Ask the Slot Expert: Why does this losing combination appear so frequently?

Question: Many times, and I mean many, the same losing result will appear on the reels. This one seems to pop up often. I'll get single bar - Double Diamond - single bar, just missing a nice payout. If not the diamond in the middle, then another symbol surrounded by the single bars at each end.

Since we agree that the results are random, seeing this result again and again would suggest that I hit the spin button at exactly the same time I have done so in the past. I get it that this losing combination may have more numbers associated with it on the RNG but, gee, it still would be a long shot for it to appear so often.

If I didn't know better I would think this is programmed to come up often, no matter when I hit the spin button.

Answer: I don't know what game you're playing. Two single bars and a Double Diamond is a nice payout on every Double Diamond machine I've played. So let's generalize your question and look at the situation of the same losing combination appearing very frequently.

If slot machines determined their results by selecting from a pool of, say, index cards with one card for each combination that could appear on the payline, then it would be very unusual to have the same combination appear so frequently. But slot designers have many techniques at their disposal to make some combinations appear more frequently than others.

On a reel-spinning slot, some symbols appear more than once on the physical reel. The single bars on your reels may appear two or even three times. The losing combination on the reels may be the same as one a few spins before, but it could be made up of different stops.

In the old days, before computer control of the slot machine, changing the number of times each symbol appeared on the reel was the only way designers could affect how frequently symbols landed on the payline. With computer control, designers have more flexibility.

As you said, more numbers could be associated with a particular combination than with other combinations. I don't like saying that more numbers from the RNG are associated with an outcome, because that implies that the designers are determining what symbol should appear for each possible number from the RNG. That is in effect what happens, but it's not what the designers do. The output from the RNG could be a number from 0 to 2,147,483,647 or more. The designers don't map each of those numbers to a symbol.

The designers do, however, create a virtual reel within the program running the slot machine. They map each stop on the physical reel to one or more stops on the virtual reel. The more times a stop on the physical reel appears on the virtual reel, the more likely that stop is to land on the payline. And the more frequently a symbol appears on the virtual reel, the more likely that symbol is to land on the payline. If the symbols in your losing combination appear many times on the virtual reels, it's not such a long shot that the combination appears so often.

Most virtual reels have between 32 and 100 stops, with a few having 200-300 stops -- far fewer stops than the range of numbers from the RNG. How do slots take a potentially huge number from the RNG and determine which stop on the virtual reel it's associated with?

They use a mathematical operation called modulo arithmetic. Modulo arithmetic is just a way to scale a set of numbers with a large range to a set with a smaller range. It's really very simple. We just divide and take the remainder.

Say we have 32 stops on our virtual reel. When we divide a number by 32, the remainder will always be from 0 to 31. We can then add 1 to get the result from 1 to 32, but in some programming languages that's not necessary because it's perfectly okay to start indexing with 0.

Suppose the number from the RNG is 1,285. The program divides 1,285 by 32 and gets a remainder of 5. We'll add 1 to that and say we want the sixth stop on the virtual reel.

The designers did not go through every number from the RNG and assign it a stop on the virtual reel. But every number from the RNG that is evenly divisible by 32 maps to the same stop, and every number that yields of a remainder of 1 maps to the same stop, and so on.

The designers associated symbols with stops on the virtual reels. Modulo arithmetic then automatically and mathematically associates each number from the RNG with a stop on the virtual reel.

So, having the same combination land on the payline twice doesn't mean the slot generated the same raw result twice. A symbol may appear on the reel more than once, and each result used a different instance of the symbol on the reel. A symbol may appear on the virtual reel more than once, and each result may have used a different virtual stop. And finally, more than one number from the RNG maps to a virtual stop and each result definitely had different numbers from the RNG.

So, two results may appear to be identical — and they may be identical as far as the player, who really only cares about winning or losing, is concerned — but they can be very different if we look at what really happened in the slot machine.