Ask the Slot Expert: I have to watch what I write - Part 4

For the past few weeks, I've written about statements I have to be careful not to write in a column.

One is writing that the number of heads and the number of tails thrown in a fair coin toss get closer to being equal after a large number of tosses. That's not necessarily what happens. What does happen is that the ratio of heads/tails tends to get closer to 1 and the ratio of heads/tosses (and tails/tosses) tends to get closer to 0.5.

I found a good illustration of this phenomenon on the Wikipedia page for the Law of large numbers. Scroll down about 1/3 of the page to the section on the Weak Law. The right side of the page has a simulation showing a fair coin toss. One side of the coin is red, the other blue. The simulation tosses the coin and fills two bar graphs with the results of the toss. One bar shows the number of blues and the other, the reds. To the right of the bars is a pie chart that shows the proportion of red and blue. Even though there is sometimes a big difference between the heights of the red and blue bars, the pie chart is very close to half blue and half red.

Another thing I have to be careful not to write is that a run of generosity or Scroogeness on a machine will be balanced out by an opposite run. That's not necessarily what happens. What does happen is that this blip is such a small part of a machine's overall performance that it has very little effect on a machine's actual payback percentage.

The two things that tend to happen are a result of the same effect: a large imbalance of heads versus tails or a run of luck on a slot machine have little effect when the number of samples is large.

Another thing I have to be careful about writing is not mathematical. It's connotational and I haven't figured out the best way to avoid writing it.

To figure out the long-term payback of a machine, you add up how much all the winning combinations pay and divide that sum by the product of the total number of combinations possible multiplied by the bet per spin, (Total Paid) / (Total Combos * Bet). That gives you a machine's long-term payback percentage.

On a high level, a machine determines the result of a spin by choosing one of the possible combinations at random and then paying off the combination according to the paytable. If the combination doesn't appear in the paytable, it's not a winning combination and it pays nothing.

I've stopped writing that a machine is programmed to pay back a certain percentage. The word programmed suggests that the program running the slot machine is intentionally taking steps to pay back that percentage.

The only things a machine is programmed to do are the steps in my high-level description: choose a combination at random, pay the player if it's a winner. There's no function to force a machine to pay back a percentage. How much a machine has paid out in the past isn't a factor in determining the outcome of a spin.

The payback percentage is a result of the reel layouts and the paytable, not any algorithms in the program. The slam-dunk proof of that is that you change the payback of a machine by changing the reel layouts or paytable, not by changing the program. You don't have to change the program to change the payback.

It's long overdue that I make my usual disclaimer: These statements apply to RNG-based, Class III machines in the United States. Unlike with some other methods to determine an outcome and in some other countries, the largess or stinginess of an RNG-based machine in the U.S. is determined only by probability. There's no governor function steering a machine towards a long-term payback percentage, either in the short or long run.

Instead of writing that a machine is programmed to pay back a certain percentage, now I simply write that a machine pays back a certain percentage.

This phrasing doesn't imply a means by which a machine achieves that percentage. It doesn't suggest that a machine is actively trying to achieve that percentage.

I sometimes add a follow-up, clarifying statement that machines "make their numbers" not because of some programming in the machine, but because of the magic of Random Sampling with Replacement.

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