Slot Machines
The three-reel slot machine, invented in San Francisco in 1898, underwent substantial evolution over the course of the 20th century. For example, while classical slots were purely mechanical or electro-mechanical, modern ones are electronic and controlled
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Slot Machines
What a fierce excitement of doubt, hope, and pleasure! What tremendous hazards of loss or gain! What were all the games of chance he had ever played compared to this one? William Makepeace Thackeray, Vanity Fair
The three-reel slot machine, invented in San Francisco in 1898, underwent substantial evolution over the course of the 20th century. For example, while classical slots were purely mechanical or electro-mechanical, modern ones are electronic and controlled by microprocessors with random-number generators. Slot machines are the only casino games for which evaluating the house advantage requires information not generally available to the gambling public. In this chapter we consider three slot machines, two classical ones and a modern one, for which the required information is available. In Section 12.1 we evaluate the expected payout for each machine. In Section 12.2 we address volatility and ruin issues.
12.1 Expected Payout We begin by quoting an academic-sounding definition of a slot machine that was published in 1978 (see the chapter notes): The slot-machine is essentially a cabinet, housing 3 or more narrow cylindrical drums, commonly called reels, which are marked with symbols. Vertically disposed on a common axis, the reels are caused to revolve freely, when player activates machine and pulls a lever-like handle affixed in the side of the cabinet. Awards, which are paid automatically, are based on the horizontal alignment of symbols, when the spinning reels come to a position of inertial rest.
Unstated but implicit in the definition was the requirement that the player insert one or more coins into a slot (hence the name “slot machine”) in order to activate the machine. S.N. Ethier, The Doctrine of Chances, Probability and its Applications, DOI 10.1007/978-3-540-78783-9 12, © Springer-Verlag Berlin Heidelberg 2010
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12 Slot Machines
With only minor changes, the definition also applies to modern slot machines, even though they work rather differently. The main distinction is that almost all slots manufactured since about 1985 are electronic and controlled by a microprocessor. The microprocessor typically contains an EPROM (erasable programmable read-only memory) on which is programmed a random-number generator that operates continually.1 The moment the player pulls the handle or presses the button to activate the machine, the most recently generated random numbers (one for each reel) determine the outcome almost instantly. The machine’s reels (if it has physical reels, not just video representations of them) are controlled by what are called stepper motors, which ensure that the reels stop in a position consistent with the predetermined result. Despite all this, the underlying mathematics of the modern slot machine is not much different from that of the classical machine, the primary distinction being that the stopping positions of the reels need not be equally likely. There are a few other inconsequential differences as well. Paper currency is preferred to coins, with the player recei
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