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RNGs and Multi-Coin Plays
Does limiting your investment limit a machine's value?
by Lou Krieger & Arthur Reber

We get letters, and letters... We're not up in that rarefied domain inhabited by the greats, like Dear Abby and Miss Lonelyhearts, but we're not doing badly for a couple of amateurs. And, besides, slots don't really stoke people like stories of failed marriages or spurned suitors. Most of our readers write to us wondering how they can: (a) beat the slots, or (b) lose less while still having fun.

The answers to the first kind of question are best delivered by the classic Brooklyn wise-guy expression: fuggedaboutit. No matter what you do, the odds are against you beating the slots in the long run. The only way you can manage to beat them is to get lucky. And while everyone knows you'll need lots of luck to beat the slots, no one can show you how to make certain Lady Luck dances your way.

The second question is more complex, and the answers depend on the particular machine and how it is played. The question that provoked this column came from "Robbie," a reader who noted:

My favorite machine is Blazing 7, a "buy-a-pay" slot. I often see people play with a single coin, which causes them to miss out on the jackpot and other high-pay combinations. Aren't people limiting their payback when they do this? Would this machine still meet the state-mandated payout? Or does the casino control commission figure that most players will play the maximum number of coins and use this as the basis for the payback?

Robbie had asked a fascinating question with a surprisingly complex answer. If Robbie or any other player does not play max-coin, the jackpot is taken out of the game. Playing less than max-coin will cost a player some value in the long run. How much value is lost depends on the exact paybacks offered for each additional coin. The key concept is long term. In the short run, a player is likely to have better results---or more precisely, results that aren't as bad---by only playing a single coin. Sure, you may miss the occasional monster payout, but those are all unlikely.

Second, the payback will depend in large measure on the machine's basic wager. On nickel machines, the payback percentage is always very low and multiple-coin players are probably better off moving to a machine with a higher base bet and a better payback percentage.

Third, the machine's payback is set by the manufacturer when it is built and the random number generator chip, or RNG, is installed. It makes no difference how many coins an individual player puts in the machine on any spin. Sure, playing only a single coin reduces the size of payouts, but it does not change the underlying programming of the chip. In most venues, no casino is permitted to change a chip without the local commission's permission.

Fourth, state commissions do not have mandated payouts. Individual casinos submit requests to the commission to install machines with particular paybacks. If the Blazing 7 machine you are playing is a nickel machine, its payout is almost certainly set around 90 percent (give or take a percentage point or two), and if it's a quarter machine, the payback will be a bit higher. The bigger the base bet, the higher payback percentage a player can expect to receive; you can verify this by perusing the payback data in the back of this magazine.

We sent this to our friend Robbie, who promptly fired back another e-mail containing the full payback for a Blazing 7 machine, which we won't bother to reproduce here, along with the following comment:

I still think one-coin players are not paid their fair share. Am I wrong? Must a machine pay back its percentage long-term average for every coin played? Or does the commission figure their payback on three coins only? Do one-coin players on these machines get the same percentage payback over the long run?

Robbie is absolutely correct about the reduced payback for one-coin players, but not about the nature of the machine's RNG or the role of the various state commissions that control organized gaming in the country.

It's important to understand that it's impossible to decipher the expected value of a machine by looking at its payout schedule and the features of the wheels. That expected value is coded into the chip that controls the machine.

We could build a nickel machine with a payout schedule where each and every outcome of the thousands of possible arrangements that could appear in the window paid $5,000---except one. And we could program this machine so that its expected payback was something horrific like 80%. All we have to do is program the chip in the machine so that almost every random number that the RNG picked was linked to that one "no payback" outcome.

It would be an incredibly frustrating machine to play and no one would play it for long because it would go for thousands of spins before it actually landed on one of the $5,000 payback outcomes. But if you'd just walked up to this machine, you'd have no idea about its devious programming. From the payback schedule, it would look like a lead-pipe cinch for you to make a bundle. And it wouldn't take you very long to go from thinking you've found Nirvana to attacking the machine with a jackhammer.

The answer to Robbie's question about how the paybacks on a Blazing 7 machine are modified by multiple-coin play is unknown to us. It looks like the kind of machine that increases the expected value of a play when larger wagers are made. As we and others have often noted, percent payback expectation is frequently increased when you bring larger payouts into play.

But the percentage payback, taken by itself, is not the key factor. In terms of the extent to which any machine will erode your bankroll, it is critical to remember that the increase in long-term expectation is based on percent return of investment. This does not necessarily map into a long-term increase in actual cash payback.

Let's take a hypothetical example to clarify this point. Suppose this Blazing 7 machine is programmed so that it will pay back 91% when played single-coin with the higher paybacks "off-line," and 95% when played max-coin. Since it is a three-coin machine, the max-coin player will be putting three times as much money at risk as the single-coin player.

If you wager a total of $1,000 at 91%, your expected loss is $90. But if you wager $3,000 at a 95% return, your expected loss is $150! So just because you've put the jackpot and other larger paybacks in play doesn't necessarily mean that you've increased your long-term payback. Is this machine really programmed to work this way? We don't know for sure---but we strongly suspect it is. You can also be fairly sure that the machine's long-term payback is determined primarily by its basic bet size, as we explained earlier.

As a final word, we'd like to remind you that much of what you sometimes see when you look at people's playing results comes under the heading of a "small sample." The "long run" is really, really long. To get a feeling for this, just take another glance at the payback figures in the back of this magazine. If you've saved a couple of month's issues, go back and look at them, too. You'll discover that the percentage payback from the same-bet-size machines in the same casinos often changes from month to month. These changes do not represent changes made to the machines. They represent random fluctuations that are produced by the RNG's in each machine. Even a month of play by thousands of people on hundreds---or even thousands---of machines isn't enough to completely stabilize the paybacks.

When thinking about how modern slot machines are designed, keep these facts in mind: (a) the higher the base bet, the higher the payback percentage you can expect, (b) how the machine will pay off in the long run is coded into the chip---a miniaturized computer of sorts that controls the operations, and (c) the long run---where experience and expectation theoretically converge---is a lot longer than most folks realize.

We hope this helps and thanks, Robbie, for asking such stimulating questions.

Gambling For Dummies is in your neighborhood bookstore now. Both Lou Krieger's and Arthur Reber's other books are available on line at www.ConJelCo.com and at www.Amazon.com. When not writing about gambling, Arthur Reber, Ph.D. is a Professor of Psychology. He can be reached through e-mail at areber@brooklyn.cuny.edu. Lou Krieger is a host at Royal Vegas Poker.com and can be reached at www.loukrieger.com

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