Slot machine odds used to be easy to calculate. When you’re dealing with three reels, ten symbols on each reel, and a limited pay table, then it’s just a simple math problem. But the rise of electromechanical slot machines and (later) video slots added some complexity to the situation.
This means that the chance of hitting the jackpot image on one reel is 1 in 64. If all of the reels are set up the same way, the chances of hitting the jackpot image on all three reels is 1 in 64 3, or 262,144. For machines with a bigger jackpot, the virtual reel may have many more stops. This decreases the odds of winning that jackpot.
How Probability Works
Probability has two meanings. One is the likelihood of whether or not something will happen. The other is the branch of mathematics that calculates that likelihood. To understand the odds as they relate to slot machines (or any other gambling game), you have to understand the basic math behind probability.
Don’t worry though. The math isn’t hard. Probability involves addition, subtraction, multiplication, and division, all of which you learned in middle school.
The first principle of probability is that every event has a probability of between 0 and 1. If something has no chance of ever happening, then its probability is 0. If something will always happen, no matter what, then its probability is 1.
Probability is, therefore, always a fraction. It can be expressed in multiple ways, as a decimal, as a fraction, as a percentage, and as odds.
A simple example is a coin flip. The probability of getting heads when you flip a coin is 50%. That’s common sense, but how is it determined mathematically?
You simply take the total number of possible outcomes, and divide the outcome you’re trying to determine the probability of it by that number. There are two possibilities when flipping a coin, heads or tails, but only one of them is heads. That’s 1 divided by 2, which can be expressed as ½, 50%, 0.5, or 1 to 1 odds.
Odds are expressed as the number of ways something won’t happen versus the number of ways that something will happen. For example, if you’re rolling a single six-sided die, and you want to know the odds of rolling a six, you’re looking at 5 to 1 odds. There are five ways to roll something other than a six, and only one way of rolling a six.
When you want to determine the probability of multiple things happening, you use addition or multiplication, depending on whether you want to determine whether one OR the other event will occur, or whether you want to determine whether one event AND the other event will occur.
If you’re looking at an “OR” question, you add the probabilities together. If you’re looking at an “AND” question, you multiply the probabilities by each other.
So if you want to know what the probability of rolling two dice and having one or the other come up with a six, you add the probabilities together. 1/6 + 1/6 = 2/6, which is rounded down to 1/3.
Odds Of Winning Casino Games
If you want to know the probability of rolling two dice and having BOTH of them come up six, you multiply the probabilities. 1/6 X 1/6 = 1/36.
How Slot Machine Odds USED to Work
Early slot machines were mechanical devices. They had three metal reels that had ten possible stops each.
To calculate the odds of a single symbol appearing on a reel, you just divide the one symbol by the total number of potential outcomes. So if you had one cherry on a reel, your odds of hitting that cherry were 1/10, or 10%.
To calculate the odds of getting three cherries, you multiple 1/10 X 1/10 X 1/10 and get 1/1000, or 0.1%.
If the odds of hitting that symbol are the same as all the others, then you have 10 possible jackpots you can win, which means that your chances of winning SOMETHING are 10/1000, which is 1%.
Most people wouldn’t play a slot machine that lost 99 times out of 100, though, so slot machine designers added additional, smaller prizes for getting two symbols out of three for certain symbols. And as long as they paid out less in prizes than the odds of hitting those jackpots, then those slots are guaranteed to make a profit in the long run.
For example, if a prize for hitting three cherries was $1000, you’d be playing a break-even game, but if the prize were $750, it’s easy to see how the casino would be guaranteed a profit. The difference between the odds of winning and the payout odds is where the casino makes its money.
How Slot Machines Work Now
Modern slot machines use a computer program called a random number generator to determine the outcomes of the various spins of the reels. This creates an imaginary reel with a number of symbols limited only by the program in question.
A mechanical slot machine with 256 symbols per reel would be huge, too large to play, much less to build. But a computer can create an imaginary reel with 256 symbols per reel and take up no more space than an iPod Shuffle.
To make things even more interesting and entertaining, slot machine designers can program different probabilities for each symbol to come up. Most symbols might come up once every 256 spins, but others might come up twice as often, while still others might only come up half as often.
This enables slot machine designers and casinos to offer slot machine games with far larger jackpots than they were able to when they were limited by mechanical reels. And they’re able to offer these large jackpots and still generate a healthy profit.
How Does This Relate to Payback Percentages?
The payback percentage is the amount of money that the slot machine is designed to pay out over an enormous number of spins. This number is almost always less than 100%. The difference between 100% and the payback percentage is the house edge, and that’s where the casino makes its profits.
A simple example can help illustrate how this works. Suppose you have a slot machine with three reels with ten symbols on each, and it only pays out when three cherries hit. The odds of winning that jackpot, as we determined earlier, is 1/1000.
If we set the jackpot as $900, and charge $1 per bet, the payout percentage for that game will be 90%, or $900/$1000. Of course, no one would play a slots game which only paid out once in every 1000 spins, which is why there are various smaller payouts programmed in.
There’s no way to tell what the payback percentage on a particular game is unless you have access to the par sheet for that machine. Casino management has that information, but players never have access to that info.
The best slot machine odds are almost always found in real casinos. If you see slot machines in an airport or a bar, be aware that the payback percentages on those games is much lower than you’ll see in a real casino.
In a modern slot machine, the odds of hitting a particular symbol or combination of symbols depends on how the virtual reel is set up. As we saw in the last section, each stop on the actual reel may correspond to more than one stop on the virtual reel. Simply put, the odds of hitting a particular image on the actual reel depend on how many virtual stops correspond to the actual stop.
Odds Of Winning Slot Machines
In a typical weighted slot machine, the top jackpot stop (the one with the highest-paying jackpot image) for each reel corresponds to only one virtual stop. This means that the chance of hitting the jackpot image on one reel is 1 in 64. If all of the reels are set up the same way, the chances of hitting the jackpot image on all three reels is 1 in 643, or 262,144. For machines with a bigger jackpot, the virtual reel may have many more stops. This decreases the odds of winning that jackpot considerably.
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The losing blank stops above and below the jackpot image may correspond to more virtual stops than other images. Consequently, a player is most likely to hit the blank stops right next to the winning stop. This creates the impression that they 'just missed' the jackpot, which encourages them to keep gambling, even though the proximity of the actual stops is inconsequential.
A machine's program is carefully designed and tested to achieve a certain payback percentage. The payback percentage is the percentage of the money that is put in that is eventually paid out to the player. With a payback percentage of 90, for example, the casino would take about 10 percent of all money put into the slot machine and give away the other 90 percent. With any payback percentage under a 100 (and they're all under 100), the casino wins over time.
In most gambling jurisdictions, the law requires that payback percentages be above a certain level (usually somewhere around 75 percent). The payback percentage in most casino machines is much higher than the minimum -- often in the 90- to 97-percent range. Casinos don't want their machines to be a lot tighter than their competitors' machines or the players will take their business elsewhere.
The odds for a particular slot machine are built into the program on the machine's computer chip. In most cases, the casino cannot change the odds on a machine without replacing this chip. Despite popular opinion, there is no way for the casino to instantly 'tighten up' a machine.
Machines don't loosen up on their own either. That is, they aren't more likely to pay the longer you play. Since the computer always pulls up new random numbers, you have exactly the same chance of hitting the jackpot every single time you pull the handle. The idea that a machine can be 'ready to pay' is all in the player's head, at least in the standard system.
When you hit the slot machines in a casino, you'll have dozens of gaming options. Machines come with varying numbers of reels, for example, and many have multiple pay lines.
Most machines with multiple pay lines let players choose how many lines to play. For the minimum bet, only the single line running straight across the reels counts. If the player puts more money in, he or she can play the additional horizontal lines above and below the main pay line or the diagonal lines running across the reels.
For machines with multiple bet options, whether they have multiple pay lines or not, players will usually be eligible for the maximum jackpot only when they make the maximum bet. For this reason, gambling experts suggest that players always bet the maximum.
There are several different payout schemes in modern slot machines. A standard flat top or straight slot machine has a set payout amount that never changes. The jackpot payout in a progressive machine, on the other hand, steadily increases as players put more money into it, until somebody wins it all and the jackpot is reset to a starting value. In one common progressive setup, multiple machines are linked together in one computer system. The money put into each machine contributes to the central jackpot. In some giant progressive games, machines are linked up from different casinos all across a city or even a state.
Some slot-machine variations are simply aesthetic. Video slots operate the same way as regular machines, but they have a video image rather than actual rotating reels. When these games first came out, players were very distrustful of them; without the spinning reels, it seemed like the games were rigged. Even though the reels and handles in modern machines are completely irrelevant to the outcome of the game, manufacturers usually include them just to give players the illusion of control.
These are only a few of today's popular slot variations. Game manufacturers continue to develop new sorts of machines with interesting twists on the classic game. A lot of these variations are built around particular themes. There are now slot games based on television shows, poker, craps and horse racing, just to name a few.
To learn more about modern slot machines, including strategies to increase your chances of winning, check out the links below.