Understanding the random nature of slot machines
By John Grochowski
For many years, Strictly Slots has 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 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.
Q: 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?
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 way 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 they 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, 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 pays 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 paybacks 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 payback 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.
Q: 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.
A: That mix—programmed, yet random—is something that has confused many a player in the decades since slots went electronic. Slot manufacturers must 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—numbers one 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.”
Slots work more or less the same way, except that there are 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 one shows up, the reel shows a jackpot symbol; with numbers two, three or four, it shows a seven; with numbers ﬁve through nine, a triple bar; and so on. The possibilities are programmed, but when they turn up it is random, just as it’s random when a 17 turns up in roulette.
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 pay table 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.
Q: I’ve read that your picks make a diﬀerence in video bonus rounds. If slots are really random, how can picks make a diﬀerence and still have a programmed payback. Doesn’t one make the other impossible?
A: 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 event 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 the 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.
Q: If slots are really random, why don’t I win more often? Shouldn’t winning symbols come up as often as losers?
A: “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, and then lets random chance take its course.
When you play, may the chance be with you.
Q: I’ve been at a casino when a slot attendant told me that a particular machine was “hot’ or due to pay out and I should play it. Is there any truth to this?
A: Many players do feel that a slot attendant or other ﬂoor person who is on location all day can tell you you which machines are “hot.” This advice is simply not true and a waste of money. Even if a certain machine has been paying oﬀ all day, this is no indication it will continue to pay oﬀ later that night. A slot machine’s cycles are not predictable.
Sure machines get hot, but they also get cold. Through the cycle of a machine, it’s a percentage to pay out a certain amount over a period of time based on the number of handle pulls the machine receives. However, the hot and cold cycles are not predictable and purely random.
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