RVUG is based in West-Central New Jersey, just an hour's drive from Atlantic City on the Jersey Shore. In the past twenty years Atlantic City has become one of the world's capitals of casino gambling. Being so close to the "action," RVUG members are constantly kept aware of happenings at the Atlantic City casinos by reports and advertisements in the public press.

Some of the most interesting news, in a mathematical sense, concerns slot machines. It has always puzzled me that people are eager to play slot machines in spite of the fact that the inner workings of these machines are concealed from the player. Other casino games have rules and are pretty much out in the open, but with slot machines the rules are known only to the machine.

I have seen gambling advice both in the public press and on the World Wide Web which, though well-intentioned, is incorrect. Just as in the game of Chuck-a-Luck, people are making faulty conclusions about certain gaming propositions through an imperfect knowledge of the laws of probability. I also am convinced that the casinos do not know the true value of some of the propositions they offer.

One piece of advice, found on a web site, concerns a popular type of slot machine which offers multiple payout lines depending on how many coins are inserted per spin. With one coin there is a payout on the middle row. Additional coins will activate payouts on the top and bottom rows and two diagonals. The given advice is that by playing five coins and activating all payout lines the player will maximize his total return from the machine. There is a good chance that this advice is incorrect.

I have been experimenting with a computer simulation of such a machine. Although I have not been able to determine the number and relative positions of all of the symbols on each of the wheels, I am quite sure that there is only one bar on each wheel. Of all of the possible symbol combinations, three bars gives the highest payout. I'll call three bars a "Jackpot."

Let's state the problem thus: if you are trying for a Jackpot, are you better off playing one coin at a time or five? By playing five coins you are obviously increasing your chances of hitting a Jackpot on a per spin basis, but not on a per coin basis. That is because multiple play lines do not win or lose independently of one another. Since there is only one bar on each wheel, if you play five coins at a time you can win on only one of them. If you play them one at a time you can win on more than one or perhaps on all of them. Calculating the return from the lesser payouts, cherries for example, is more complicated because there is more than one symbol on each wheel, and one would need to know the layout of the wheels.

Two Atlantic City casinos, Trump Castle and Harrah's Marina, recently offered similar propositions to new players. There was an editorial treatment of the propositions in the Philadelphia Inquirer which included the customary incorrect analysis.

The two casinos now issue magnetically encoded "player cards" which identify the player when he inserts it into a slot machine and lets the casino keep track of his play. Use of these cards is optional, but one must register and get a card in order to take advantage of the propositions. Here are the rules:

1. You must use the player card in order for your play to be counted.
2. You may play any slot machine you wish, but you must play continuously for a minimum of one hour.
3. If you comply with the above, the casino will reimburse you for any net loss you may incur in that first hour up to a maximum of $100.

Actually, the minimum period is one hour at one of the casinos and a half-hour at the other. In considering these propositions the following questions arise:

1. Which is more attractive, the half-hour minimum period or the one-hour?
2. Should you play quickly or slowly, or, should you play high denomination machines or low ones?
3. When should you stop?
4. What is the proposition worth? That is, if you could sell it, what would be a fair price?

I won't try to answer all of these questions, since they make good topics for debate, but here are some things to consider:

Although the player's expected net return from slot machines is negative when he plays with his own money, this is not the case when he plays with the casino's money. Although he is more likely to lose it than not, he is being given a free chance at a jackpot. Consequently the player's net expectation from the proposition will be positive provided that he follows certain self-imposed rules.

As long as the player can invoke the casino's offer to cover all of his losses, he is playing with the casino's money. This is not the case when

1. He plays for less than an hour (or half hour)
2. Hey plays for more than an hour (or half hour)
3. His losses total more than $100
4. He has accumulated enough winnings during the first hour that he could not be down before the hour is up.

These considerations lead to the following rules. For "one hour" read "one half hour" where appropriate.

1. The player should play for exactly one hour.
2. He should pace his play to attain the goal of losing exactly $100 in that hour. That maximizes his use of casino money and gives him the greatest chance at a jackpot without incurring any risk.
3. If he wins enough that he cannot attain that goal within the hour, he should quit immediately. From that point on he is playing with his own money.

The following questions are thrown out to the floor:

1. Which compulsory time period is more attractive, one hour or one half hour? Don't assume that this is a trivial question.
2. What is the value of the propositions, or, what data must one collect in order to calculate it?

Here is another question: do you know of a good slot machine simulator for the Commodore?

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