# How slot machines work

## aka, How a specific payback is achieved aka, Slot Machine math

Last update: February 2023

“Michael Bluejay's comprehensive explanation of how slot machines work [is], in my opinion, the best one out there.” Gaming the Odds

Notes:
Many Native American casinos instead use "Class II" slots based on bingo or the lottery because local laws don't allow regular slots.  Class II machines look pretty much the same on the outside as regular slots, and you still get a random result, the machine just arrives at that random result a bit differently from what's described below.
(2) This article covers traditional slot machines.  The new skill-based slots are covered on a separate page.
(3) Programmers don't need this.  Programmers don't need to know the math, since since they can use "par sheets" where the math has already been done for them.  Such programmers can skip to my "How to Program a Slot Machine" article.

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## Slots are random

Before you see how slots work, you simply have to understand that the outcome of each spin is random.  This is a pretty easy concept, but many people just refuse to believe it.  If you're not convinced that slots are random, then see my article on how slot machines are random first, then come back here.  Don't worry, I'll wait.

## Picking the symbols

On a slot machine, a random number generator (RNG) picks a random number for each reel, which each number matching a stop on its reel.  Then the machine directs the reels to stop on the spots selected by the RNG.

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 visible reels—you could just put your money in and the machine could tell you whether you how much (if any) you won.  Wrap your head around that one for a minute.  The presence of the visible reels makes no difference in the game—they're just there to show you what the computer already picked.

## How the stops are selected

A typical non-progressive video slot has dozens of stops per reel.  An electro-mechanical slot uses an (invisible) "virtual reel" 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 it's the big one that's used in the computer program. (example source)

If you saw a worker open up an electro-mechanical 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 #75, 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.  On our sample machine, 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 or five, 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.

## 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 our reels are 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 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) 2000 7 7 7 300 Ξ Ξ Ξ 100 = = = 75 — — — 40 3 of any bar 35 3 cherries 12 2 cherries 9 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 2000 0.76% 7 7 7 0.000244 8/128 x 8/128 x 8/128 300 7.32% Ξ Ξ Ξ 0.000635 11/128 x 11/128 x 11/128 100 6.35% = = = 0.001048 13/128 x 13/128 x 13/128 75 7.86% — — — 0.001953 16/128 x 16/128 x 16/128 40 7.81% 3 of any bar 0.030518 ( (16+13+11)/128 ) ^3  - (11/128)^3 (3 triple bars)  - (13/128)^3 (3 double bars)  - (16/128)^3 (3 single bars) 35 32.26% 3 cherries 0.000060 5/128 x 5/128 x 5/128 12 0.21% 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) 9 3.96% 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 32.46% Total 98.99% Note: I updated the paytable and the calculations on 2/16/23. The version that somebody else coded earlier on GitHub returns 94.2%, though it might be listed there as 96.3%.  The older paytable was 1666 / 300 / 100 / 50/ 25 / 12 / 12 / 6 / 3.

So this is a 98.99% machine, meaning that if you played it forever, you'd get back 98.99¢ 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 play, the closer your return will come to 98.99%—meaning you will have lost 1.01% 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 hundreds of random numbers per second. (NV Gaming Regulations, Technical Standards, 1.400)  The moment you press the button or pull the lever, the RNG picks its 3 or 5 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 fraction of a second 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 even the fantastically remote possibility that anyone could predict the outcome.

## Par sheets

Slot makers create a "Par sheet" for each slot which lists the reel symbols and the paytable.  From this the payback can be calculated, and a programmer can write the computer code for the slot.  This data is similar to the tables I provided above for my fictional slot.  I have a separate page about par sheets, along with several actual examples.

## Near misses

Earlier we saw how the symbols on electromechanical slots are weighted.  There are only 11 blanks on the physical reel, but chances the RNG will pick a blank is much higher than 1 in 11.  In fact, it will favor the blanks immediately above and below the jackpot symbol.  Hitting these blanks gives players the illusion that they almost landed the jackpot symbol, because the jackpot symbol is physically close to the payline.  But it's not mathematically close.  In reality, the player wasn't close to landing the jackpot symbol on the payline at all.

As you might expect, research shows that the near-miss effect keeps players playing longer. (Journal of Gambling Studies)

The Wizard of Odds cites an unnamed source who said that Nevada regulations say that a stop on a reel can't be weighted more than six times more than either stop next to it. (link)  However, I scrutinized Regulation 14 and can't find any such requirement.

Video slots show the actual reels rather than virtual reels.  As such, the kind of near-miss described above won't artificially appear on video slots.  (In theory, there might be some video slots that use virtual reels, but I haven't seen any evidence of this.)  However, video slots use another method to make a near-miss effect:  they put fewer jackpot symbols on the 4th and 5th reels vs. the 1st, 2nd, and 3rd reels.  When players line up the symbol on the first three reels they'll feel they were close to getting a 4th and maybe 5th symbol, but the reality is that it's much harder to get those right-hand symbols.

In 1988, it was discovered that certain machines were using a different, illegal kind of near-miss technology.  The slot would first choose the stops randomly, and if it was a losing combination, rather than showing the actual combination selected, it would choose another combination to display, which was more likely to show jackpot symbols just above or below the payline. (source)

## Do I have free will in the bonus round?

In a bonus round where you can pick from multiple boxes which reveal a prize, players often wonder, "Does it matter which box I pick?  Are the various prizes truly scattered among the boxes, or am I gonna get (say) 10 credits no matter which box I picked?"

For the answer to that we turn to the authority on these kinds of questions, the Wizard of Odds, who says:  "Based on seeing par sheets and speaking to industry insiders I can confidently say that if the alternative choices are shown at the conclusion of a bonus round then the game is honest about them. In other words the prizes were randomly determined and what you see at the end is truly how they were hidden. However in games where the alternative choices are not shown the odds are likely similar to a prize wheel, with lower probabilities for the higher wins." (source)

## Play slots online

I suggest you play something other than slots because slot odds are so bad.  You could also play online with fake money, because then it doesn't matter if you lose.  A good casino for free-play is Bovada, since it requires no download and no registration.  (If you see a registration box, you can close it and continue without registering.)  You can play with real money too, though I hope you won't (or at least won't bet more than you can comfortably afford to lose). (advertisement)

### All my slot machine articles

Practice gambling with play money

Before you throw down your hard-earned cash in a casino, PRACTICE FIRST!  Learn the games with play money where it doesn't cost you anything if you lose.  Seriously.

You can play Bovada's games (below) right away without registering for an account.  Most every other online casino makes you give up your email address just to play the fake-money games — ugh.  That's the main reason Bovada is the only online casino that gets advertising space on my site.  (When you see the registration box, you can cancel it and proceed to the game without registering.)

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