profit for the operator over the long run. This guarantee for the operator is given by the mathematical design of the game.
All the numbers associated with the construction elements of the game become parameters or variables for the mathematical models that stand behind any slot machine.
When a slots game is designed mathematically, once the symbols and number of reels have been chosen, the process continues by establishing the configuration of each reel and the payout schedule.
The configuration of a reel is the distribution of the symbols over the stops of that reel and the arrangement of the symbols. Each symbol is present in various instances on the stops of a reel, and these numbers form a vector called the symbol weighting of that reel.
Establishing the symbol weighting is done together with the payout schedule such that the outcomes over the long run meet the conditions imposed by the producer: each winning outcome and some particular non-winning outcomes have a certain relative frequency, the overall payout of the machine to be a fixed percentage of the player’s wagers, and the return of prizes to have a certain average distribution in time.
In general mathematical terms, that reverts to choosing the model’s parameters and variables, such as the probabilities of the winning combinations and some statistical indicators (mean, variance, standard deviation) to get certain values or ranges within certain intervals. This is of course, a mathematician’s job and the final result is a mathematical model that provides the producer with the expected statistical data that ensure the profitability of the game and determines a specific version of slots.
Therefore, there are so many versions of slots as there are mathematical models behind them, and the possibilities are countless.
The outcome of any slots games consists of the combination of symbols placed in the visible stops on the paylines after the spin, that is, one symbol on each reel.
In mechanical slots and some early versions of the electromechanical slots, the outcome is determined mechanically by the stops that are visible on each reel when the spin stops. It works exactly as in roulette. Given that the high velocity of the spin ensures a large number of rotations of the reels, such mechanically-produced outcomes are considered enough random.
However, with the evolution of slots, more and more symbols and stops have been added to the reels and turned the physical reels into virtual reels. For the virtual-reel slots, the generation of outcomes could no longer be done mechanically, and a new construction element has been added to slots, namely the Random Number Generator (RNG). RNG is a computer algorithm able to generate numbers from a given set randomly, that is, by no rule and without any dependence on previous outputs.
The generating of the outcomes by RNG in slots works through mapping: Each stop on a reel is indexed through a number. The RNG picks a number for each reel, which is mapped onto the stop with that number on that reel. Then the machine directs the reels to stop on the spots selected through the RNG.
By the time the reels are spinning, the game is actually already over. The RNG has already selected the stops, and the reels spin sort of as a courtesy to the player, in an illusory motion.
Even the outcome of electromechanical slots is generated by RNG. They use an invisible virtual reel holding far more stops than the visible physical reel, which isn’t big enough to hold all the stops that are needed. So it’s the virtual reel that is used in the computer program using RNG. The idea was to have a reduced weighting of the symbols on the physical reel such that the reel to display as many symbols as possible while making the actual weighting on the virtual reel. The virtual reel is mapped onto the physical reel: Several stops with the same symbol on the virtual reel are mapped into one stop on the physical reel. The RNG generates the stop to be selected from the virtual reel, which commands the physical reel to stop on the associated physical stop.
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This mapping technique creates another illusion for the player: If you somehow know what the symbol distribution on the physical reel is, you may estimate the chances of a symbol occurring at a spin by doing the ratio between the number of instances of that symbol on the reel and the total number of stops. However, this ratio should be done on the virtual reel instead, as the stops of the physical reels are no longer equally probable.
So let’s note illusion as a common feature of all modern versions of slots. We talked about the illusion of spin and the illusion of random spin of the physical reels, but there are more, as we shall see further.
The mathematical models behind slots are able to produce different versions of the game when the slot designers choose different values for the parameters involved in a sort of applied-math manipulation for diversity. However, another kind of manipulation is possible and actually in effect with another goal, that of creating false near-misses.
A near miss in slots is a non-winning combination differing in one or two elements from a winning one. For instance, an outcome holding three award symbols on a payline needing four such symbols to be winning is a near-miss.
For the slot games displaying grids of more than one row, the near-miss can be also related to elements below or above the payline, or to the left or to the right of it). For instance, if a missing winning symbol on a payline is displayed right above the spot where it was expected, this extended outcome is perceived as a near-miss by the player.
Near-misses are seen by the slots producers as factors determining slot players to continue playing under the illusion that they are close to a win.
The near-miss effect is a gambling-specific cognitive distortion and is considered by problem-gambling experts as an important risk factor in the development of problematic gambling behaviour.
By manipulating the game’s parameters and the arrangements of the symbols on the reels, slots designers can produce such engineered near-misses. They were in effect in early slots games and even more so in modern versions of slots.
There are two main techniques for making apparent near-miss to occur frequently either on the payline or adjacent to the payline.
One is called award symbol ratio and works on a payline. Basically, a symbol that forms a high prize combination is weighted in a high ratio on two or more reels and in a very low one on one reel. For modern slots, the technique of creating false near-misses adjacent to the payline is called clustering. The basic idea is to place a stop with a high-award symbol on the virtual reel between several stops with low-award symbols or blanks, mapped into the corresponding positions on the physical reel (for electromechanical slots) or directly on the virtual reel visible in the payline window.
The illusion of a near miss adds to the illusions that the slots games may create, among which is also the illusion of control through a stop button for many versions of slots.
Slots have a unique feature among the games of chance, which is not necessarily a feature of the game itself, but rather of its producers: the parametric configuration of the game is kept secret. We know how many numbers are on a roulette wheel and how many decks of cards are used in a blackjack game, we know how many lottery numbers are in the urn, but we don’t know much about the internal design of slots.
Except the number of reels and perhaps the number of symbols, players know nothing about the other parameters of the game, that is, the distribution of the symbols on the reels and the weighting of each reel. The lack of this information prevents players and experts to compute probabilities and other statistical indicators associated with the game. Since such information could stand as objective criterion for choosing a game or another, or to stop playing a game, this secrecy also raises ethical issues.
There is a small exception in regard to this secrecy – many producers choose to expose the RTP (return to player) of their games. The RTP indicator reflects the percentage of the total wagers that the machine returns to players as prizes over the long run.
While the exposure of the parametric configuration of a game is not yet a legal obligation in most of the jurisdictions, there is no rational reason for the producers to keep it secret. They should not be concerned about competition since the mathematical models behind slots are not subject to copyright or patents; mathematics is a common good. They should not be concerned about players avoiding slots when they will find how low are the winning odds either – this did not happened in lottery, which is known as the game of chance offering the lowest odds.
Besides the legal, ethical, marketing, and logical aspects of this secrecy, it remains a common feature for all the games of slots. The only way to retrieve such missing information is through legal intervention or by statistical methods based on observation and recording the outcomes of the games in thousands of spins.
The popularity of slots is tightly related to the diversity of slot games on the market. There are mathematical models behind slots that allow such diversity through the variation of their parameters. Thus, these mathematical models in their abstract form, are the essential element that all versions of slots have in common. In the concrete realm of gambling, another element that the games of slots have in common, still related to the mathematical models, is the illusion of near-misses, along with other illusions such as that of motion (for the slots with virtual reels) or that of control. These illusions may be funny elements for the players. However another common feature of the slot games, namely the secrecy of their parametric configuration, remain an issue of concern, at least for the experts.
Author: Dr Catalin Barboianu PhD Catalin Barboianu PhD is a games mathematician and problem-gambling researcher. He authored ten books on gambling mathematics and several academic articles in the field of problem gambling and philosophy of science. Catalin is a science writer and consultant for the mathematical aspects of gambling for the gaming industry and problem-gambling institutions. Read MoreAbout the Author
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