Slot machines are designed to yield random results, or at least results as random has humans can program a computer to be. Slot machines also are programmed with specified payback percentages to give the house an edge. Players sometimes have a difficulty reconciling those two statements. How can a slot machine be random if it has a programmed payback percentage?
Other questions follow from the first. Doesn’t a programmed payback percentage imply that slots must have cold streaks to make up for hot streaks or big jackpots? How else can slots hit their programmed percentage?
And what about bonus rounds? Can they really be random if they have to be part of the programmed payback? Don’t your results have to be predetermined so they can be included in the payback percentage calculations?
The short answers are that slots can both be random and have a programmed payback percentage, that their doesn’t have to be any makeup time after big hits for slots to reach their target percentage in the long haul, and that variable – and random – bonus results can be part of the calculations without any need to short-circuit randomness.
Let’s take each of those issues on at a time.
SLOTS ARE BOTH RANDOM AND HAVE A PROGRAMMED PAYBACK PERCENTAGE
In that respect, slots are the same as nearly every other casino game. All give the house an edge by paying less than true odds on winning bets.
Craps is random in that any two-dice total can come on any roll, but has the equivalent of programmed payback percentages in the house edge. Roulette is random in that every number can turn up on every spin, but long-term results also will lead to an expected payback percentage.
Take the one-roll bet on 12 in craps. There are 36 possible combinations of two six-sided dice, but only one of them yields a total of 12 – 6s on both dice.
Shooters will roll 12s an average of once per 36 rolls, making the true odds 35-1. If you bet on 12 and win, you’re paid 30-1.
If you bet $1 per roll, you’d risk $36 in an average 36 rolls. On the one winner, you’d get to keep your $1 bet and get $30 in winnings. That would leave you with a total of $31 of your original $36, and the house would have $5 profit.
That $5 profit, or 13.89 percent of your wagers, represents the house edge. You can flip that, subtract 13.89 from 100 and get a payback percentage of 86.11 percent.
That’s the same way you get a payback percentage on slot machines. Slots can have many more random numbers per reel than the six per die, and the total combinations can run into the tens or hundreds of thousands or even millions rather than 36, but the principle is the same.
The odds of the game will lead slot reel combinations to turn up in expected proportions over a very long time. The house pays the winning combinations at less than true odds.
Together, the proportion of winning spins along with the less-than-true-odds paybacks lead to a house edge and payback percentage.
Any result can show up at any time. That’s random. But the house can count on the odds leading to an expected payback percentage.
DOESN’T THERE HAVE TO BE MAKEUP TIME TO HIT THE PERCENTAGE?
The house doesn’t panic when table players go on a hot streak. It knows that the multitude of results that follow will drag the overall results back toward the expected house edge.
Let’s say you’re betting $1 per spin on a slot that returns 90 percent in the long run. Some slots pay more, some pay less, but we can use 90 as an example.
Next, imagine you win a $5,000 jackpot on your first spin.
Doesn’t that throw the percentages out of whack? Won’t the slot have to go cold for a while until it gets back to its expected 90 percent?
No. There’s no need for that. You may walk away a winner – and if you’re smart, you will. And that’s OK with the house. Casinos need winners to go off and tell their families and friends so they’ll want to play, too.
But there’s always another player after you, and after that, and another.
All that’s needed is for the machine to pay at its normal rate, and your jackpot will fade into statistical insignificance.
Imagine that your $5,000 winner is followed by a million spins in which the game pays its normal 90 percent. There will be other jackpots in those spins – they’re part of the normal odds of the game.
There will be cold streaks and there will be hot streaks. None will come at any predictable time. Results will be random.
In those millions spins for a total of $1 million, the 90-percent payback means players are getting $900,000.
Add your one spin, and the total wagers are $1,000,001 and total returns are $905,000. The payback percentage is 90.5 percent.
Normal results after you jackpot have taken the payback percentage to within half a percent of the target with no need for any makeup time.
You can win big in a short session. You also can lose big in a short session. But the house is there for millions upon millions of spins, and it knows any big wins or unusual streaks will fade into statistical insignificance with random results.
HOW DO YOU ACCOUNT FOR BONUS EVENTS?
In pick-a-prize bonus events, your choices make a difference. When different icons hide different prizes, and you touch or click on an icon, you get the credit prize it has hidden.
If you picked a different icon, you’d get a different prize. If all the potential prizes are revealed at the end of the round, that’s tantamount to advertising the prizes. In licensed jurisdictions, any advertised prizes must actually be available.
So your prize in such a bonus event is not predetermined. It’s up to the luck of the touch or click, and could win big, small or in between on each pick.
That leaves players to wonder how a truly random machine could cope with that. Doesn’t a prize have to be predetermined in order for a programmer to include it in a payback percentage?
The answer is no, the prize does not have to be predetermined. The programmer can use an average result because in the long run, results will drive the awards toward that average.
Imagine a bonus round that gives you a choice of icons A, B, C, D or E, and the available prizes are 10, 20, 30, 50 and 100 credits. The credit amounts are randomly distributed behind the icons, so the big prize might be behind D this time, A the next and E or any other icon the time after that.
You get whatever prize is behind the icon you choose, and there is no way of telling what the amount will be.
However the average award will be (10+20+30+50+100) divided by the five possible choices. That’s 210 / 5, or 44 per pick.
The programmer can use 44 credits as the average outcome of a bonus event, and build that into the overall payback percentage.
Your choices matter, the prize is variable and there doesn’t need to be a predetermined prize.
And just as in the other programmed-yet-random dilemmas players find in the slots, random results will drive the game toward its expected payback percentage.