A shuffle through the gaming mailbag

NOTE: Today's mailbag is an e-mail exchange with a reader who had a further question after the initial answer. Both questions are from the same reader.

Q. I read that the random number generator on slot machines is constantly moving and constantly generating new numbers, whether the machine was in use or not. Also, the RNG's pace or rate of selection had nothing to do with the rate of play.

If this is the case, how is it that the casino is able to set its payback rate to within a specification by state law? I don't seem to be able to get my head around the total separation of the RNG from the play of the machine that would permit the setting of payback rates.

A. Programming for the RNG sets odds of the game, just like using six-sided dice set the odds at craps. With one 6 on each die, a total of 12 will show up an average of once in 6 x 6 trials — once per 36 rolls of the dice. That doesn't mean a 12 has to show up once in every set of 36 rolls, just that the odds on every roll are 1 in 36. Over thousands of rolls, the results will come very close to that 1 in 36 average, but in the short term, the 12 can turn up two or three times in a row, nor not at all in a hundred rolls. The results are random, but the odds will push them toward a statistical norm in the long term.

Same deal on a slot machine. If a game is programmed with 32 random numbers on each of three reels, with only one number on each reel corresponding to a red 7, then three red sevens will turn up an average of 32 x 32 x 32 spins — once per 32,768 spins. That doesn't mean the three red sevens have to turn up once in every set of 32,768 spins. They can turn up twice in a row, or several times in short order, or not at all in 100,000 spins. The results are random, but the odds will push them toward a statistical norm in the long run.

Just as setting that statistical norm in craps will yield a house edge of 13.89% when you bet the 12 in craps, the statistical norm will lead to the targeted payback percentage on the slot machine. It just keeps generating those random numbers according to the odds of the game. If you hit a couple of big payoffs in a row and the payback percentage soars to several thousand percent in the short term, the RNG still just keeps generating those numbers randomly. In the long run, periods when big payoffs show up more often than normal and extra-long cold streaks just fade into statistical indifference, overwhelmed by hundreds of thousands or millions of spins a slot machine gets.

Q. So, from what you say, the payback percentage is based on the programmed return of the random number generator and not from any actual payback that would be programmed into the machines for some type of return based upon money wagered?

A. There are two different numbers here. The machine's targeted payback percentage is theoretical, based on the odds of the game, just as craps or blackjack or roulette have a house edge based on the odds of the game.

The machine's actual payback percentage as reported to state gaming boards is based on actual wager amounts and paybacks, just as hold percentages in table games are based on buy-in and actual results. If you see the listings of payback percentages in Slot Manager magazine or on state gaming board website, those are based on actual results.

The theoretical payback percentages and the actual payback percentages will not be identical, although given enough trials they will be very close. If the casino orders a chip from the manufacturer designed to yield 93% payback, the actual results over a thousand trials could be anything —perhaps a 150% payback if someone hits a fairly substantial jackpot, or they could be a 50% payback if there's a cold streak with no big hits.

But over hundreds of thousands of trials, the odds of the game will lead to something very close to a 93% return, just as thousands of times rolling the dice will lead to something very close to — but not exactly — one 12 per 36 rolls.

When a machine pays out 92.8% for a month, that doesn't mean it was programmed to pay out 92.8%. It was programmed with odds that would lead to a 93% return, or perhaps to a 92% return, and random fluctuations from the norm led to the payback to be slightly different from, though very close to, the targeted percentage.