What are the odds of winning the lotto twice?

keane2097 wrote: »

1. What part of "a theorem is a statement that has been proven" is a lie?

It's an incomplete definition. A deliberate misrepresentation in fact, since you went as far as Wikipedia to find it, then knowingly omitted the part of the sentence which didn't look good for your point.

Do you deny doing this?

keane2097 wrote: »

2. How is the proof of the theorem "2 + 2 = 4" any different to the proof for the optional stopping theorem?[/U]

Because the proof to the theorem "2 + 2 = 4" is demonstrably correct. I can give you two apples, then give you another two, and you will have four apples, i.e. reality clearly agrees with the theorem.

This is not the case for the second theorem, where results in reality do not tally with the expected results.

You have done absolutely nothing to convince me of the validity of this theorem. Your argument seems to be "if 2+2=4 then the optional stopping theorem must be correct".

keane2097 wrote: »

This is a much lampooned notion known as "the Chewbacca Defence".

keane2097 wrote: »

It's actually pretty embarrassing for a guy attempting to use mathematics to be condescending to end up on such ridiculous ground.

keane2097 wrote: »

3. The mathematical odds that 4 comes out in the next 10 draws are exactly equal to any other number, regardless of how long its been since 4 last came out. The odds do not change at any point along those 10 draws regardless of whether you take it as 1 series of events or 10 single events. True or false?

Over a series as small as ten events it's probably correct.

keane2097 wrote: »

4. Can you give your definition of "non-mathematical possibility", "likelihood" or "chance"?

I've already done this repeatedly. If you hadn't been frothing at the mouth in some feeble attempt to look intelligent on the internet you probably would have seen it.

keane2097 wrote: »

You seem to be trying to argue that 2+2=4 is not a valid theorem now.

This is an unexpectedly bizarre standpoint for you to adopt.

I'm seriously starting to think you're just trolling now?

COINCIDENCES, those surprising and often eerie events that add spice to everyay life, may not be so unusual after all, researchers say.

After spending 10 years collecting thousands of stories of coincidences and analyzing them, two Harvard statisticians report that virtually all coincidences can be explained by some simple rules.

Some of the analyses performed by them or other statisticians showed that events that looked extremely unlikely were almost to be expected. When a woman won the New Jersey Lottery twice in four months, the event was widely reported as an amazing coincidence that beat odds of one in 17 trillion. But when carefully analyzed, it turned out that the chance that such an event could happen to someone somewhere in the United States was more like one in 30.

It was an example of what the authors, Dr. Persi Diaconis, a professor of mathematics at Harvard University, and Dr. Frederick Mosteller, an emeritus mathematics professor at Harvard, call ''the law of very large numbers.'' That long-understood law of statistics states, in their formulation: ''With a large enough sample, any outrageous thing is apt to happen.''

Some of the findings are published in the December issue of The Journal of the American Statistical Association; others are now appearing in other professional journals. Dr. Diaconis, whose work also led to the recent discovery that seven shuffles are needed to mix a 52-card deck randomly, said the findings on coincidence were meeting mixed reactions. ''Some people are enormously relieved, but others are furious,'' he said. Not everyone who supplied an amazing coincidence to the researchers wanted to hear that a cherished dramatic story was really nothing special.

''I think the whole subject is fascinating,'' said Dr. Erich Lehmann, a statistician at the University of California at Berkeley. Although it can be a difficult statistical problem to decide just how unlikely an event is, Dr. Lehmann said, there is no dispute about the validity of the findings of Dr. Diaconis and Dr. Mosteller, some of which have been discussed at statistical meetings in recent years.

The two Harvard statisticians reviewed a large body of calculations and analyses of coincidences performed by other researchers, and they devised new techniques and approaches for studying the phenomenon in a wide range of circumstances. The research results, Dr. Diaconis said, ''are aimed at very basic problems of inference that arise in messy, real statistical problems.''

Dr. Bradley Efron, a statistician at Stanford University, said coincidences arise ''all the time'' in statistical work. When researchers find clusters of odd cancers or birth defects or other diseases, statisticians are asked ''to decide which events are the luck of the draw'' and which may reflect some underlying cause, Dr. Efron said. ''That's what Persi and Fred are trying to unravel,'' he added. ''I think it's a very interesting enterprise.''

Dr. Diaconis said one application of the new analyses is in scrutinizing data from clinical trials of new drugs. ''As you are looking around in that mass of data,'' he said, ''you find that in a certain subgroup, there are twice as many deaths in people taking drug A as there are in people taking drug B.'' Is it a coincidence or an indication that drug A is so dangerous to some patients that the trial must be stopped?

Dr. Diaconis and Dr. Mosteller said they decided to study coincidences because they were fascinated by the role these odd events play in everyone's lives. ''All of us feel that our lives are driven by coincidences,'' Dr. Diaconis said. ''Who we live with and where we work, why we do the things we do often rest on slim coincidences.'' These chance events ''touch us very deeply,'' he said. The two statisticians defined a coincidence as ''a surprising concurrence of events, perceived as meaningfully related, with no apparent causal connection.''

Dr. Diaconis and Dr. Mosteller began with the presumption that there are no extraordinary forces outside the realm of science that are acting to produce coincidences. But they also recognized that seeming coincidences are an important source of insight in science and so should not be dismissed out of hand. What looks like a coincidence may in fact have a hidden cause, which can lead to a new understanding of a phenomenon. A sequence of odd blips on a chart, a clustering of cases of a rare disease can tell researchers that a new event is occurring.

Anthologies of Happenstance

A decade ago, Dr. Diaconis and Dr. Mosteller started asking their colleagues, friends and friends of friends to send them examples of surprising coincidences. The collection quickly mushroomed. Dr. Mosteller said he had 13 notebooks, each three and a half inches thick, full of coincidences. ''These notebooks are eating up the shelves in my den,'' he said. Dr. Diaconis said he had 200 file folders full of coincidences.

When they began to study these coincidences, they learned that they fell into a several distinct groups. Some coincidences have hidden causes and are thus not really coincidences at all. Others arise from psychological factors, like selective memory or sensitivities, that make people think particular events are unusual whether they are or not. But many coincidences are simply chance events that turn out to be far more likely statistically than most people imagine. The analyses often required the researchers to develop new statistical methods, but in the end almost all coincidences could be analyzed.

The law of truly large numbers, which explains the double winner of the New Jersey Lottery, says that even if there is only a one-in-a-million chance that something will happen, it will happen eventually given enough time or enough people. ''It's the blade-of-grass paradox,'' Dr. Diaconis said. ''Suppose I'm standing in a large field and I put my finger on a blade of grass. The chance that I would choose that particular blade may be one in a million. But it is certain that I will choose a blade.'' So if something happens to only one in a million people per day and the population of the United States is 250 million, ''you expect 250 amazing coincidences every day.''

''If a one-in-a-million thing happens to you, you start telling people about it,'' Dr. Diaconis went on. ''You might say to me, 'So what do you think of that, wise guy?' And I say, 'It's an example of the law of truly large numbers.' ''

Right Answer, Wrong Question

When a New Jersey woman won the lottery twice in a four-month period, it was reported as a one-in-17-trillion long shot. Narrowly speaking, that is correct. But as Dr. Diaconis and Dr. Mosteller reported, one in 17 trillion is the odds that a given person who buys a single ticket for exactly two New Jersey lotteries will win both times. The true question, they say, is, ''What is the chance that some person, out of all the millions and millions of people who buy lottery tickets in the United States, hits a lottery twice in a lifetime?''

That event was called ''practically a sure thing'' by Dr. Stephen Samuels and Dr. George McCabe, two statisticians at Purdue University. Over a seven-year period, they concluded, the odds are better than even that there will be a double lottery winner somewhere in the United States. Even over a four-month period, the odds of a double winner somewhere in the country are better than one in 30.

Another principle that demystifies many coincidences is what the researchers call ''multiple end points'' - occasions when what might qualify as a coincidence is not spelled out ahead of time, and when many chance events would qualify. This could apply, for example, at a party, where two people might discover that they come from the same town. This may seem a surprising coincidence. But the truth is that almost anything two strangers have in common would count as a coincidence - the same first or last name, the same birthday, the same item of clothing.

''Clearly, the chances of getting a match in any of several things is bigger than if you look at just one thing,'' Dr. Diaconis said. He and Dr. Mosteller have developed a formula that can evaluate such problems.

Multiple end-point coincidences often sound amazing on the surface. For example, Dr. Diaconis said, ''I had a friend who said, 'Gee, I was watching a James Bond movie and there was a four-digit code on a bomb that was exactly the same as the code on my Israeli bank account.' '' It sounded extraordinary, since there are 10,000 possible four-digit numbers. But Dr. Diaconis went on: ''If you know 120 numbers - Social Security numbers, bank codes, telephone numbers of friends - there are even odds that four digits of two of them will match,'' he said.

keane2097 wrote: »

I actually haven't postulated any new mathematical theorems personally, I wager a shiny new penny nobody who's posted in this thread has either.

keane2097 wrote: »

I haven't been betting on the UK lotto yet, but since you've done a lot of the donkey work for me there I'll be keeping an eye on the 23 and 38 balls. Thanks Mellor.

robbie7730 wrote: »

Well yet again if you read my posts, did it sound like i was agreeing with the poster that said they can work out trends? Yes or no?

No you changed it because you thought i was an idiot based in a single post you read, then realised you better not say that, as this forum has rules too.

If you can not read your own post before pressing the post button, then its hard to believe you read the whole thread before posting your "hasty" comment, then correcting it.

Its obvious you did not read the whole thread, as if you did, you would see where i stand on the randomness thing. You simply seen one post, and said i was an idiot.

And your edited repost. Now if you meant to put in "being an idot" like you refer to in first quote above, you did not do a great job, as now i need my head checked according to this.

The concept of martingale comes up a lot, there is nothing wrong to see the sense in it to begin with.
But the people that can't see how its wrong after its explained to them, are, in my opinion, idiots.

Read my posts, what do i need explained, do i need to quote my own posts, or is it you that can not get past a single post?? Slow down, dont be so hasty.

Ditto for trends. It is idiotic for anyone to think there might be trends in the numbers. Evryone makes mistakes, nobody's perfect etc. But if they (you keane or who ever) continue to insist their are or could be, well then they become an idiot.

What have i insisted on? Im waiting o great sir.