Random, Random, Random by John Grochowski

Not a month goes by without an email that includes some variation on the theme, if slots are really random, then why …

Why are there more jackpots on busy nights? How can a programmed payback percentage be random? How can there be streaks? Win cycles and loss cycles aen’t random, are they?

There must be some other explanation than random chance for those oh, so sweet wins and those all too frequent losses, or so many players think. But slot machine results really are as random as humans can program a computer to be. Let’s try to clear up a few misunderstandings, based on reader mails.

“I went to a casino grand opening, and it was packed. 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 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.”

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 percent 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 percent 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.

On every slot machine in a licensed casino, 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.

I don’t get how slots can be both random and programmed. If a slot machine has to pay out, say 93 percent, how can it be random? The programming must keep it on track to pay 93 percent.
That mix, programmed, yet random, is something that has confused many a player in the decades since slots went electronic. Slot manufacturers have to be able to program payback percentages to comply with the law in states that set minimum and maximum returns. And the machines still have to be able to meet state randomness standards.

The confusion seems to be over exactly what it is that the programmer is programming. It’s not a matter of telling the game that it must pay a designated percentage. It’s a matter of setting the possibilities and the odds of the game so that random results eventually will lead to the desired return.

In that way, slots are like table games. Take roulette. On an American double-zero wheel, the game is “programmed” with 38 possible results, the numbers 1 through 36 plus 0 and 00. The numbers come up randomly, and when you win on a single number, you’re paid at 35-1 odds, a bit less than the true odds of 37-1. That gives the house an edge of 5.26 percent, or to turn it around, gives the game a programmed payback percentage of 94.74 percent.

There is nothing to keep your number from coming up two or three times in a row, and nothing that says it has to come up within several dozen spins or more. But given enough trials, the random results and the odds of the game will lead to something very close to roulette’s “programmed percentage.”

Same deal in craps. By using two six-sided dice, we “program” the game with 36 possible outcomes, one way to make 2, two 3s, three 4s, four 5s, five 6s, six 7s, five 8s, four 9s, three 10s, two 11s and one 12. The odds of a given roll combined with how much the casino pays for a winner yield a “programmed” house edge, or payback percentage.

The probability of rolling any given number remains constant, but it is possible to roll the same number several times in a row. When you do, it doesn’t make it any more or less likely that you’ll roll it again next time. The odds just remain the same, and in the long run any hot or cold streak will just fade into statistical insignificance.

Slots work more or less the same way, except that there are hundreds or thousands of possibilities instead of 38. For regular play on the reels, randomly occurring numbers are programmed, each corresponding to a reel symbol. To make up an example, the programmer might write it so that every time the random number 1 shows up, the reel shows a jackpot symbol; with Nos. 2, 3 or 4, it shows a 7, with Nos. 5-9, a triple bar, and so on. The possibilities are programmed, but when they turn up is random, just like it’s random when a 7 turns up in craps.

After a big win, the machine doesn’t go into makeup mode. Over a long period of time, normal results according to the odds of the game will yield a normal payback percentage, and your big win fades into statistical insignificance.

Just as when a table games designer sets the rules of a card, dice or wheel game, the slot programmer sets the possible outcomes, and the paytable gives you back a little less than the true odds of hitting the winners. You can hit several winners in a row, or none for a number of spins. Results are random, but over hundreds of thousands of plays they will lead to something very close to the programmed payback percentage.

Programmed, yes. Random, yes. Just like any other casino game, but in an electronic sort of way.

I’ve read in Midwest Gaming & Travel that your picks make a difference in video bonus round. If slots are really random, how can picks make a difference and still have a programmed payback. Doesn’t one make the other impossible?

Your choices do make a difference in pick’em-style bonus events, but not in any way you can predict or control. The programmer, on the other hand, knows that over a very long time, the bonus even will yield an average payback.

Let’s make up a simple bonus event, in which you pick one of three symbols to reveal a bonus award. If you touch one symbol, you get 25 credits, if you touch a different one, you get 50, and if you touch the other you get 75.

The amount you get isn’t predetermined. You will get the amount assigned to whichever symbol you pick. If you’re able to pick the 75-credit space, good for you.

However, no system for trying to determine which symbol hides the 75 will work. The shuffling of the symbols is random. The 75 could be on the left three times in a row, or not at all for several trials, or any other number. Over a very long time, hundreds of thousands of trials, players will pick the 75 about a third of the time, the 50 about a third of a time, and the 25 about a third of the time.

The odds of the game lead to an average payback of 50 credits on that particular bonus event. In determining a target payback percentage for the game, the programmer knows that, and that’s built into calculations.

Real-life bonus events have more possibilities and the math is more complex, but the principle is the same. Over time, an average win will emerge, and the programmer can build that into the targeted payback percentage.

I assume a slot machine has to be in the black. Otherwise, how could they hit a 94 percent payback, or whatever number. How can slots be random if they have to be in the black at all times? Doesn’t that mean they can’t pay off until there’s money in the bank?

The slot machines we find in state-licensed casinos and in most Native American casinos do not always have to be in the black. The house banks the game, and if a machine pays out more than it takes in, the payoffs come out of house funds.

It is possible for a slot machine to pay its top jackpot on the first spin and be in the red for a long time. It doesn’t keep track of how much it has paid out, and make sure it stays at the targeted percentage.

The situation is different when we talk about the Class II games found in some Native American casinos. Those games, recognizable by the bingo logo on the screen or glass, are fixed-pool wagering, with multiple games linked so that payoffs come from a pool created by bets on all games. Rather than being true individual random number generator games, all Class II games are really electronic bingo, with slot reels or video poker cards just a user-friendly was of showing us the outcome that has been determined by a bingo draw.

But Class III games that dominate in Indian casinos are the same slot machines you’ll find in commercial casinos. And they don’t have to be in the black at all times.

If slots are really random, how do you account for streaks? Sometimes I’ll be winning, and then the machine just goes ice cold. Maybe I’ll lose 20 or so times in a row before I either hit something or give up and change machines. I think the machine knows I’ve been winning, and decides to take it back.
Streaks are a normal part of the probability of the game. Let’s take a three-reel game with a 12 percent hit frequency, you’ll have a winner an average of once per 8.333 spins. On your first spin, there’s an 88 percent chance it’ll be a loser. There’s a 77 percent chance you’ll lose two in a row, 68 percent chance you’ll lose three in a row, and so on.

At 20 in a row, the number tossed out there by the reader who sent the email, there’s still a 7.8 percent chance of every spin being a loser. That’s easily within normal probability. Anyone playing a machine with a 12 percent hit frequency for very long will have streaks of 20 or more losses.

Same deal if you’re counting the times between bonus events on a video slot machines. That’s something I like to do. In the same session, I’ve gone to the bonus round twice in a row, and had 100 plays between bonus events. Both the short turnaround and long cold snap grow out of the natural odds of the game.

Let’s say the odds of the game are set so the bonus event occurs an average of once per 30 spins, so you have a 3.333 percent chance of going to the bonus event on any given spin. By random chance, you have a 0.111 percent chance of going to the bonus twice in a row. That’s roughly once per 900 trials, you won’t see it happen every time you play, but if you’re at the machine often enough, the bonus twins will happen.

What about going 100 times in a row without a bonus look? On our example game, there’s a 96.667 percent chance you won’t go to the bonus on any given spin. Two in a row with no bonus will happen 93.444 percent of the time, with percentages falling to 71.247 percent at 10 in a row, 18.358 percent at 50 in a row, and 3.370 percent at 100 in a row.

Note that the chances of going 100 spins in a row without a bonus are as good as the chances of getting the bonus on the next spin. There’s no need for a game to “decide” to take anything back. Streaks — with cold streaks longer than hot streaks — are just a part of the normal odds of the game.

Some three-reel slots have hit frequencies higher or lower than 12 percent. Some video bonuses happen more than once per 30 spins, many happen less often. All games have streaks growing out of normal probability, and all are random.

If slots are really random, why don’t I win more often? Shouldn’t winning symbols come up as often as losers?

“Random results” is not the same as saying “equal results.” A game doesn’t have to be programmed so that a jackpot symbol shows up as often as a blank space, or a bonus symbol as often as a cherry.

The odds of the game are set so that blank spaces will show up more often than winning symbols and small winners will show up more often than big winners. On three-reel slots, that will lead to there being more losing spins than winners, and on five-reel video games it will lead to more “wins” for amounts less than the size of your bet than bigger winners.

The programmer sets the odds of the game, then lets random chance take its course. When you play, may the chance be with you.

— John Grochowski is the author of The Casino Answer Book, The Slot Machine Answer Book, The Video Poker Answer Book and the Craps Answer Book, available online at: www.casinoanswerman.com.