Slot machines have risen in prominence over the past two decades to become one of the most widely played casino games overall. There are hundreds upon thousands of slot machines available at various casinos, each having its own unique layout, plot, reels, symbols, regulations, payout schedule, and rewards. Every year, major slot machine manufacturers’ designers, mathematicians, and market analysts work to create innovative new slot games. It makes sense from a business perspective to provide players a wide variety of options; after all, different people have different preferences when it comes to not just how they want to gamble and what kinds of games appeal to them.
In this piece, we’ll examine the ideas and fundamental features shared by all different variations of slots and discover how the design of slots allows for such variety.
Slot machine ubiquity
How come slot machines are all the rage now? There are five primary factors that have led to this widespread acceptance:
Slots games are played in a more secluded setting, with just the player and the machine, than in a traditional casino table game.
The time it takes to insert credits and end a spin on a video game is negligible.
design that is both aesthetically pleasing and functional. This includes, but is not limited to, the graphics of the symbols, the user interface, and even the case.
sensations: Unlike other casino games, slot machines are designed to provide players with a unique sensory experience through their layout, noises, and sights, all of which contribute to the presentation of the game’s outcomes.
Player profiles, ambitions, and even interests can inform a player’s selection from a vast range of games that differ in terms of rules, attributes, and design.
In this piece, I want to zero in on this most recent development.
Structure with built-in slots
Slots design encompasses not only the visible elements of a slot machine, such as its shape, graphics, visuals, and sounds, but also the underlying elements and principles that allow the game to function to the benefit of the operator and keep players engaged indefinitely.
The reels, the symbols, the layout of the symbols, the display, the paylines, and the prize schedule are the fundamental components of a slot game’s design. In early mechanical and electromechanical slot machines, the reels were literal reels with strips attached around their circumference, on which the symbols were laid out in the order in which they would appear after a spin. A stop is any location on a reel that has a symbol.
In today’s video slot machines, the’reel’ is not a physical device but rather an ordered list or set of symbols with indexed stops that can have a variety of different layouts. Whether we’re talking about real-life or online slots, a reel will always have multiple occurrences of the same symbol.
In contrast to the fixed number of stops on a real reel (typically 22), newer slot games allow for an infinite number of stops on each virtual reel. It’s easy to observe the components that contribute to the wide variety of slot games from this basic “deconstruction” of a machine, since each component has a unique numerical value. First, the number of reels in a slot machine can vary from one to five. Each reel can have anywhere from ten to hundreds of stops. Every slot machine game has its own unique set of symbols and rules. Multiple instances of every symbol populate the reels. After the rotation, the stops are displayed in a grid with rows and columns of varying sizes (1 x 3, 3 x 3, 4 x 3, 1 x 5, 3 x 5, etc.). The winning outcomes in this grid can occur on any of the one or more paylines that have been activated. Finally, the probabilities of winning vary from game to game.
It’s no surprise that slot machines come in so many varieties, given the sheer number of permutations available when it comes to the numbers connected with their various building blocks. However, because every game must guarantee the profit for the operator over the long term, the combining possibilities for the internal design are limited and subject to technical-scientific study. The mathematical structure of the game provides this assurance for the operator.
Slots of varying mathematical complexity and design
In the mathematical models that underpin every slot machine, all the numbers involved in the game’s components become parameters or variables.
After selecting the symbols and the number of reels, the next step in the mathematical design of a slots game is to choose the reel configuration and the payment schedule.
Reel configuration refers to the organization and distribution of symbols throughout the stops of a certain reel. The symbol weighting of a reel is a vector that contains the frequency with which each symbol appears on the reel’s stops.
Together, the payout schedule and the weighting of symbols determine whether or not the long-term results satisfy the producer’s requirements, which include, but are not limited to, the following: the relative frequency of each winning and certain non-winning outcomes; the overall payout of the machine being a fixed percentage of the player’s wagers; and the return of prizes having a certain average distribution over time.
That boils down to adjusting the model’s parameters and variables, including the odds of a winning combination and various statistical indicators (mean, variance, standard deviation), to obtain desired values or ranges within predetermined intervals (in more broad mathematical terminology). This is the domain of mathematicians, and their work yields a mathematical model that specifies a version of slots based on the expected statistical data that ensures the game’s profitability.
Consequently, the number of possible slot machine variations is infinite, since there are an infinite number of underlying mathematical models.
Iterative mapping and random number generation
After a spin, the outcome of a slot machine game is determined by the combination of symbols that land on the visible stops of the paylines.
Each reel has visible stops that decide the outcome of a spin in mechanical slots and early versions of electromechanical slots. Like in roulette, it’s a sure bet. Such mechanically manufactured outcomes are believed to be sufficiently random since the high velocity of the spin guarantees a large number of rotations of the reels.
However, as slots have progressed, additional symbols and stops have been added to the reels, transforming the once-physical reels into their digital counterparts. Slot machines now use a Random Number Generator (RNG) as an additional design feature because of the need to generate outcomes mechanically for virtual-reel games. A random number generator (RNG) is a computer algorithm that can generate numbers from a specified set arbitrarily, i.e., without any rules and independent of past outputs.
The random number generator (RNG) in slots produces results via mapping: A reel’s stops are numbered to indicate their location. Each stop on each reel is assigned a number based on the RNG’s selection. Next, the RNG determines where the reels will halt, and the machine brings them there.
The game is ended by the time the reels start turning. The random number generator has already chosen the stops, and the reels spin in an illusionary motion as a courtesy to the player.
The outcomes of electromechanical slot machines are also produced at random. The physical reel is too small to accommodate all of the required pauses, so they resort to an invisible virtual reel instead. Thus, the RNG computer program employs the utilization of the virtual reel. In order to maximize the number of symbols shown on the reel, it was decided to give less importance to each symbol on the real reel and instead do the actual weighting on the virtual reel. Multiple stops on the virtual reel with the same symbol are mapped into a single stop on the actual reel. The RNG decides which of the virtual reel’s stops will be chosen, and then the actual reel is instructed to stop at the corresponding physical stop.
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Another deception is induced in the player by this mapping technique: You may roughly calculate the odds of a symbol appearing at a spin by dividing the number of times that symbol appears on the reel by the total number of stops, assuming you know how the symbols are distributed on the physical reel. Since the stops of the physical reels are no longer equally probable, this ratio must be calculated on the digital reel instead.
So, it’s important to remember that all slots, even the most cutting-edge ones, rely on deception. We’ve already covered the spin illusion and the random spin illusion of the actual reels, but there are more, as we’ll discover.
Slots with artificially created close calls
Slots are based on mathematical models, and these models may be manipulated using a form of applied mathematics to generate a wide variety of games by just changing the values of a few parameters. Another form of manipulation, designed to generate phony close calls, is also feasible and has been implemented.
In slot machines, a near miss is a losing combination that is only off by one or two symbols. For instance, an almost winning outcome would include three reward symbols on a payline that requires four such symbols.
For slots with many rows, the near-miss can also be associated with components outside the payline’s immediate vicinity (below, above, to the left, or to the right). For example, if a person is playing a slot machine and a winning symbol doesn’t appear on a payline but instead appears directly above the position where it should, they may feel as though they came close.
The designers of slot machines believe that players will keep wagering because they always feel like they’re on the cusp of a big payout.
Experts on the subject of problem gambling have identified the near-miss effect as a key contributor to the onset of compulsive gambling.
Such contrived close calls can be generated by slot machine manufacturers by adjusting game parameters and rearranging the positions of symbols on the reels. They functioned in the first slots games and continue to function in the most advanced slots of today.
There are two basic methods for increasing the frequency with which apparent near-misses occur on or near a payline.
One of them uses a payline and a concept known as the award symbol ratio. A high-paying symbol is given more importance on reels where it contributes to winning combinations, and less importance on reels where it does not. Clustering is the term for the current slot machine strategy of intentionally creating fake near-misses next to the payline. The basic concept is to map the positions on the physical reel (for electromechanical slots) or directly on the virtual reel shown in the payline window to stops with low-award symbols or blanks, leaving space for the high-award symbol on the virtual reel.
Many variations of slot machines feature a “stop” button to give the player the illusion that they are in control of the game.
Keeping the rules of the game a secret
Slot machines are distinguished from other forms of chance gambling by a trait that is more attributable to the game’s developers than to slots themselves: the secrecy with which the game’s parameters are configured. Roulette wheels, blackjack shoe counts, and lottery ticket tally sheets are all well-known, yet slot machines’ inner workings remain a mystery to the general public.
Aside from the number of reels and the symbols, the players have no idea how the symbols are distributed across the reels or how much weight each reel carries. Players and analysts can’t calculate probability and other statistical indicators of the game without it. This secrecy also presents ethical concerns, as such knowledge could serve as an objective basis for choosing one game over another, or for discontinuing play altogether.
There is one notable exception to this rule, however: many developers prefer to make their games’ return to player (RTP) numbers public. The long-term theoretical payout percentage of a slot machine is represented by the RTP metric.
Parametric configurations of games are not required to be made public in most jurisdictions, although there is no reason for their creators to keep them hidden. Because mathematics is a public good, they need not worry about competitors copying or patenting the mathematical models behind slot machines. They should not be concerned that gamblers will shun slots once they see how slim their chances of winning are; after all, the lottery, often regarded as the game of chance with the slimmest odds of winning, has not seen a decline in participation.
All slot games share this trait despite its obvious drawbacks from a legal, ethical, marketing, and logical perspective. Such missing data can only be recovered by legal action or statistical procedures based on tracking the outcomes of thousands of spins.
Conclusion
The variety of slot games available on the market has a direct effect on the industry’s appeal. The varying characteristics of the underlying mathematical models of slots are what make it possible for them to accommodate such variety. Slots, in their various forms, share a common denominator with these abstract mathematical concepts. In the real world of gambling, the illusion of near-misses is shared by slots alongside other illusions such as the illusion of motion (for slots with virtual reels) or the sense of control, all of which have their roots in the underlying mathematical models. It’s possible that the gamers will find these illusions to be humorous. However, another aspect of slot games that is shared by all of them is the secrecy of their parametric setting, which continues to be a source of worry for experts.