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.
International Game Technology, which, as the world’s largest manufacturer of slot machines, has made many of the 900,000-plus slot machines in the U.S., earned $2.1 billion in revenues in fiscal.
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.
- Most people wouldn’t play a slot machine that lost 99 times out of 100, though, so slot machine designers added additional, smaller prizes for getting two symbols out of three for certain symbols. And as long as they paid out less in prizes than the odds of hitting those jackpots, then those slots are guaranteed to make a profit in the long run.
- Though today’s New Yorker cartoonists write their. Against all odds, I sold a cover to the magazine on my first try and I was hoping lightning could strike twice. I would be taking a slot.
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.
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
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
Many people will be visiting a casino this summer, whether on a trip to Vegas, on a cruise ship, or just at a local casino during a 'staycation.'
But before you go, you may want to know which games give you the best chance of winning.
So we went behind the scene at two casinos, and spoke with the game managers, to find out which games give you an edge.
Table Games Your Best Bet
Jay Bean, a Caesar's floor manager, agreed to sit down with us and talk about the games with the best odds.
He said many people don't realize that table games have much better odds than slots. They are intimidated by thoughts of card sharks taking their money, with images of an intense Texas Hold 'Em tournament in their minds, and so they stick with the safe games: the slots.
But they are doing themselves a disservice, he said.
The New Yorker Magazine Slot Machine Odds Against
Bean's advice? After you've spent some time on the slot machines, move on to the Blackjack table, and start by just observing.
1. Blackjack
Blackjack has the best odds of winning, with a house edge of just 1 percent in most casinos, Bean said.
Plus, you are playing against only the dealer, not hooded poker champions.
'Blackjack is one of our easiest games to play,' Bean said. 'You're just looking for a number that beats the dealer's number without going over 21.'
If you're a novice, Bean said to sit down during a less busy time, such as the afternoon, and the dealer will walk you through the game.
But the same is not true with poker: You should practice the game with your friends first, at home, Bean said, until you are comfortable with it. Bean said novices are best off passing on the poker tables, where yes, the competition can be tough.
You can find out more information about the game of blackjack at the following link:
http://wizardofodds.com/games/blackjack/
2. Craps
So from the Blackjack table, he suggests moving on to the dice game Craps, the game with the second best odds, also nearly 50-50.
The Craps table can be a bit intimidating for the beginner with all the boxes on the table, Bean admitted. But it's really not tough, and it has one of your best chances of winning. In the end, all you are really doing is betting on a dice roll.
For more information on craps, visit:
http://wizardofodds.com/games/craps/
3. Roulette
Bean said your next stop should be the Roulette wheel. It's simple, and pays fairly well.
'So you bet on your favorite numbers,' Bean said. 'The dealer spins, and if your number comes in you win.'
The New Yorker Magazine Slot Machine Odds At Columbus Ohio Casino
If you stick to betting on just Reds or Blacks, you have nearly a 50-50 chance of walking away a winner. If it lands on red when you choose red, you will double your bet, Bean explained.
While it may seem you have an even chance of winning by simply choosing a color, there is one catch that gives the house its edge: the extra green 0 and 00 position on the wheel. It's on all American roulette wheels.
Or, if you feel lucky, play just one number. It's hard to win, but if you do it pays out 36 to 1.
For more information on roulette, visit:
http://wizardofodds.com/games/roulette/
Worst Odds
The New Yorker Magazine Covers
Your worst odds? The casinos, understandably, did not want to talk about games with poor odds.
So we turned to Forbes Magazine, which in a report about Best Bets at the Casino, said two popular games -- the Wheel of Fortune and the ever-popular slot machines -- have the lowest odds of winning, with a house edge of 10 percent or more.
The Experts Agree
The New York Magazine
Professor of Analytics Michael Magazine has crunched the numbers, and agreed that blackjack is the best way to go home with money in your pockets. He said if you take a little time to learn the game, you have the best odds of winning.
'You are somewhere between 44 percent to 48 percent in every single hand of winning,' he said, noting that no other casino game gives you odds that good.
But Magazine cautioned that he's not promoting gambling, because he said even games with the best odds still favor the house.
'Play it long enough and you will lose. In the long term the house doesn't lose,' Magazine said.
If You Love The Slots....
Finally, if you really enjoy playing the slots, here is some good information to know, from state casino reports we examined.
With slots, the more money you put in per bet, the higher your chance of winning. If you put the max in a penny machine, which is usually around 50 cents, you have much better odds than if you put in 2 cents.
In addition, penny slots have the lowest odds, with $1 and $5 slots paying much better.
Always gamble responsibly, and don't waste your money.
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You can learn more about specific odds of slots machines in each state that has casino gambling by visiting the American Casino Guide.
Don't Waste Your Money is a registered trademark of the EW Scripps Co.
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