Ask the Slot Expert: What determines the payback percentage on a slot machine?

Question: I vaguely understand the EPROM chip and its function. As you, and most readers, are fully aware, casinos order slot machines with a certain payback percentage for each machine. What determines the payback percentage on reel slot machines?

Answer: Let's look at what happens during a spin and I think you'll see what determines the payback percentage on a slot machine before I say it.

After you hit the Spin button, the program running the slot machine spins the reels — physical or video — on the machine. Now it has to determine where to stop each reel. The program gets a number from the random number generator (RNG) and uses it to set where the first reel will stop. The program gets a separate number from the RNG for each reel.

The range of the numbers produced by the RNG is much larger than the number of stops on a reel, so the program has to do a little mathematical magic (modulo arithmetic) to scale the number from the RNG to fall in the range of the number of stops. The reels in a traditional, reel-spinning slot machine typically have 22 stops (blanks and symbols). The size of the symbols on the reels, the size of the reels themselves, and the size of the slot machine all limit the number of stops that can be put on a physical slot reel. The reels in a video slot, on the other hand, can be as large as the developers want because the only limitation on the number of stops on a video reel is the amount of memory in the slot machine.

Computer memory is also used to expand the number of stops on a reel-spinning machine beyond the 22 stops on the physical reel. With 22 stops on the reel, the least likely we can make a winning combination is by putting one — and only one — jackpot symbol on each reel. That gives chances of 1 out of 10,648 (22 cubed) for hitting the jackpot.

Clearly that's far too likely for the machine to have a jackpot over 10,000 credits, let alone many millions of dollars. The program in a reel-spinning slot uses a table in the computer's memory to increase the effective number of stops on the reel by mapping the physical stops to one or more places in the table. For example, the stop with the jackpot symbol on reel one might appear in the table only once, while the blanks above and below the jackpot might appear two, three, four or even more times. Using this virtual reel table, the developers can lower the chances of landing a symbol on a reel on the payline from 1 out of 22, to 1 out of 32, 1 out of 64, 1 out of 256 -- 1 out of any number they want. As with the video reel, the only limitation on the size of a virtual reel is the amount of memory in the machine.

Now that the program has stopped each reel, it looks at the symbols that have landed on the payline and pays off accordingly.

Perhaps you can already see now what determines the payback percentage on a slot machine. The number of times each symbol appears on the video reel or virtual reel determines how likely it is to hit each winning combination. The pay table tells us how much each combination is worth. The pay table and reel layout determine the payback percentage on the machine.

Let's look at how we calculate the payback percentage. For each winning combination, you take the number of ways to hit it and multiply by how much it is worth. Add up these products for all the winning combinations and divide by the total number of combinations (the number of stops, video or virtual, on the first reel times the number of stops on the second reel times the number of stops on the third reel. . .). You also divide the sum by the number of coins played when determining the worth of the winning combinations. The result of the division, the quotient, gives us the long-term payback of the machine — or, more specifically, that combination of pay table and reel layout — expressed as a decimal.

Another way to think about how the long-term payback is calculated is to do this thought experiment. Image that all of the reels in a slot machine have stopped so that stop number 1 on each reel is at the top of the window or screen. Calculate how much is won on the payline(s), 0 for a losing spin. Now advance the rightmost reel one stop. Note that the physical reel on a reel-spinning slot may not move because that stop appears more than once in the virtual reel table. Again, calculate how much is won on the payline(s) and advance the rightmost reel one stop. Repeat the process. When you reach the last stop on the rightmost reel, you'll also advance the reel to its immediate left one stop, odometer style. Keep repeating the process until your slot reel odometer is back to 00000, the starting position. Add up all of the numbers to get the total amount that can be won from the pool of possible outcomes. Divide that sum by the number of results you wrote down, i.e., the total number of combinations. Also divide by the amount you assumed was bet in determining how much was won. The result is the long-term payback expressed as a decimal.

To sum up, the payback percentage on a slot machine is determined by the pay table and the number of times each symbol appears on each reel.

The subject of your e-mail was "Russia - Clinton - private and confidential".

No, wait. That was a different e-mail. Your subject line said to exclude video poker. But let's contrast determining the payback percentages on slot and video poker machines.

On a video poker machine, the developers are not able to make some cards appear more frequently than others. All hands must be dealt from a fair deck, with each card remaining in the deck equally likely to appear when a card is needed. The only way to change the payback on a video poker machine is to change the pay table.

On a slot machine, in addition to changing the pay table, the developers can also change how frequently the symbols appear. In practice, though, they almost always keep the pay table the same for a given game and change the symbol frequency. All Game of Thrones slots may have the same pay table, but the ones in the locals casinos have higher payback percentages than the machines on the Strip because the machines have different reel layouts.

So, to change the payback on a machine: On a video poker machine, you change the pay table. On a slot machine, you change the symbol layout.

Now, a few words about EPROMs. Computers have two general types of memory: RAM (random access memory) and ROM (read-only memory). The difference between the two is that RAM is volatile -- it forgets what was stored in it when the power goes off. ROM is non-volatile, it remembers even without power.

PROM stands for programmable read-only memory. This chip can be programmed by a user. EPROM stands for erasable programmable read-only memory. This chip can be programmed, erased and re-programmed by a user.

Slot manufacturers may store the programs running the slot machines on EPROMs. They may also store the reel layouts on EPROMs to make it easy to change the payback on a machine in the field by swapping EPROMs. Details are scant, even misleading, because manufacturers don't want to help cheats who want to figure out how the software works.