By John Grochowski
Maggie is a friend of a friend of my wife’s, someone I met at as holiday party when someone told her I was just the person she needed to talk to about slotmachines.
“Tell me how to win,” she said, and I laughed. That’s the most common request I get about slot machines, and it’s one I can’t fulfill. There’s nothing you can do to change the resultsdetermined by a machine’s random number generator.
“All right then. Tell me something. I was in a casino last week, and they had a sign up that said ‘Our slots pay back 93 percent.’ Does that mean every machine pays 93 percent?”
No, it doesn’t, I told her. Each casino has a wide range of payback percentages within its game mix. By and large, higher denominations givemore money back to players --- dollar machines pay more than quarters which pay more than nickels which pay more than pennies.
Even within the same denomination, there’s room for a range of paybacks. In a casino whose nickel games return 89 percent of money wagered to players, there’s likely to be games that pay inexcess of 90 percent, and games that pay 85 or 86 percent.
For that matter, it’s possible for games of the same denomination and theme to have different payback percentages. A quarter Red, White and Blue machine that returns 93 percent could sit rightnext to one that returns 89 percent. That’s not as common as it once was, but the game chips to make that possible are available to casinos.
“So if there are all those different paybacks, how can they say, ‘Our slots pay back 93 percent’? Where does that come from?”
That depends. Was it a plaque on a wall somewhere? Was it a sign over a particular bank of machines?
“It was on a wall, not really next to any particular games.”
OK, I’ve seen that in a few casinos, but not everywhere. It’s a casino-wide average. The total of all money won by the casino at all electronic gaming devices --- including video poker, videokeno and video blackjack as well as slot machines --- is divided by the total number of wagers at those games. Multiplied by 100, that gives us a casino hold percentage. Subtract that from 100,and you have the payback percentage to players.
For example, if $1 million is wagered on a casino’s electronic gaming devices, and the casino keeps $70,000, dividing that $70,000 by $1 million give you .07, which multiplied by 100 tells usthe casino kept 7 percent of all wagers. Subtract that from 100, and we find that 93 percent of money wagered has been returned to players. That’s the payback percentage.
“But not every machine is paying 93 percent?”
Right. Some payback percentages will be in the 80s. Some will be in the high 90s. Most will be in between. Most of the low-denomination slots will pay less than 93 percent. Most of thehigh-denomination games will pay more. But the casino-wide average in the casino where Maggie plays will come to 93 percent. Other casinos will have their own averages.
“I don’t suppose you could tell me how to tell which games have the better paybacks.”
I’m afraid not. Two slot machines that look identical on the outside can have different payback percentages.
She sighed.
“Oh well. Trial and error it is. At least keep your fingers crossed for a jackpot for me, will you?”
Will do.
Maggie was asking about a sign that listed a casino-wide average, but sometimes you’ll see a sign over a bank of machines that says, “95 percent payback,” or “Up to 98 percent payback.”
Such signs refer specifically to that bank of machines. If it’s specific, with no qualifiers, such as “95 percent payback,” most states require that all machines in the bank be programmed for95-percent return. There’s room for some short-term variation. If you sit down at a 95-percent machine and have a cold streak, running through a hundred bucks with zero return, there is norequirement that the next player get back 190 percent to even things out. Over time, with enough play, your cold streak will simply fade into statistical insignificance, overwhelmed by theresults of hundreds of thousands of reel spins.
Conversely, if you hit a big jackpot, there is no requirement that the machine then go ice cold to get down to the 95 percent target. The machine will keep operating as normal, and over timeyour jackpot will be overwhelmed by hundreds of thousands of plays and fade into statistical insignificance.
When the sign does have a qualifier, such as “Up to 98 percent payback,” then let the player beware. At least one machine in the bank is likely to be a 98-percenter, but others can be lower.Not all states permit such fudging, and this ploy isn’t as common as it was a decade ago, but when you see it, be wary.
John Grochowski writes a syndicated newspaper column on gambling,
and is author of the 'Casino Answer Book' series from Bonus Books.
Betting slot machine tricks “Bet Max” is what a regular gambler hears all the time when playing on slot machines. There is a common misconception that if you do not bet the maximum bet every time you will always lose to the casino in the long haul. However, that’s not quite how it works.
Today, the mathematics of slot machines. The University of Houston mathematics department presents this program about the machines that make our civilization run, and the people whose ingenuity created them.
Mathematicians first got interested in randomness by studying games of chance. Ever since, the histories of mathematics and gambling have been intertwined. Clever gamblers use mathematics to look for the smallest advantages, and casinos use sophisticated mathematical tools to devise new ways of drawing in players.
Indeed, a patent granted to the Norwegian mathematician Inge Telnaes in 1984 transformed the gambling industry. Prior to Telnaes’ invention, slot machines were essentially mechanical devices. Besides being difficult to tune and maintain, mechanical slot machines suffered from an essential problem: Let’s look at a machine with three reels, each with 12 symbols, with one of those 12 symbols a cherry. The likelihood of getting three cherries, and winning the jackpot, is 1 in 1,728. If the casino wants to make money, the jackpot payout should be, say $1,700 on a $1 bet. That does not seem attractive by today’s standards. However, the only way to increase the payout is to decrease the chances of hitting a jackpot.
Adding another reel is a possibility. For instance adding a fourth reel in the previous example would get us to a jackpot of about $20,000. But people do not like machines with more reels — they intuitively, and rightfully, feel that extra reels diminish their chance of winning. Another possibility is to put more symbols on each reel. But the astronomical jackpots you see in casinos today would then require truly enormous machines.
Inge Telnaes proposed a simple solution: Let a random number generator — a computer chip — determine the combination of symbols that appear when the reels stop. In other words, use a chip to control where the reels stop on a spin, but create the illusion that the wheels stopped on their own. The number of possible outcomes on the slot machine does not change. However, by reprogramming the chip, the operator has full control over the likelihood of each of the different outcomes. For instance, the operator could make the three cherries appear only once in a million spins.
What Does Retrigger On A Slot Machine Mean Spiritually
This was a brilliant insight: Suppose I pick a number between one and a million. Would you be willing to bet that you can guess that number? The answer is probably not. But let a computer chip pick such a number, put the chip in a machine with blinking lights and spinning reels, and many people will be more than willing to make the bet. It is simply because what people assume is happening in a slot machine is very different from what is actually happening.
The Magician oil painting by Hieronymus Boschfrom between 1475 and 1480
What Does Retrigger On A Slot Machine Mean Machine
The history of gambling is also intertwined with that of a less reputable group — tricksters and swindlers. In the long run, the only sure way to make money by gambling is to create the illusion that your opponent can win, while keeping the odds firmly on your side. And that gives those who know math a very solid advantage.
I'm Krešimir Josić, at the University of Houston, where we're interested in the way inventive minds work.
NOTE: In the example with three cherries, I assumed that one only wins in the case the spin results in three cherries, and there is no other winning combination. In actuality, there are typically many winning combination, and as a result, the jackpot would have to be even smaller.
The following story in Wired Magazine shows the drawbacks of the new generation of slot machines — they are easier to hack and to counterfit than their mechanical counterpart http://www.wired.com/magazine/2011/07/ff_scammingslots/.
Here is a more exhaustive discussion of the history of slot machines, and the random number generators within them http://catlin.casinocitytimes.com/article/non-random-randomness-part-1-1243. You may want to scroll towards the end of the article to read about how flaws in the design of gambling machine resulted in somebody picking 19 out of 20 winning numbers in a game of KENO — and doing so 3 times in a row. That person walked away with $620,000, but only after some controversy.
Both images are from Wikipedia. The slot machine image was taken by Jeff Kubina.
For more mathematics in everyday life, visitkjosic.wordpress.com.
This episode was first aired on September 7th, 2011