If slots are random, then . . .

Not a month goes by that I don't receive at least one e-mail with a slot machine question that starts, "If your randomness theory is correct, then . . . "

I have to issue a disclaimer. That slot machine results are determined by random number generators is not my theory. It's not a theory at all. It's a fact of slot machine life, and it certainly didn't originate with me.

The information I pass on here is fact, things I've picked up in a couple of decades of speaking with casino slot directors, game manufacturers, designers, programmers and engineers in a couple of decades of covering the gaming industry both for players and for publications targeted at industry professionals. I've picked up information from others who cover gaming, too, and I hope I've contributed my share in return.

What brings this all up now is my latest "if your theory is true" e-mail from a reader who turned out for the grand opening at a recently remodeled and rethemed casino.

"It was packed," she wrote. "I heard somebody who worked there say, 'Big crowd means we'll be paying out a lot tonight,' and he had a big smile on his face. He was wearing a suit, and had a casino ID badge on his lapel, so I went up to him and asked if he meant jackpots and he said, 'Oh, there'll be some jackpots.'

"My question is this. If your randomness theory is true, how could he know they'd be paying out a lot? The casino must have control over the payouts if they can make them pay big for a big crowd."

Now, slot machine results remain random no matter how many people are playing, and the casino employee the player consulted knows that. More money will be paid out when more people are playing just because more wagers are being made. The payback percentages remain the same, the chances of any individual winning or losing remain the same, and the casino will both take in and pay out more money.

Let's make up a hypothetical casino in which the slot machine odds are programmed so that random results will lead toward players getting back 90% of all money wagered. If there are only 100 customers, each making $1,000 worth of wagers, that's $100,000 in wagers. On the average, paybacks to players will be $90,000 — 90% of the money wagered.

Now let's say it's a busy weekend night, and instead of 100 players we have 1,000 customers, each making $1,000 worth of wagers. Now instead of $100,000 in wagers, we have $1 million in wagers, and on the average payouts shoot up to $900,000.

Ten times the wagers on the average will bring 10 times the payouts.

We can do the same thing with big jackpots. Let's say odds on the machines are set so that, on the average, they'll pay out the top jackpot once per 25,000 plays. And let's say each of the customers is betting $1 per spin, so that our small crowd is spinning the reels 100,000 times and the bigger crowd is spinning 1 million times. Then in an average session, the group of 1,000 players will see 40 jackpots, while the group of 100 players will see only four.

In a real casino, not all the slot machines will have the same payback percentage, nor will they all have the same frequency of big jackpot hits. Depending on specific location, there'll be penny machines — lots of them — with returns below 90% and dollar machines from about 93 to 96%. There'll be lots of credit denominations and payback percentages in between the pennies and dollars, and $5 and up games that pay even higher percentages than the dollars.

There'll be rapid-hit slots with relatively small top jackpots that occur as frequently as once in 10,000 plays. In most jurisdictions there'll be wide-area progressives with top jackpots in hundreds of thousands, and sometimes millions of dollars, that will average millions of spins between top jackpot hits. And there'll be the majority that fall somewhere in between.

On every one of them, the results are determined by a random number generator. The casino can't control when the payouts come. Still, if you have 10 players sitting at a bank of dollar machines, it's more likely that at least one of them will hit a big pay than if only one customer was playing, just because more spins of the reels mean more chances for that big win to come up.

That's all the casino employee was saying, in many fewer words. It's not that the casino controls payouts so there are more in big crowds. It's that the natural odds of the game lead toward more money being paid out when more money is being taken in.

That's no theory. It's just how the games work.