How slot machines work

How the random number generator picks the stops

by Michael Bluejay | 2002-13
See also how to play: Baccarat | Blackjack | Craps | Roulette | Texas Holdem | Video Poker

This page explains how slot machines actually work.
Unless you're interested in the math, you'll probably find my
general information about slot machines more useful.
 

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Slot machines are random, period

Slot machines are pretty simple.  A random number generator (RNG) picks random numbers, which are then mapped to the symbols on the reels, and the machine stops on those symbols.  The selection is truly, completely random, and isn't influenced by anything at all.  There's no such thing as a "payout cycle" when a machine supposedly will pay out more than normal.  A machine is never "due" to hit.  Every spin is just like every other spin:  completely random.

That makes sense, because the whole foundation of casino gaming is randomness.  Every other game in the casino, from craps to roulette, works the same way.  The outcome is random, and the odds are simply tilted in the casino's favor.  There's no mystery about slots, just like there's no mystery about craps.  Why would there be?  The casino wants its slots to work like all its other games:  randomly.

Even if they wanted the machines to operate otherwise, they don't have a choice.  Gaming regulations demand that the machines are completely random.  For example, this is from Nevada Gaming Regulation 14 (PDF):
"[A gaming device] must use a random selection process to determine the game outcome of each play of a game...Each possible permutation or combination of game elements which produce winning or losing game outcomes must be available for random selection at the initiation of each play....The selection process must not produce detectable patterns of game elements or detectable dependency upon any previous game outcome, the amount wagered, or upon the style or method of play."

There you have it.  Slots aren't affected by the presence (or absence) of a player's card, how long it's been since the last jackpot hit, or anything else.  They're random, period.  Slots don't have periods where they pay out more to "make up" for earlier periods where they paid out less.  They're random, period.  Anyone who says otherwise is simply pulling B.S. out of thin air and declaring it to be fact, with no evidence to support their delusions.  (My own evidence includes the regulations mentioned above, as well as actual slot machine par sheets, the fact that I've programmed online slots for hire, and my work with the legendary Wizard of Odds for ten years.)


The Basics

In a three-reel game, a random number generator (RNG) picks three random numbers, each of which corresponds to a stop on each reel, then the machine directs the reels to stop on the spots selected by the RNG.  The principle is the same for five-line video slots: five random numbers, one for each reel.

Note that by the time the reels are spinning, the game is already over.  The RNG has already selected the stops, and the reels spin sort of as a courtesy to the player.   Slot machines don't even need reels -- you could just put your money in and the machine could tell you whether you won or lost.  The presence of the physical reels makes no difference in the game -- they're just there to show you what the computer picked.


How the stops are selected

A typical non-progressive video slot has 35 to 50 stops per reel.  A mechanical slot uses a "virtual reel" inside its programming of 64 to 256 stops, which are mapped to the 22 stops on the physical reel.  The physical reel isn't big enough to hold all the stops that are needed, so the real reel is the big one in the computer program.  (source)

If you saw a worker open up a slot machine you might see a reel like the one on the right, if it were unfolded.  There are various symbols spread across 22 stops.  Yes, the blanks count as stops.  You might think that since there are 11 blanks you have a 50% chance of hitting one, and since there's only one jackpot symbol you have a 1-in-22 chance of getting it.  But it doesn't work that way, because we're not really working with a 22-stop reel.  We're really working with an invisible reel of like 128 or so stops, controlled by the computer.  The computer will pick a number from 1-128, each of which is mapped to a specific symbol.  Here's a hypothetical map for the reel shown at right:

Selected Number
Symbol Picked
Total no.
of symbols
1-73
Blank
73
74-78
Cherry
5
79-94
Bar
16
95-107
Double Bar
13
108-118
Triple Bar
11
119-126
Red 7
8
127-128
Jackpot
2

Say the computer picks #53.  That's a blank, and it tells the reel to stop on a blank.  If it picks #82, then it tells the reel to stop on a cherry.  If it picks #127, then the reel tops on the jackpot symbol.

Most of the numbers are for the lower-paying symbols, so that's what's more likely to get chosen. That's what we mean when we say the reel is weighted. Some symbols are more likely to be chosen than others, even if they appear the same number of times on the physical reel.

So you don't really have a 1 in 22 chance of hitting the jackpot symbol on this reel. Your odds are actually 2 in 128, or 1 in 64.

And of course, the most likely symbol is a blank. You have a 73 in 128 chance (57%) of drawing one of those.

Speaking of blanks, when the computer picks a blank, it actually picks a specific blank. Same for the other symbols that appear on the reel multiple times, like cherries and certain bars. The table above was simplified to make things easier to understand, but now that we've come this far, let's now look at how every single position on the reel might be weighted.

Stop

Symbol

Selected
Number
Number
of Chances
1
cherry
1-2
2
2

3-7
5
3
8-12
5
4

13-17
5
5
7
18-25
8
6

26-30
5
7
31-35
5
8

36-41
6
9
cherry
42-43
2
10

44-49
6
11
==
50-56
7
12

57-62
6
13
cherry
63
1
14

64-69
6
15
=
70-75
6
16

76-81
6
17
82-87
6
18

88-93
6
19
ΞΞ
94-104
11
20

105-115
11
21
jackpot
116-117
2
22

118-128
11

The fourth column (Number of Chances) shows the weighting. We've got a 2 in 128 chance of landing on the first stop (a cherry), and an 8 in 127 chance of hitting stop #5, the Red 7. Notice how the blanks surrounding the Jackpot symbol, #20 and #22, are heavily weighted. They're more likely to be selected, resulting in the "near-miss" effect. You think you just almost got the jackpot symbol, but it's really an illusion. You weren't close at all. It's like the blanks above and below the jackpot have little magnets on them.

So far we've talked about only one reel, though most slots have three, and each reel is actually weighted differently. As you go from reel to reel the weighting gets heavier, so you're more likely to hit higher paying symbols early on. By the third reel the higher-paying symbols are even less likely. This results in another kind of near-miss effect: How many times have you gotten JACKPOT, then another JACKPOT, and then... a blank? After the first two hits you're holding your breath for the third reel, but in reality your odds are poorer for getting that third jackpot symbol than they were for getting either of the first two symbols. However, for the rest of this discussion, we're going to assume that each reel is in fact identical in order to make the math easier.

A Par sheet details the probabilities for a particular machine.  Slot makers guard them religiously, but a few have made their way into the public's hands.  From them we can see that the principles are exactly as I described.  Here are the publicly-available Par sheets I know about:

  • Academic report by Canadian researchers, based on various Par sheets they obtained (PDF)
  • Blazing 7's slot by Bally, obtained by a slot machine collector (PDF)
  • Red White & Blue, obtained by mathematician Michael Shackleford (web page)

 


Jackpot Amount
Odds
Source

Double Diamond

2500 coins
1 in 46,656
Par sheets obtained by Canadian researchers (PDF)
Blazing 7's
5000 coins
1 in 93, 312
Bally's par sheet (PDF)

Phantom of the Opera

5000 coins
1 in 114,131
to
1 in 155,345
Par sheets obtained by Canadian researchers (PDF)
Red White & Blue
2400 coins
1 in 262,144
Wizard of Odds
Double Strike
5000 coins
1 in 500,000
Wizard of Odds (estimate)
Money Storm
10,000 to 50,000
1 in 2,188,411

Par sheets obtained by Canadian researchers (PDF)

Lucky Larry's Lobstermania

10,000 to 50,000
1 in 8,107,500

Megabucks

$8 to $33 million
(progressive)
1 in 49,836,032
John Robison in Casino City Times
Note that there are often different versions of machines with the same name, so the numbers above might not apply
to every flavor of the named machine.  What you should take from this is that as the jackpot goes up,
so does the difficulty in actually hitting it.

Hitting the jackpot

So now that we know the weighting of the reels, we can answer that elusive question: What are the odds of hitting the jackpot? Here's the answer. Assuming we have three identical reels as listed above, then the odds of getting the jackpot symbol on any reel is 2/128. The probability of hitting the jackpot on all three reels is 2/128 x 2/128 x 2/128 = 1 in 262,144. (If you played fast at 800 spins for 8 hours a day, you'd hit the jackpot on average once every 41 days.)  This in fact is the odds of hitting the jackpot on Red White & Blue.  (See the main slot article for more on jackpot odds.)

Calculating the payback

Now that we know the weighting of the reels, we can calculate the payback for this machine, which the percentage of money the machine would pay back over an infinite number of spins.  Of course you can't play for an infinite amount of time, but the point is, the longer you play, the closer your return will come to what the payback suggests.

Our slot has the following paytable.

Bluejay Bonanza Slot Machine paytable
Symbols
Payout
Jackpot (3 JP symbols)
1666
7 7 7
300
Ξ Ξ Ξ
100
= = =
50
25
3 of any bar
12
3 cherries
12
2 cherries
6
1 cherry
3

To find the payback of the machine, we multiply the probability of each winning hit times the payout for that hit, then add them all up, as shown in the following table. I included a "How Calculated" column if you're interested in seeing how I derived the probabilities. The numbers I use there came from the first table, above ("Total no. of symbols" column).

Bluejay Bonanza Slot Machine
Symbols
Probability

How calculated

Payout
Prob. x Payout
Jackpot (3 JP symbols)
0.000004

2/128 x 2/128 x 2/128

1666
0.7%
7 7 7
0.000244

8/128 x 8/128 x 8/128

300
7.3%
Ξ Ξ Ξ
0.000635

11/128 x 11/128 x 11/128

100
6.4%
= = =
0.001048

13/128 x 13/128 x 13/128

50
5.2%
&emdash; &emdash; &emdash;
0.001953

16/128 x 16/128 x 16/128

25
4.9%
3 of any bar
0.030518

(16+13+11)/128 x (16+13+11)/128 x (16+13+11)/128

12
36.6%
3 cherries
0.000060

5/128 x 5/128 x 5/128

12
0.1%
2 cherries
0.004399

((5/128)x(5/128)x(128-5)/128)x3
(prob. 1st reel x prob. 2nd reel x prob. NOT 3rd reel; then multiply all by 3, to account for the 2 cherries appearing in any of 3 different positions -- 1,2 or 2,3 or 1,3)

6
2.6%
1 cherry
0.108211

(5/128x(128-5)/128x(128-5)/128)*3
prob. 1st reel x prob. NOT 2nd reel x prob. NOT 3rd reel; then multiply all by 3, to account for our single cherry appearing on any one of the three reels

3
32.5%

Total

96.3%

So this is a 96.3% machine, meaning that if you played it forever, you'd get back 96.3 for every $1 you put into it.  Of course you can't play it forever, and in the short-term anything can happen, but the longer you player, closer your return will come to 96.3% -- meaning you will have lost 3.7% of all the money you bet.

Of interest is that the small payouts account for most of the payback.  The single cherry alone provides nearly a third of all the money you get back from the machine.  Same for "any bar / any bar / any bar".  The jackpot itself comprises less than 1% of the total payback.

Note that some figures are not exact due to rounding.

 

The RNG is constantly picking numbers

The RNG is always working, even when you're not playing, picking thousands of 3-number combinations per second.  The moment you press the button or pull the lever, the RNG picks its 3 numbers for your play.  So if someone hits a jackpot on a machine you were just playing, relax, you wouldn't have gotten it had you kept playing, because you would have hit SPIN at a slightly different time than they did.  Every millisecond you delay in hitting the SPIN button results in a different combination.

The reason the machine constantly picks numbers is so that no one can discern any pattern in the number-picking process and therefore predict a winner. It's extremely unlikely that anyone could do so even if the RNG didn't keep picking random numbers all the time, because the number of random numbers in a complete cycle is astronomical, but having the RNG pick numbers all the time removes any remote possibility that anyone could predict the outcome.

 

If you liked this article, see also my general information and strategies about slot machines.

 

The Wizard on Slots

Nobody knows more about the math of casino gambling than the Wizard of Odds (Michael Shackleford). His investigation into slot returns of Las Vegas casinos was groundbreaking and legendary.  His site probably has more info about slots than any other, and what's more, it's extremely reliable.  Highly recommended.

I hope this article has been helpful to you. Have fun!
See also how to play:

 

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Gambling Problem?
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