The Math Behind Slot Machines

You pull the lever, and the icons whirl. One stops. Another. They match – you just need the third. But the wheel spins just a bit too far, and you miss the jackpot. You were so close! Weren’t you?

The next time you play, you get another two matches and the final wheel stops just barely in time to give you the jackpot. You’ve won! But my goodness, that was close. Right?

Actually, in both cases, the outcome of your game was determined from the start. Slot machines are fun because they create a little show out of winning or losing, but in reality, the real game happens behind the scenes – in the circuit boards and moving parts of a physical slot machine, or in the computers and servers of an online casino.

The Math Behind Slot Machines

How slot machines work

Slot machines have always been random. Early slot machines use three wheels to determine the outcome, meaning that your result really was up in the air until the last wheel stopped spinning. Modern slot machines still have those wheels, but they don’t work that way anymore.

The problem with old-school slot machines is that even the most unlikely outcome is still fairly possible (by slot machine standards, anyway) – for example, a three-reel machine with 10 items on each reel will still produce the rarest outcome a minimum of on time out of 1,000 (0.1%). If hundreds of people come through a casino and pull the lever on that machine a few times each, there’s a good shot that the casino will be paying out a jackpot or two every day! And that means that the jackpot can’t be worth all that much, or the casino would go out of business pretty quick.

That’s no fun, but technology has solved the problem. Beginning in the 1980s, slot machine manufacturers were able to use computers within the machine to weight certain outcomes. Now jackpots could be made rarer, and their payouts proportionally more enticing.

Random number generators

In modern slot machines, a computer determines the outcome. And the easiest way to do this is to determine the outcome ahead of time. This is also the easiest way to make sure that the odds are exactly where the casino wants them to be – which is important, because many states and countries regulate the odds of slot machines to varying degrees.

The theater and fun of a slot machine are both still present on modern machines – you may even get to slap a button to stop the reels – but it’s all for show. The outcome of your game is actually determined by a random number generator the moment you first press the button or pull the lever.

What’s a random number generator? It’s exactly what it sounds like: a computer process that generates a random integer. This isn’t much different from what casinos have been doing for ages (a die is just a mechanical random number generator, after all), but the souped-up power of computers lets slot machines generate a huge range of random options (a die is limited to one through six – the computer’s range is astronomically larger). A range of values will give different results. Many of the generated numbers will give you a small win or a loss, while comparatively few numbers will lead to a win. These numbers, which you never see, are all that matters – everything else is for show.

The difference between online slots and physical slots

So what’s the difference, then, between online slots and physical slots?

Well, on one, you’ll physically push a button or pull a lever. On the other, you’ll click a button or press something on your keyboard.

Yes, that’s it. There may be differences in things like payout (just as there are from one brick-and-mortar casino to another), but there are no difference in function. Under the hood, both things work exactly the same way: with a random number generator. This is obvious on a digital slot machine, which is clearly little more than a computer in a box. But it is equally true on slot machines with physical reels – behind those spinning wheels is a computer determining the outcome. Slots on a screen can add extra options to the reels (since they don’t have to fit these symbols on a physical object), but mechanical slots can simulate the same effect on the odds by just making some stops more likely than others. There are no longer any slots that really determine your win reel by reel.

So gamble away at the online slots (though remember that odds on slots are never in your favor), and rest assured that you’re getting the exact same experience that you would in a casino.