In brief
A slot machine takes a stake, displays a combination of symbols on its reels and pays if that combination appears in its paytable. The result of each spin is decided by a program, not by the movement of the reels. The player makes no decision that changes the probabilities: only the stake and, on some games, the number of lines can be chosen. In the long run the machine returns, on average, a fixed share of the stakes, set when the game is designed.
The random number generator
At the heart of the machine is a random number generator (RNG), a program that produces numbers continuously, even when nobody is playing. At the moment a spin is started, the machine takes the current value and turns it into the positions where the reels will stop. The result is settled at that moment.
The reels, whether mechanical or drawn on a screen, only display a result that has already been decided. Their animation, sounds and speed influence nothing. Stopping the reels early with a button only shortens the display. Every spin is independent of the ones before.
Reels, lines and the paytable
Classic machines have three reels; video machines usually have five or more, with several visible rows of symbols. A payline is a path across the reels along which combinations are read. On a machine with several lines, the total stake is the stake per line multiplied by the number of active lines. Many modern games use other systems instead of lines (for example, matching symbols on adjacent reels win, from left to right, in any row) and have special features, described on each game's information screen.
The paytable shows what each combination returns, as a multiple of the stake. It does not show the probabilities, though: how many positions each symbol takes up on a reel cannot be seen. On modern machines, the "virtual" reel in the program can have many more positions than the symbols displayed, and some symbols can be much rarer than they look. What is shown on screen does not reveal how often a combination comes up.
RTP and the house edge
RTP (return to player) is the share of stakes the machine returns on average, over a very large number of spins. It is a property of the game, set at design, not of any particular session. As a rule, the value is checked by independent testing laboratories, game by game, and the same game may exist in several configurations with different RTPs; the figure that applies is that of the installed version. The house edge is the rest: the share of stakes that does not return to players.
RTP does not describe a session. A player who stakes a small amount on a machine does not get back exactly the share RTP indicates: they may win a lot or lose everything. The figure comes close to the actual result only over very many spins. The link between the two ideas is explained in the article on the house edge and RTP.
Volatility
Two games with the same RTP can behave very differently. A low-volatility game pays small amounts often; a high-volatility game pays rarely, but sometimes a lot, with long runs without a win between payouts. Volatility is measured by the standard deviation of the result of one spin: the larger it is, the more widely the results of a session are spread around the average. Some games show a volatility level on their information screen, in words or on a scale. The details are in the article on variance and the law of large numbers.
An imaginary machine, fully calculated
The machine below is invented for this page and does not exist. Its purpose is to show how a slot's figures are calculated, because here everything that stays hidden on a real machine can be seen. Real machines have their own reels, weightings and paytables, and their figures are set by the manufacturer and certified for each game.
The machine has three reels and a single line. Each reel has 20 positions, and the generator picks one of them on each reel, all equally likely. That gives 8,000 equally likely combinations. The reels are identical:
| Symbol | Positions on a reel (of 20) |
|---|---|
| 7 | 1 |
| BAR | 3 |
| cherry | 5 |
| blank | 11 |
The paytable, for a stake of one unit:
| Combination | Returns | Probability |
|---|---|---|
| 7 – 7 – 7 | 300 × the stake | 0.0125% |
| BAR – BAR – BAR | 40 × the stake | 0.34% |
| three cherries | 20 × the stake | 1.56% |
| exactly two cherries | 3 × the stake | 14.06% |
"Returns" includes the stake: at "3 × the stake", a stake of 1 unit brings back 3 units, a net win of 2. Any other combination loses the stake.
Because there is a single 7 on each reel, the 7–7–7 combination corresponds to a single arrangement of the reels and has a chance of 1 in 8,000. Multiplying each payout by its probability and adding up the results gives the machine's RTP: 90.69%. The house edge is 9.31%.
A few things follow from this calculation:
- Most spins pay nothing. The hit frequency, the chance that a spin brings any payout, is 15.97%.
- The big prize matters least. The two-cherry combination pays little but comes up often, so it makes the largest contribution to the RTP of all the combinations. The top prize, 7–7–7, contributes the least, precisely because it is so rare.
- Results are widely spread. The standard deviation of one spin is 4.83 units for every unit staked, several times more than for a bet on red in European roulette (1.00). Over short sessions, the result can be far from the average, in either direction.
A real machine is calculated on the same principle, only with many more positions, more lines and special features, and a far larger number of combinations.
Myths
"The machine is due to pay"
The machine has no memory. After a long run without a win, the chance on the next spin is the same as on any other spin. RTP is an average over very many spins, not a debt the machine has to "pay back" to a player. The idea that a result "is due" after a long absence is a well-known error of reasoning, described in the article on the gambler's fallacy.
The near miss
Two 7s on the line and the third just above or below it look like a sign that the prize is close. It is not: that combination loses, like any other that is not in the paytable, and it says nothing about the next spin. On the imaginary machine, the chance of a 7 on the third reel is the same whatever is on the first two. On machines with virtual reels, what can be seen around the line says nothing about the real probabilities.
"Hot" and "cold" machines
A run of wins or losses on a machine does not show how the next spins will go. The time of day, the moment the button is pressed or the fact that someone else has just won do not change the probabilities. On the machines described here, each spin is decided independently, with the same probabilities.
Terms
- House edge: the share of each stake the house keeps on average.
- RTP: the share of stakes that returns to players on average.
- Variance: how widely results are spread around the average.