Machines

How a reel game is actually designed

A reel machine is the one game in this family where the sample space is deliberately hidden from view, and the reason is arithmetic rather than secrecy for its own sake.

Fanfeud desk note. Figures on this page are worked out from the rules stated beside them.

The earliest reel machines were honest in a limited sense: three physical wheels, each carrying a fixed number of symbols, spun independently. The probabilities were visible because they were physical. If a reel carried twenty symbols and one was a bar, the bar appeared once in twenty.

That design has an arithmetic ceiling. With three reels of twenty positions, there are eight thousand possible combinations in total, so no outcome can be rarer than one in eight thousand. A top prize cannot be made large without either making the machine unprofitable or adding physical positions, and a reel can only be so big.

The virtual reel

The solution, and the single most important idea in the design of these games, is to insert a mapping between the internal random selection and the visible reel position. The machine selects from a larger internal list of stops, and many internal stops can point at the same visible symbol. A symbol occupying one physical position on the reel might be reachable from one internal stop, while a blank beside it is reachable from twelve.

The visible strip therefore stops being a probability display. Two symbols that look equally represented on the reel can differ in likelihood by an order of magnitude, and there is no way to recover the real distribution by watching the reel. The table above shows the shape of such a mapping, using round numbers for illustration rather than describing any particular machine.

The paytable and the return

Once the probability of every combination is known, the designer sets the paytable, and the return follows arithmetically. The expected return per unit staked is the sum, over every winning combination, of its probability multiplied by its payout. The edge is one minus that figure. The design process usually runs backwards from a target return: the return is chosen first, and the paytable and weighting are adjusted until the arithmetic lands on it.

The internal document that records all of this, combination by combination, is called a par sheet. It is the definitive statement of what a machine does, and it is the document a testing laboratory examines when a machine is submitted for approval. Everything a player can observe, the reel strips, the animation and the sounds, is downstream of it.

Volatility

Two machines can be built to the same return and feel completely different. If most of the return is delivered through frequent small payouts, results cluster near the average and sessions feel steady. If most of it is concentrated in one rare combination, the same average is reached through long dry stretches punctuated by a large event. That is volatility, and it is variance under a commercial name.

Volatility is a design parameter, chosen deliberately, and it has no effect whatever on expectation. A high-volatility machine and a low-volatility machine with equal returns retain the same proportion of everything staked. They differ only in how the shortfall is distributed across sessions, which is a question about the shape of the distribution rather than about its mean.

Why the display is not the game

Two familiar effects follow directly from virtual reels. The first is that combinations appearing just above or below the payline can be made to occur far more often than the paying combination itself, simply by mapping many internal stops to the positions adjacent to it. The second is that the frequency of any symbol on screen tells a player nothing reliable about that symbol's real probability. Both effects are consequences of the mapping, and both are among the reasons that disclosure of return figures became a regulatory question rather than being left to inspection of the machine.