RANDOM QUESTIONS
Understanding the random nature of slot machines
By John Grochowski
Way back in 2011, Strictly Slots addressed concerns of readers wondering how their observations and results squared with the idea that results are random on slot machines. The questions would start, “If results are really random …”followed by something that just didn’t add up. One reader wondered how a casino executive could anticipate a big night with lots of jackpots if his games were random. The reason was simple: There was a big crowd, so more people than usual were playing, leading to more opportunities for both big wins and losses. Still, randomness is a hot-button issue with slot players, and readers continue to ask whether outcomes they’ve experienced refute the idea that the games are random. Let’s explore a few of the ideas readers have floated.
Q: 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.
A: 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.
The same deal applies if you’re counting the times between bonus events on a video slot machine. 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 percent-ages 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 “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.
Q: I assume a slot machine has to be in the black. Otherwise, how could they hit a 94 percent payback, or what-ever 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?
A: 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 Native American 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.
Q: How can casinos make money if the games are really random? They have to be able to control the results to know how much money then can count on a game producing.
A: Casinos don’t have to control individual results to know what to expect from a game. It’s enough to control the odds of the game, and the odds are set so that the payout is less than the true odds of winning your bet. That’s how the house makes money on table games, it’s how it makes money on video poker, and it’s how it makes money on slot machines.
There are many more possibilities on slot machines than on table games, and the math behind it is a lot more complex on slots. So let’s make up a simple example. Pretend there’s a game where all the stops are either single bars or blank spaces, and the only paying combination is three single bars. Let’s further pretend the odds of the game are set so there’s a 25 percent chance of a winner, so the odds are 3-1 against you on every spin. If you’re betting $1 per spin, you risk $100 per 100 spins, and for it to be a breakeven game, then each winner would have to pay $4. But if the machine pays only $3 on each winner, then an average 100 spins will bring back only $75 for your $100 in wagers.
That’s basically how the games make profits for casinos. There’s more than one winning combination on actual slots, and bonus events complicate the math, but the bottom line is that the casino pay less than the true odds of winning the bet, and that drags long-term results toward an expected payback percentage.
Let’s look at it another way. Say you’re betting $1 per spin at a slot set up to return an average of 90 percent of money wagered back to players—it doesn’t matter if you’re playing a reel-spinner or if you’re betting two cents per line on a 50-line penny slot or any other combination. And let’s say you’re playing a modest pace of 500 spins per hour, risking $500 per hour. One more step: Let’s say you’ve just won a $5,000 jackpot.
Does the casino have to control the results to overcome that jackpot? Does it have to send the machine into some kind of makeup mode?
No, it does not. The normal odds of the game will drag the overall payback percentage back toward 90 percent. Let’s say that you and other players keep averaging $500 in wagers per hour, meaning a 90 percent game would average $450 in pay-backs per hour. In one day, there would be $12,000 in wagers, with $10,800 in non-jackpot paybacks plus your $5,000. The machine has paid out $15,800 for the day, so its one-day pay-back percentage is 132 percent.
But after six more days of normal paybacks to bring the total to a week, wagers are $84,000 and paybacks are $80,600, and the return is 95.6 percent. After two weeks, wagers are$168,000 and paybacks are $156,200, or 93.0 percent. After three weeks, the return is down to 92.0 percent, and so on, drawing ever closer back toward the expected percentage.
The casino doesn’t have to control individual results to get something very close to its targeted percentage. Random results and the odds of the game will accomplish that.
