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Downloadable games are not the reason your machine turned cold11 December 2006
Downloadable games are being tested in the United States, but only on a limited basis. It is still true, much more often than not, that the payback percentage on a machine in a U.S. casino can only be changed by physically swapping chips in the machine. I just want to remind players you are not likely to have played a download-capable slot, and the reason the machine was hot yesterday and cold today is normal randomness and not the result of downloading a new reel layout to the machine.
A casino could have a schedule for a machine such as you described, but the schedule is set up on the server, not the machines themselves. Downloadable games is a "push" technology. Only one payback program for a game at a particular denomination is resident in the machine at any given time. The machine itself can't change payback programs on its own.
Casino closed? Most casinos in the United States are open 24 hours a day, 7 days a week. Nevada's regulations require that a machine be idle four minutes before and after a configuration change takes place. That regulation ensures that a machine's configuration cannot be changed while a person is playing it. Nevertheless, I anticipate getting many letters from players claiming that a configuration change did take place while they were playing a machine because the machine went from hot to cold. (Very few people write to complain about a machine going from cold to hot!)
In any case, the paybacks you gave are not legal in most U.S. jurisdictions — 80% is too low and 100% is too high. It's not enough that the average payback be in the legal range; the machine can never, even for an instant, have an illegally low payback. The manufacturers won't even offer for sale in a state a payback program that is illegal there.
Now, you said that the cost (about $1,500) of having an additional payback program licensed for a machine "doesn't seem much, compared to what profit a machine brings over a long period." These machines probably earn less per day than you think they do. You can see some average wins per day at http://gaming.unlv.edu/abstract/slotwin.html. These numbers are averages. A particular machine's win per day is affected by its denomination and the amount of action it gets. The numbers range from about $80-$140 per day in Nevada to over $500 per day in Illinois.
Let's say a casino is going to run 92% payback during the week and 88% payback on the weekends. The house edge increases by 50% from 8% to 12%, so the average win per day per machine will also increase by 50%. A machine earning $80 per day is now earning $120 per day, and a machine earning $500 per day is now earning $625 per day. At $625 per day, a machine will pay for the license of the additional payback program in a little over two days. The machine earning $120 day takes 12.5 day to pay for the additional license.
But this isn't the right way to figure out how long it takes to break even on the license. The machines were already earning a certain amount of money per day. We have to look at the incremental profit and see how long it takes that figure to pay for the license.
The incremental on the $120/day machine is $40. Now it takes 37.5 gaming days to pay for the license. Assuming only two gaming days per week using the lower-paying program, it takes almost five months to pay for the license. The incremental profit on the $625/day machine is $125. The break-even period now is 12 gaming days or six weeks, which isn't bad at all.
These break-even periods assume there are no other expenses associated with the additional revenue. Many states take a percentage of slot win right off the top, so the casino doesn't keep all of the incremental revenue. More importantly, states have to be informed whenever paybacks are changed on a slot floor. That alone may be enough of a cost to prevent casinos from changing paybacks as you described.
Now, I don't have an MBA and this may not be the way casino bean counters analyze whether it is worthwhile licensing multiple payback programs for a machine. There may, for example, be another use for the money that will yield additional profits every day instead of just two days a week.
The bottom line is that the most likely reason that machines turn hot or cold is because of randomness, not because the machine's payback program has been changed.
Moving on to your second section, I've had slot and video poker machines take $500 and more from me in I-don't-know-how-many hands and not give me anything big in return. On the video poker machines, I was playing at 99.5% payback. It's perfectly reasonable to have poor results after 3,000 spins on a high-payback machine.
If you can program a computer, you can see how widely spread results can be after only 3,000 spins. First, you need to know how likely each payout on a machine is. Video poker is easy. The probabilities of drawing to each hand are available on many programs, websites and in many books. Slots are tougher. You need the par sheet to know the probability of each payout. Fortunately, example par sheets are in slot books and on websites.
Once you have those probabilities, you could write a program that simulates playing the machine 3000 times. You can note your results at the end of each run, then plot the amount won or lost versus the number of times you achieved that result to get a graphical look at the range and how likely you are to get a particular result.
You have another option for the program. You can write a process that I used for analyzing video poker pay tables. Each hand has a limited number of outcomes — royal flush down to bust — and we know the probabilities of drawing to each hand. We'll do 3,000 iterations. For each iteration, we take each possible outcome we had coming into the iteration and apply all the possible outcomes to get all possible results we could have achieved after that number of hands.
Let me illustrate with a simpler problem. We're drawing marbles from a bag at random. There are 60 red marbles, 30 blue marbles, and 10 white marbles, so the probabilities of drawing a red, blue, or white marble are 0.6, 0.3 and 0.1, respectively. We return each marble to the bag after noting its color (sampling with replacement), so the probabilities never change.
After the first iteration, there's a 0.6 probability that we drew a red marble, a 0.3 probability that we drew a blue and 0.1 probability that we drew a white.
For the second iteration, we start with the red result from the first iteration. There are three possible outcomes -- red, white, or blue-- and the probabilities are still the same for drawing the colors. There was a 0.6 chance that we got a red in the first iteration, so there is (0.6)(0.6) or 0.36 probability we have two reds in the second iteration. We could draw a blue, and the probability is (0.6)(0.3) or 0.18. For red and white, the probability is (0.6)(0.1) or 0.06.
Now move down to the blue outcome from the first iteration. There is a 0.3 chance we drew a blue on the first draw. We could get a red next, and the probability of blue-red is (0.3)(0.6) or 0.16, same as red-blue. Here it gets a little tricky in my example. We don't care about order, red-blue is the same as blue-red (full house-flush is the same as flush-full house, in terms of total money won), so we add this probability to the one for red-blue, and we change the way we describe each outcome to a total number of each color drawn (e.g., R2-W0-B0, R1-W0-B1).
When you're done, you'll have the probabilities of ending up with R3000-W0-B0 to R0-W3000-B0 to R0-W0-B3000 and everything in between.
For video poker and slot machines, the results for which we'll calculate the probabilities at the end of each iteration is the total amount won, instead of colors drawn. If you can do this exercise, you'll find that it is much more likely than you think it is to have lost $500 after 3,000 spins on a high-paying machine.
Slot machines are different from elections. In elections, a small sample size can give a very accurate prediction of the final results because there are fewer choices that matter in an election than there are winning combinations on a slot machine. The slot machine requires a much larger sample size than an election to get an accurate prediction of the population.
Here's another example of rare events in a population requiring an increase in sample size. In the United States 30 years ago (before cable TV), there were only three TV stations that most people watched each evening. A sample size of 1,400 households was sufficient to get a very accurate estimate of the total number of people who watched each program.
Today, we have 100+ channels from which to choose, many of which have fewer than 1 viewer per 1,400. We need a larger sample to get accurate ratings for these stations and current TV ratings are done with a larger sample than before.
A three thousand spin sample is not sufficient to get an accurate prediction of the payback for a slot machine. See Don Catlin's article, Sample Size, this month on this site for more information about the sample size 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.
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