Stay informed with the
NEW Casino City Times newsletter!
Best of John Robison
Is it possible for a slot machine to never pay?25 July 2009
You're right, there is the possibility that a machine would never pay off. Let's look at how likely that would be. Assume we have a machine with a 10% hit frequency. That means that 9 spins out of 10 are losers.
The probability that your next spin will be a loser is 0.9. The probability that your next two spins will be losers is 0.81 (0.9 squared). The probability that your next five spins will be losers is 0.59049, your next 10 0.35, your next 100 0.0000265, and so on.
There is the possibility that the machine would never pay off, but it is incredibly unlikely. In any case, you are correct that machines that never hit anything would be very bad for the casino.
Now, you asked how casinos can advertise that their machines pay off 94.3% of the time? I think you misunderstood what they're saying. A casino may say that a machine pays back 94.3%, which means that in the long run it pays back 94.3% of the money played through it. Individual players will win or lose, but if they play $100,000 in total through the machine, the machine will have won about $5,700 from them.
To answer your question, let me ask you one. How can the results from tossing a pair of dice yield the pyramid of craps if the results of each toss are random?
What's random on the dice toss is the result of the next toss. Still, we know that in the long run, 7 tosses out of 36 will be a seven, 6 out of 36 will be a six or eight, and so on.
The results of a spin on a slot machine are the same as the results of a toss of the dice. On the dice, we don't know the total that will be thrown next, but we can calculate the probability of throwing each possible total. On the slot, we don't know what symbols will land on the payline next, but we can calculate the probabilities of those symbols landing on the payline by looking at the distribution of symbols on the virtual reels. If we take into account how much each winning combination is worth and the cost to play, we can calculate the long-term payback.
The mathematical name for the process that takes place in a slot machine is Random Sampling with Replacement. The key point of this type of sampling is that the probability of achieving any particular result is the same on each observation.
The process you described of having some function in the machine override the results yielded by polling the RNG is called a "secondary decision" and is illegal in the United States. All gaming jurisdictions in the United States follow Nevada's regulation that the results of polling the RNG must be displayed to the player and the program can't ignore or change the result if the program doesn't like it for some reason.
Furthermore, the function isn't needed. Research Random Sampling with Replacement to see why it's not needed.
Best of luck in and out of the casinos,
Send your slot and video poker questions to John Robison, Slot Expert, at email@example.com. Because of the volume of mail I receive, I regret that I can't reply to every question.
This article is provided by the Frank Scoblete Network. Melissa A. Kaplan is the network's managing editor. If you would like to use this article on your website, please contact Casino City Press, the exclusive web syndication outlet for the Frank Scoblete Network. To contact Frank, please e-mail him at firstname.lastname@example.org.
Best of John Robison