The odds and probability behind slot machines are easier to understand than you might think. If you can handle middle school multiplication and division, along with some fractions and percentages, then you can handle slot machine odds. This page explains everything you need to know to play slots like a champ.
Probability in general
Probability is the mathematical study of how likely it is for something to happen (or not happen). For any event, the probability of it happening is a number between 0 and 1. Something that has a probability of 0 will never happen, while something with a probability of 1 will always happen. You can have a probability anywhere in between, too.
Probabilities are often expressed as fractions, percentages, or decimals. All of these forms are valid, but percentages seem to be the most meaningful to most people. If I tell you that there’s a 50% chance of rain tomorrow, you know what that means immediately. That’s one example of a probability.
To determine an event’s probability, you divide the number of ways it can happen by the total number of events that could happen. For example, when you flip a coin, you have a total of two events that can happen: 1-heads, 2-tails. If you want to determine the probability of getting heads, you divide 1 by 2, and you get ½ or 50%.
Gamblers use probability to determine a bet’s expected value. That’s the amount you can expect to win or lose on any given bet, based on the size of the bet and the probability of winning versus the probability of losing. It also takes into account the size of the payout when you win.
If I played a simple gambling game with you based on flipping coins, and I paid you $1 every time it landed on heads, but you had to pay me $2 every time it landed on tails, you’d understand immediately that I had the advantage. The expected value of that bet works this way. 50% of the time you’ll win $1, so you have a positive $0.50. 50% of the time you’ll lose $2, so you have a negative $1. Add the two together, and your expectation is -$0.50.
All casino games offer a similar payout. They always (with rare exceptions) pay bets out at less than the odds of winning. That’s how the casino maintains its house edge.
How odds used to work with slot machines
Mechanical slot machines consisted of three reels with ten symbols on each. Your odds of getting any given symbol on a single reel are 1 in 10 or 10%. To calculate the odds of getting that same symbol on all three reels at the same time is calculated by multiplying, so you calculate 1/10 X 1/10 X 1/10, for a total probability of 1/1000.
As long as the casino pays out less than 1000 to 1 on such a bet, they are guaranteed a profit as long as people continue to play the game. They can even offer payouts of more than 1000 to 1 on certain combinations, as long as they pay out correspondingly less on other symbols.
Smart players will immediately see how the size of the jackpot on a game like this is limited. That’s where modern slots come into play.
How slots odds work now
Modern slot machines don’t have physical reels. Most of them just use video screens, but even the ones which look like they have actual reels don’t use them to determine their outcomes. Modern slots use a random number generator that goes through a list of thousands of numbers every second. The split second that you press the spin button, the RNG stops at the number it’s at. Each of those numbers corresponds to a combination of reel symbols and a payout.
This enables slot machine manufacturers to create winning combinations that pay out far greater than they ever could before. Each reel symbol can be programmed to come up with a varying degree of frequency. Low payout symbols might come up 20% of the time, while higher paying symbols might not come up more often than 0.5% of the time.
That’s why modern slots can offer jackpots in the 7 and 8 figure range. Even though the jackpots are paid for via contributions of various wagers (albeit, at a tiny percentage), the casinos still need to have astronomical odds of winning to justify the size of even the smallest progressive jackpot. The use of RNGs to run the odds behind the spinning reels is what enables that.
Your odds of winning on slots in the short run aren’t bad, but in the long run, the house always has the edge. They achieve this by paying off bets at less than the true odds of winning those same bets. Now that you know this, you’ll only play with money you can afford to lose, and you’ll treat it like any other entertainment expense, right?