reel machines

From physical reels to a mapping

An early mechanical machine had physical reels with a fixed number of stops, and the probability of a symbol was simply how many stops it occupied. That put a hard ceiling on jackpots: three reels of twenty stops give eight thousand combinations, so the top prize could not be large without making the machine unprofitable.

Virtual reel mapping removed the ceiling. The machine draws from a long internal list of positions, and many of those positions map onto the same physical stop. A symbol can therefore occupy one visible position on the reel while occupying one internal position in a hundred. What the player sees is a display of a result, not the mechanism that produced it.

physical reel:   22 visible stops, jackpot symbol appears once
naive reading:   p(jackpot on this reel) = 1/22 = 0.0455

virtual reel:    256 internal positions mapped onto those 22 stops
                 the jackpot stop is reached from 1 internal position
actual value:    p(jackpot on this reel) = 1/256 = 0.0039

three such reels: 1/256^3 = 1 in 16,777,216
the strip is a label; the mapping is the game

The random number generator

The draw is made by a random number generator running continuously, and the result is fixed at the moment of the request. The spinning animation that follows is presentation. Nothing about the duration of a spin, the moment a button is released, or how long a machine has gone without paying enters the computation.

This is the point at which regulation becomes technical rather than moral: a supervisory regime for machine gaming is largely a regime for verifying that the generator behaves as claimed and that the mapping in the shipped software is the mapping that was tested.

Two numbers, not one

RTP states the long-run share of stake returned. Volatility states how that return is distributed — whether it arrives as frequent small wins or as rare large ones. Two machines advertising the same RTP can behave entirely differently, and the difference between them is not a matter of luck but a design parameter chosen deliberately.

A high-volatility design reaches its stated RTP only over an enormous number of rounds, because most of the return is concentrated in outcomes that occur very rarely. Quoting RTP without volatility is quoting a mean without a spread, which for this family of games conceals most of what a player would actually experience.

Presentation and the arithmetic