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. Texas holdem poker zynga. 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.

Slot machines come in different denominations, like penny slots, 5-cent slots, dollar slots, etc. Dollar slots have bigger payouts, but more risk and you might hit your loss limit faster. Penny slots won’t bankrupt you, but you won’t win big, either. However, you can spend a lot of entertaining time playing. I am VegasLowRoller and here you will see my BIG WINS from the slot machine wins I upload to youtube. This includes a big win, a huge win, and even the occas. Ontario removes video slot machines flashing winning images. Manitoba and the Atlantic provinces either have no Konami games, or the games on their Konami slots don't have the symbols. Generally, the more cash you put into a slot machine, the higher its payout percentage is going to be. The slots that require at least $1 pay out 95-99%, where 25 and 50 cent slot machines pay out less, 92-95%. Now for the sake of comparison, let’s say a certain slot machine has an RTP of 92% and it costs you $1 to spin its reels. 644 winning slot machine stock photos are available royalty-free.

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.

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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

Ontario's provincial gambling operator has pulled 87 video slot machines out of service or physically removed them from its casinos after a CBC investigation found what appear to be subliminal messages flashing at players.

Ontario Lottery and Gaming,the recently rebranded Ontario Lottery and Gaming Corp., is concerned about three games on video slots made by a company called Konami. Deerfoot inn and casino location map. Itshutthem down as a precaution on Friday, and is looking into the issue.

The games flash winning jackpot symbolsat players for a fifth of a second, long enough for the brain to detect even if the players are not aware of the message, some psychologists told CBC News.

It's not clear if messages are influencing gamblers' behaviour. That would take further testing,experts said.

But players who stick to a machine are seeing a winning image every two seconds, the time it takes for one spin, and that concerns Roger Horbay, an electronic gaming specialist who has treated hundreds of problem gamblers.

'I think it's part of them trying to make their games more attractive to the players to keep them at the game longer so their machines are more profitable,' hesaid.

However, Konami, the company behindthe games, said the jackpot symbols are a technical problem that it is fixing.

'It is simply a software glitch that our engineers have identified in four game titles, and wehave identified [that] three of those titles have been shipped into Canada,' said Konami spokesmanSteve Sutherland.

'The company is not going to risk its licensing to do this. It is purely a software error that the company is fixing.'

The game titles with the symbols are: Most Wanted, Sergeant Fritter and Billionaires. (A fourth called Sticks and Stones has only had limited release in the United States.)

But OLG, similar bodies in other jurisdictions and the Ontario gaming regulator, are all taking the messages seriously.

'Well, we are going to take a look at it further and see if there really is anything that we need todo and we will take the appropriate action,' said Sukhi Grewal, head of game testing at the regulator, the Alcohol and Gaming Commission of Ontario.

U.S. states consider pulling games

Gaming Laboratories International, the privatelab in the U.S. that t

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