Slot Machine Odds and Probability
Understanding probability and odds as they apply to slot machine gambling is not difficult. In fact, there are few games in the casino as straightforward as slot machines. If you read the right sources, casinos will even tell you the return they expect on individual slot machines. Try asking the stickman at a craps game what the house's expected return is and tell me how well that goes.
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When it comes to slot machine gaming, the most important statistical details are a machine's return and a machine's payback. We'll look at those in more detail later, but here's a quick "intro to slot machine odds" lesson.
Slot Machines and Probability
Before the days of the random number generator, slot machine odds were really basic. Each reel of the machine had a specific number of symbols, and the odds of hitting a symbol would be one divided by the total number of symbols. If an old-school slot machine had 3 reels with 10 symbols on each reel, the odds of hitting a particular symbol would be 9 to 1. That means 9 "losing" symbols and 1 "winning" symbol per spin of the reel.
If you want to hit 3 symbols in a row to hit a jackpot, you simply multiply your chances of each spin turning up a symbol three times by itself. That equation looks something like this-- 1/10 X 1/10 X 1/10. The result? 1/1000, or odds of 999 to 1 against hitting the jackpot. That means you'd have 999 chances of being wrong and one chance of being right.
Ultimately this implied that if you spin the reels 1,000 times, you'd
be likely to hit the jackpot only once. This is only theoretical, of
course, because each individual spin could come up a jackpot at any
time.
With the advent of slot machines that run on random number generators, figuring odds on slot machines got a bit more complicated. Without going into too much technical detail, just know that a modern slot machine has an unlimited number of symbols and even an unlimited number of reels. Making things even hairier is the fact that the RNG is actually programmed to give certain symbols better odds of coming up than other symbols. Because of programming, figuring out a slot machine's "odds" is practically impossible.
That is why things like a slot machine's return and its payback percentage are so important today. If you know a slot machine's theoretical payback percentage, as reported by the casino, you have a better chance of picking a machine that is less likely to bankrupt you.
Slot Machines: Return vs. Payback
Many people use the terms "return" and "payback" as if they are
interchangeable. There's an important difference between the two.
A slot machine's return is the actual percentage of money paid out compared to the amount of money you paid in. Players keep track of these returns and use them to decide what machines to play and what machines to avoid.
Let's say you drop $100 into a slot machine and at the end of your bankroll, you've earned $90 back. That would give you an actual return of 90%. The ten percent that the casino kept is their profit. The good news is, you don't have to keep track of your own returns. Casinos are legally required to report their slot returns to local governments, and that information is made public. Pick up a copy of Casino Player or Strictly Slots magazine for information on slot returns.
Slot Machine Payback Percentages
Payback percentage is a purely theoretical number that indicates how much a given slot machine should pay back. Remember that payback percentage is based on an infinite number of spins, not an hour or a set amount of money. If a specific slot machine is programmed to pay back 95%, that number is only accurate in terms of infinite plays, and that given enough time, the machine will pay back 95 cents for every dollar put in.
So how can you use payback percentage to plan your slot machine gaming session? Every time a casino orders a new slot machine, the casino specifies the payback percentage it wants. Casinos are required to operate slot machines within a certain range, usually a minimum of 75% payback. But a 75% payback machine wouldn't be very much fun for casino customers, so they generally set payback between 88 and 98%.
Winning 98% of the time sounds good until you realize that it
guarantees a casino income from the machine. A 98% payback percentage
means the casino is always earning two cents for every dollar you put
in. A popular example of why high payback percentages are popular shows
how bad this can get--if a slot player is playing on a $1 machine with
two credits at a time, they can easily hit 800 spins an hour. After just
one hour, that player has put $1600 into the slot machine. The casino's
5% take on a 95% payback percentage means that player is actually losing
$80 an hour. That's how casinos make money on slot machines.
Unfortunately for slot machine fans, there's no good way to find out a slot machine's payback percentage. That's why understanding your actual return on a machine is important. But even if you tracked your play at the same slot machine for twenty years, you could never actually pin down a machine's payback or return. That's because math is constant and infinite and you are a human being. Just because a machine is programmed to pay back 90% doesn't mean that you will literally win 90 cents for every dollar you plug in. Still, having a basic understanding of your likelihood to win on a given machine can help you make better slot machine play choices.
