Welcome To South Asian Union Forum
( NEW = Guests Can Reply On News Articles..)

You are currently viewing the forum as "Guest" which doesn't give you the same privilege as members to ask questions, post news or post comments in all forums. Click the Register button below to unlock the limitations of this website to start posting what ever the problam you may want to share...

Auto Membership. you can log in soon after registering with us.....

Login Name=
Any E-Mail Address=
Password=

Thats It......
Welcome To South Asian Union Forum

This is a discussion table for millions of south Asians living around the world to express their thoughts on the latest events. www.SouthAsianUnion.info is a powerful tool for all ethnic groups to share information, knowledge and wisdom.
 
HomeHome  CalendarCalendar  FAQFAQ  SearchSearch  MemberlistMemberlist  RegisterRegister  Log in  
India Breaking News
Pakistan Breaking News
Sri Lanka Breaking News
Bangladesh Breaking News
Afghanistan Breaking News

Share | 
 

 What's luck got to do with it? The maths of gambling

Go down 
AuthorMessage
GeeK
Technical Service
avatar

Sex : Male
Posts : 32
Join date : 2009-08-04
I Am From... I Am From... : london

PostSubject: What's luck got to do with it? The maths of gambling   Tue Aug 11, 2009 4:10 pm

What's luck got to do with it? The maths of gambling


FIVE years ago, Londoner Ashley Revell sold his house, all his possessions and cashed in his life savings. It raised £76,840. He flew to Las Vegas, headed to the roulette table and put it all on red.

The wheel was spun. The crowd held its breath as the ball slowed, bounced four or five times, and finally settled on number seven. Red seven.

Revell's bet was a straight gamble: double or nothing. But when Edward Thorp, a mathematics student at the Massachussetts Institute of Technology, went to the same casino some 40 years previously, he knew pretty well where the ball was going to land. He walked away with a profit, took it to the racecourse, the basketball court and the stock market, and became a multimillionaire. He wasn't on a lucky streak, he was using his knowledge of mathematics to understand, and beat, the odds.

No one can predict the future, but the powers of probability can help. Armed with this knowledge, a high-school mathematics education and £50, I headed off to find out how Thorp, and others like him, have used mathematics to beat the system. Just how much money could probability make me?

When Thorp stood at the roulette wheel in the summer of 1961 there was no need for nerves - he was armed with the first "wearable" computer, one that could predict the outcome of the spin. Once the ball was in play, Thorp fed the computer information about the speed and position of the ball and the wheel using a microswitch inside his shoe. "It would make a forecast about a probable result, and I'd bet on neighbouring numbers," he says.

Thorp's device would now be illegal in a casino, and in any case getting a computer to do the work wasn't exactly what I had in mind. However, there is a simple and sure-fire way to win at the roulette table - as long as you have deep pockets and a faith in probability theory.

A spin of the roulette wheel is just like the toss of a coin. Each spin is independent, with a 50:50 chance of the ball landing on black or red. Contrary to intuition, a black number is just as likely to appear after a run of 20 consecutive black numbers as the seemingly more likely red.

This randomness means there is a way of using probability to ensure a profit: always bet on the same colour, and if you lose, double your bet on the next spin. Because your colour will come up eventually, this method will always produce a profit. The downside is that you'll need a big pot of cash to stay in the game: a losing streak can escalate your bets very quickly. Seven unlucky spins on a £10 starting bet will have you parting with a hefty £1280 on the next. Unfortunately your winnings don't escalate in the same way: when you do win, you'll only make a profit equal to your original stake. So while the theory itself is sound, be careful. The roulette wheel is likely to keep on taking your money longer than you can remain solvent.

With that in mind, I turned my back on roulette and followed Thorp into the card game blackjack. In 1962 he published a book called Beat the Dealer, which proved what many had long suspected: by keeping track of the cards, you can tip the odds in your favour. He earned thousands of dollars putting his proof into practice.

The method is now known as card counting. So does it still work? Could I learn to do it? And is it legal?

"It's certainly not illegal," Thorp assures me. "The casino can't see inside your head - yet." What's more, after a brief tutorial, it doesn't sound too difficult. "If you went into any casino that had basic blackjack rules, learned the method of card counting that I've taught you, you'd have a modest advantage without much effort," says Thorp.

_________________
Back to top Go down
http://www.southasianunion.info/it-news-help-and-advice-f10/
GeeK
Technical Service
avatar

Sex : Male
Posts : 32
Join date : 2009-08-04
I Am From... I Am From... : london

PostSubject: What's luck got to do with it? The maths of gambling 2   Tue Aug 11, 2009 4:11 pm

Go into any casino with normal blackjack rules and you can have a modest advantage without much effort

Basic card counting is simple. Blackjack starts with each player being dealt two cards face up. Face cards count as 10 and the ace as 1 or 11 at the player's discretion. The aim is to have as high a total as possible without "busting" - going over 21. To win, you must achieve a score higher than the dealer's. Cards are dealt from a "shoe" - a box of cards made up of three to six decks. Players can stick with the two cards they are dealt or "hit" and receive an extra card to try to get closer to 21. If the dealer's total is 16 or less, the dealer must hit. At the end of each round used cards are discarded.

The basic idea of card counting is to keep track of those discarded cards to know what's left in the shoe. That's because a shoe rich in high cards will slightly favour you, while a shoe rich in low cards is slightly better for the dealer. With lots of high cards still to be dealt you are more likely to score 20 or 21 with your first two cards, and the dealer is more likely to bust if his initial cards are less than 17. An abundance of low cards benefits the dealer for similar reasons.

If you keep track of which cards have been dealt, you can gauge when the game is swinging in your favour. The simplest way is to start at zero and add or subtract according to the dealt cards. Add 1 when low cards (two to six) appear, subtract 1 when high cards (10 or above) appear, and stay put on seven, eight and nine. Then place your bets accordingly - bet small when your running total is low, and when your total is high, bet big. This method can earn you a positive return of up to 5 per cent on your investment, says Thorp.

After a bit of practice at home, I head off to my nearest casino. Trying to blend in among the rich young things, the shady mafia types and the glamorous cocktail waitresses was one thing; counting cards while trying to remain calm was another. "If they suspect that you're counting cards, they'll ask you to move to a different game or throw you out completely," one of the casino's regulars tells me.

After a few hours I begin to get the hang of it, and eventually walk away with a profit of £12.50 on a total stake of £30. The theory is good, but in practice it's a lot of effort for a small return. It would be a lot easier if I could just win the lottery. How can I improve my chances there?
In it to win it



14 January 1995 was an evening that Alex White will never forget. He matched all six numbers on the UK National Lottery, with an estimated jackpot of a massive £16 million. Unfortunately, White (not his real name) only won £122,510 because 132 other people also matched all six numbers and took a share of the jackpot.

There are dozens of books that claim to improve your odds of winning the lottery. None of them works. Every combination of numbers has the same odds of winning as any other - 1 in 13,983,816 in the case of the UK "Lotto" game. But, as White's story shows, the fact that you could have to share the jackpot suggests a way to maximise any winnings. Your chances of success may be tiny, but if you win with numbers nobody else has chosen, you win big.

So how do you choose a combination unique to you? You won't find the answer at the National Lottery headquarters - they don't give out any information about the numbers people choose. That didn't stop Simon Cox, a mathematician at the University of Southampton, UK from trying. Ten years ago, Cox worked out UK lottery players' favourite figures by analysing data from 113 lottery draws. He compared the winning numbers with how many people had matched four, five or six of them, and thereby inferred which numbers are most popular.

And what were the magic numbers? Seven was the favourite, chosen 25 per cent more often than the least popular number, 46. Numbers 14 and 18 were also popular, while 44 and 45 were among the least favourite. The most noticeable preference was for numbers up to 31. "They call this the birthday effect," says Cox. "A lot of people use their date of birth."

Several other patterns emerged. The most popular numbers are clustered around the centre of the form people fill in to make their selection, suggesting that players are influenced by its layout. Similarly, thousands of players appear to just draw a diagonal line through a group of numbers on the form. There is also a clear dislike of consecutive numbers. "People refrain from choosing numbers next to each other, even though getting 1, 2, 3, 4, 5, 6 is as likely as any other combination," says Cox. Numerous studies on the US, Swiss and Canadian lotteries have produced similar findings.

To test the idea that picking unpopular numbers can maximise your winnings, Cox simulated a virtual syndicate that bought 75,000 tickets each week, choosing its numbers at random. Using the real results of the first 224 UK lottery draws, he calculated that his syndicate would have won a total of £7.5 million - on an outlay of £16.8 million. If his syndicate had stuck to unpopular numbers, however, it would have more than doubled its winnings (The Statistician, vol 47, p 629).

So the strategy is clear: go for numbers above 31, and pick ones that are clumped together or situated around the edges of the form. Then if you match all six numbers, you won't have to share with dozens of others.The lotto strategy is clear: go for numbers above 31, and pick ones that are situated around the edges of the ticket. Then if you do win, you'll win big





Unfortunately, probability also predicts that you won't match all six numbers until the 28th century. I bought a ticket using some of Cox's least popular numbers: 26, 34, 44, 46, 47 and 49. Not one of them came up. So I headed for the bookmaker.

Although it would be nearly impossible to beat a seasoned bookie at his own game, play two or three bookies against each other and you can come up a winner. So claims John Barrow, professor of mathematics at the University of Cambridge, in his book 100 Things You Never Knew You Never Knew. Barrow explains how to hedge your cash around different bookies to ensure that whatever the outcome of the race, you make a profit.

Although each bookie will stack their own odds in their favour, thus ensuring that no punter can place bets on all the runners in a race and guarantee a profit, that doesn't mean their odds will necessarily agree with those of a different bookie, says Barrow. And this is where gamblers can seize their chance.

Let's say, for example, you want to bet on one of the highlights of the British sporting calendar, the annual university boat race between old rivals Oxford and Cambridge. One bookie is offering 3 to 1 on Cambridge to win and 1 to 4 on Oxford. But a second bookie disagrees and has Cambridge evens (1 to 1) and Oxford at 1 to 2.

Each bookie has looked after his own back, ensuring that it is impossible for you to bet on both Oxford and Cambridge with him and make a profit regardless of the result. However, if you spread your bets between the two bookies, it is possible to guarantee success (see diagram, for details). Having done the calculations, you place £37.50 on Cambridge with bookie 1 and £100 on Oxford with bookie 2. Whatever the result you make a profit of £12.50.

Simple enough in theory, but is it a realistic situation? Yes, says Barrow. "It's very possible. Bookies don't always agree with each other."

Guaranteeing a win this way is known as "arbitrage", but opportunities to do it are rare and fleeting. "You are more likely to be able to place this kind of bet when there are the fewest possible runners in a race, therefore it is easier to do it at the dogs, where there are six in each race, than at the horses where there are many more," says Barrow.

Even so, the mathematics is relatively simple, so I decided to try it out online. The beauty of online betting is that you can easily find a range of bookies all offering slightly different odds on the same race. "There are certainly opportunities on a daily basis," says Tony Calvin of online bookie Betfair. "It's not necessarily risk-free because you might not be able to get the bet you want exactly when you need it, but there are certainly people who make a living out of arbitrage."

_________________
Back to top Go down
http://www.southasianunion.info/it-news-help-and-advice-f10/
GeeK
Technical Service
avatar

Sex : Male
Posts : 32
Join date : 2009-08-04
I Am From... I Am From... : london

PostSubject: Re: What's luck got to do with it? The maths of gambling   Tue Aug 11, 2009 4:12 pm

Arbitrage is not risk free because you might not be able to get the bet you want exactly when you need it. But there are certainly people who make a living out of it

After persuading a few friends to help me try an online bet, we followed a race, each keeping track of a horse and the odds offered by various online bookies. Keeping track of the odds to spot arbitrage opportunities was hard enough. Working out what to bet and when was, unsurprisingly, even harder. Arbitrage is not for the uninitiated.
Cut your losses



However, it's still quite addictive, especially when you get tantalisingly close to finding a winning combination. And that's the problem with gambling - even when you have got mathematics on your side, it's all too easy to lose sight of what you could lose. Fortunately, that's the final thing that probability can help you with: knowing when to stop.

Everything in life is a bit of a gamble. You could spend months turning down job offers because the next one might be better, or keep laying bets on the roulette table just in case you win. Knowing when to stop can be as much of an asset as knowing how to win. Once again, mathematics can help.

If you have trouble knowing when to quit, try getting your head around "diminishing returns" - the optimal stopping tool. The best way to demonstrate diminishing returns is the so-called marriage problem. Suppose you are told you must marry, and that you must choose your spouse out of 100 applicants. You may interview each applicant once. After each interview you must decide whether to marry that person. If you decline, you lose the opportunity forever. If you work your way through 99 applicants without choosing one, you must marry the 100th. You may think you have 1 in 100 chance of marrying your ideal partner, but the truth is that you can do a lot better than that.

If you interview half the potential partners then stop at the next best one - that is, the first one better than the best person you've already interviewed - you will marry the very best candidate about 25 per cent of the time. Once again, probability explains why. A quarter of the time, the second best partner will be in the first 50 people and the very best in the second. So 25 per cent of the time, the rule "stop at the next best one" will see you marrying the best candidate. Much of the rest of the time, you will end up marrying the 100th person, who has a 1 in 100 chance of being the worst, but hey, this is probability, not certainty.

You can do even better than 25 per cent, however. John Gilbert and Frederick Mosteller of Harvard University proved that you could raise your odds to 37 per cent by interviewing 37 people then stopping at the next best. The number 37 comes from dividing 100 by e, the base of the natural logarithms, which is roughly equal to 2.72. Gilbert and Mosteller's law works no matter how many candidates there are - you simply divide the number of options by e. So, for example, suppose you find 50 companies that offer car insurance but you have no idea whether the next quote will be better or worse than the previous one. Should you get a quote from all 50? No, phone up 18 (50 ÷ 2.72) and go with the next quote that beats the first 18.

This can also help you decide the optimal time to stop gambling. Say you fancy placing some bets at the bookies. Before you start, decide on the maximum number of bets you will make - 20, for example. To maximise your chance of walking away at the right time, make seven bets then stop at the next one that wins you more than the previous biggest win.

Sticking to this rule is psychologically difficult, however. According to psychologist JoNell Strough at West Virginia University in Morgantown, the more you invest, the more likely it is that you will make an unwise decision further down the line (Journal of Psychological Science, vol 19, p 650).

This is called the sunk-cost fallacy, and it reflects our tendency to keep investing resources in a situation once we have started, even if it's going down the pan. It's why you are more likely to waste time watching a bad movie if you paid to see it.

So if you must have a gamble, use a little mathematics to give you a head start, or at least to tell you when to throw in the towel. Personally I think I'll retire. Overall I'm £11.50 up - a small win at the casino offset by losing £1 on my lottery ticket. It was a lot of effort for little more than pocket change.

Maybe I should have just put it all on red.

_________________
Back to top Go down
http://www.southasianunion.info/it-news-help-and-advice-f10/
Sponsored content




PostSubject: Re: What's luck got to do with it? The maths of gambling   

Back to top Go down
 
What's luck got to do with it? The maths of gambling
Back to top 
Page 1 of 1
 Similar topics
-
» Son of one of the Maddie Detectives is charged with Illegal Gambling Ring

Permissions in this forum:You cannot reply to topics in this forum
Welcome To South Asian Union Forum :: The Science and Technology Forum-
Jump to: