Stay informed with the
NEW Casino City Times newsletter!
Best of John Robison
Still more "truth" about slots4 August 2008
I'll respond to some of your statements.
"Someone can hit the jackpot at the very first pull, but unfortunately just theoretically. The probability of such event is like probability that I will be President of USA. It is very close to zero."
The probability of hitting the jackpot on a machine on its first pull is the probability of hitting the jackpot on the machine. It's no more theoretical than hitting the jackpot on any other spin.
"From your description of the USA slot machines someone can get impression that they are fair. Are they?"
It depends on what your definition of "fair" is. A mathematically fair game is game that is not biased toward any player. Slot machines are not mathematically fair because they favor the casino.
The games are fair, however, as compared with carnival games, which use optical illusions and other tricks to make the games appear easier to win than they actually are. On a U.S. slot machine, it is possible to hit every combination displayed on the pay table on every spin and the machine will pay you the proper amount for a winning combination based on your bet. In this sense they are fair.
"Make a fair Outcome Calculator"
One makes a slot machine mathematically fair by altering the game so the amounts you get paid for the winning combinations are related to the probabilities of hitting those combinations. There are two ways to do this. One way by adjusting the pay tables. Using roulette as an example, the chance of hitting a straight number bet on a double-zero wheel is 1 out of 38. If the game were fair, the bet would pay 38 units instead of 35. The other way to make a slot machine mathematically fair is to alter the probabilities of hitting the winning combinations by changing the layout of the virtual reels.
In the United States, Class III slot machines (machines with RNGs) must display the outcome as determined by the number(s) polled from the RNG. No alteration of that outcome is allowed.
Time on a slot machine is measured in spins. Given that pay table and virtual reel layout for a machine, we can calculate the volatility of the pay table. Given the volatility, we can calculate the volatility index. With the volatility index, we can calculate confidence intervals, which tell us the range around the machine's long-term payback we expect the machine's actual payback to fall after a certain number of spins with a given level of confidence. You can see the calculations in Kilby and Fox's Casino Operations Management.
As the number of spins increases, the range decreases. After we've done the calculations, we can say something like "we can be 90% sure that this 95% long-term payback machine's actual payback to be between 94% and 96% after 10,000,000 spins."
Here's the 90% confidence values table for a particular Double Diamond machine:
"How can you guarantee different paybacks from 60% up to 95% without controlling either RNG or Outcome Calculator?"
It's called Random Sampling with Replacement. Look it up. Given enough plays, a machine's actual payback percentage will be very close to its calculated long-term payback percentage.
"Is it fair to offer a game to someone, where his chances to win are almost zero?"
Every casino does it every day. As long as the game isn't biased except for the house edge, and the rules of the game are well known and followed, players know what they are getting and are getting what they are paying for. Is it fair? Yes, players know there is a house edge. In addition, they don't have to play.
"But, I am telling you: RNG pattern is mayor factor in the payback determination."
Nonsense. The RNG is nothing more than a mechanism to draw a sample. (Have you read anything about Random Sampling with Replacement yet?)
A machine's long-term payback is calculated using the pay table and the layout of the symbols on the virtual reels. The RNG is irrelevant.
"To be honest I did not understand how you can determine 32 virtual stops on the machine with 22 physical stops."
It's just an example. Look for my articles and articles by others about virtual reels, expanded reel listing and Telnaes maps. You can even download the Telnaes patent.
Briefly, most modern slot machines use a virtual reel table to expand the 22 physical stops on the physical reels to 32 or more virtual stops on a virtual reel. Slot designers do this to be able to lower the probability of a stop landing on the payline below 1/22. Slot designers do that so the machine can have a larger jackpot than could otherwise be offered if the probability of landing the least likely combination was 1 over 22-cubed.
I would be happy to keep this conversation going, but no more epic e-mails, please. Limit them to one or two questions related to the same topic.
You'll also have to do your homework. I've been involved in too many exchanges in which the other people are only interested in arguing their beliefs about the way slot machines operate and are unwilling to do any research and investigation on their own.
Your homework is to read articles about Random Sampling with Replacement and virtual reels.
Send your slot and video poker questions to John Robison, Slot Expert, at firstname.lastname@example.org. 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 email@example.com.
Best of John Robison