# Slot Machine Math: Exploring Game Odds and Hit Frequency

Staff Writer
May 21, 2013
4904

Slot machines are very simple to play and donâ€™t require any specific gambling knowledge. Anyone can get in the game. Every spin is just like every other spin â€“ theyâ€™re all totally random. But just because theyâ€™re random doesnâ€™t mean that thereâ€™s no math involved. All machines have one thing in common â€“ the longer you play, the closer the payout will be to the theoretical results.

But in order to understand the theoretical odds itâ€™s important to understand a little bit more about hit frequency and payback percentage.

## Classic Slots and Classic Odds

The technology of slot machines may have changed over the years, but the game has remained the same. A player inserts a coin and pulls the handle to rotate a series of reels. Each reel has a picture or symbol printed on them. Depending on which pictures line up with the pay line, you win. And the payout depends on which pictures line up.

The classic mechanical slot machines used springs and tension to stop the reels at random. These old electro-mechanical slots werenâ€™t anymore predictable than todayâ€™s modern slots. Most old mechanical machines had three reels that held 20 symbols, while most modern slots have three virtual reels with 22 stops â€“ and a random number generator program.

For example, for an old slot machine with 20 stops on each reel there would be 8,000 different combinations. We get this number by multiplying the number of symbols on each reel (20 x 20 x 20 = 8,000). The 8,000 possible combinations are known as a cycle. Itâ€™s important to know that the cycle does not mean the cycle of winning and losing â€“ just the mathematical cycle.

In theory, if you pulled the lever 8,000 times, you would see each combination of reels once. To figure out the odds of hitting a particular combination of three reels, simply multiply your chances of landing one symbol by itself (1/20 x 1/20 x 1/20). This means your odds of pulling up any combination on a classic slot machine are 1/8,000 or 7999 to 1.

Just like with flipping a coin â€“ the odds may be 50/50, but you are not likely to see exactly 50 heads and exactly 50 tails if you flipped a coin 100 times. However, with both a slot machine or a coin flip, the higher number of times you do it, the closer the odds would be to the actually probability. So to actually get close to those odds, youâ€™d have to flip the coins millions or billions of times.

## How Random Number Generators Work

Modern slot machines are more complicated itâ€™s much more difficult to mathematically predict the odds, because the numbers are theoretical and are essentially developed from a pool of infinite spins.

Modern slot machines use a Random Number Generator (RNG). The RNG electronically generates a random value from millions of combinations. These values determine where the reel stops. Electronic slot machines generate these numbers at a rate of 300-500 per second. When you press the â€śSpinâ€ť button on an electronic slot machine, it processes the random values. The first value it chooses determines the position of the first reel, the second value for the second reel and the third value for the third reel.

## Payback Percentage

A machineâ€™s payback percentage is what percent the machine will â€śpay backâ€ť to the player in the long run. The payback percentage is programmed into the machines by the manufacturers and can be adjusted depending on how loose the casino wants the slots to be. Machines with a higher payback percentage are commonly referred to as being â€śloose.â€ť

Most machines run a payback percentage somewhere between 75 and 99 percent. For example, if a slot machine has a 90percent payback, it will theoretically pay back 90 cents on every dollar paid in. Keep in mind that these percentages are figured from an infinite pool of spins.

Say you see an advertisement for a casino boasting a 95percent payback. What this is really saying is that â€śYou put in \$100 and weâ€™ll give you back \$95.â€ť Of course, you could win big on the first dollar or lose all \$100. Think back on a random coin flip â€“ you have a 50/50 chance of winning. In a totally just game where the casino has no advantage, you bet \$100 and win you get \$100 and if you lose you lose \$100. Theoretically, over enough time, you and the casino would be even.

But with a 95 percent payback, the casino essentially pays you \$95 for your win but still takes the \$100 when you lose.Â In this scenario you are losing \$5 for every \$100 you wager. Thatâ€™s how a casino profits â€“ less winnings are paid than money gambled and lost.

## Hit Frequency

Frequency is the theoretical percentage of spins that will payout something to the player. The frequency is based on how many times each symbol appears as well as how often winning combination occurs. Machines with high hit frequencies pay out small wins more frequently and machines with lower hit frequencies pay out less often, but with more money.

The hit frequency basically tells you how many times youâ€™ll have to lose in order to win â€“ on average. A return of a couple of coins is a hit, but itâ€™s not much of a win. For most slot machines, the hit frequency ranges from 9 to 25 percent. This turns out to a hit average of 9-25 times for every 100 spins conducted. These hits could be anything from a marginal return to a huge payout.

Itâ€™s important to note that there is usually no direct correlation between payout percentage and hit frequency. Machines with high payback may still have a low hit frequency or vice versa. A machine with a high payback and low hit frequency means that it doesnâ€™t hit as often, but it pays out more. A machine with a low payback and high hit frequency pays out small wins, more often.

So whether you enjoy waiting longer for the bigger payout or getting little returns and less waiting time, youâ€™ll now be able to find a slot machine that is the perfect combination of entertainment and profit.

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