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Three questions

Am I incorrect in assuming that in a Lottery where 49 numbers (for example) are drawn randomly (mechanically), my microscopic chances of winning the Jackpot become infinitesimal if I pick six consecutive numbers? For all I know, I would have the exact same chance (no more no less) if I chose at random.

Why is it that certain numbers seem to come up more frequently than others over a given period. Pure coincidence?

I heard it said that when you ask the computers (owned by the Lottery authorities) to choose the numbers for you, your chances are even less because some of the numbers selected come up less often. Any truth in that?

You are incorrect. :)

The odds of 1-2-3-4-5-6 or any other simple pattern coming up are exactly the same as any other set of six numbers, if the contest isn't fixed. However, you are far more likely to have to split a winning jackpot from a simple pattern selection than if you choose more random numbers. There are a lot of people out there who have less imagination than you...

The "runs" of certain numbers are due to, as you said, taking the results from "a given period." Taking a larger sample will show that these "runs" will balance out. Numbers that seem to come up less often are the other side of this same situation.

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Dr. Fidelius, Charlatan

Associate Curator Anomalous Paleontology, Miskatonic University

"You cannot reason a man out of a position that he did not reach through reason."

That's assuming that the probability theory holds true. However, as stated, it's only a theory & thus not yet proven accurate. whew.

Statistician on a program on NOVA once put it this way.

If you stand on the top of the World Trade Center (either one) and know that someone has put a Dixie cup somewhere down below, in reach of your coin, and you toss a quarter over your shoulder off the top, your chances of hitting the Dixie cup are *TEN TIMES* greater than your chances of winning the lottery.

'nuff said, sucker?

The chances of hitting the Dixie cup may be right, but in so doing, your chances of getting arrested for doing this are much higher. As for me, a $4 a week lotto habit is worth the dreams of riches that it buys, even if it is only a dream.

That's assuming that the probability theory holds true. However, as stated, it's only a theory & thus not yet proven accurate.

Probability is a purely mathematical theory. It is based on a few assumptions, such as if there are two equally likely outcomes of a certain event (e.g. tossing a coin), then each outcome has probability of 1/2.

Like all mathematical theories, probability works as long as the assumptions are true.

So far in the real world it has stood up. How do you think Las Vegas makes its money? Casinos do not cheat, they just shift the odds in favor of the house. And in the long run, everything settles to its correct odds.

Probability does seem kind of soft. I mean, flip a coin ten times and you might get ten heads, and that 1/2 probability kinda turns to jello. But flip a coin an infinite times (about 100+ times is sufficient), and the probability converges to 1/2. But as any professional gambler knows, the law of probability is hardcore. You might as well try to jump off a cliff and fly than try to beat the house.

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¾È ³ç, ÁÖ µ¿ ÀÏ

Way back in my misspent youth, I worked at a convenience store that sold lottery tix (I was in Missouri at the time and they had lotto long before Texas, where I am now). One week the winning six numbers had four in sequence, I think it was 22-23-24-25, and two other numbers. No one won, but can you imagine if you let the computer pick your numbers and came up with that combo? You'd raise holy hell and refuse to buy the ticket.

(while I was working there I once decided to buy ten scratch-off tickets and then decided to get nine tix and a coke...the next person to buy a ticket won $500. Expensive soda.)

Probability theory seems pretty iron clad to me, but not randomness. I've always understood that no computer is able to create truely random numbers on its own. For scientific research that requires truely random series of digets, they use the decay of a radioactive element to pick numbers, but I doubt that the Lotto uses that. Is any of this right, or have I been misled?

That computers cannot generate truly random numbers I've heard somewhere also.

Randomness is a strange beast. Probability comes close enough to describe it, but not exactly.

Anyhow, probabililty is close enough so that Las Vegas can make boatloads of money.

In a casino, the pit boss often shuffles dealers and replaces cards during a night. Ummm..., I have a lot of thoughts on this but I'll just end with: randomness is a strange beast.

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¾È ³ç, ÁÖ µ¿ ÀÏ

Computers don't generate random numbers. They use a function which generates numbers which have qualities of randomness; however, you will get the same exact series of numbers from the formula every time. So the function is "seeded" with a number to start the sequence in a different spot. Usually the current time in seconds is used to seed the function. This is random enough for most applications.

Lotto drawings are not done by computer. The one in Texas (and I believe most others) are done with an elaborate contraption that bounces numbered balls around and spits them out one a time. Every few months they change the balls out. More often if one number is coming up frequently.

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Mastery is not perfection but a journey, and the true master must be willing to try and fail and try again

Stating the obvious - The thing that keeps them coming back is: if you don't choose any numbers at all your chances of winning are a big fat zero.

Stating the obvious - The thing that keeps them coming back is: if you don't choose any numbers at all your chances of winning are a big fat zero.

True, but your costs of playing are also zero.

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www.sff.net/people/rothman (http://www.sff.net/people/rothman)

zyada, true computers don't generate random numbers, but many now use latent typing speed and mouse movement to generate the nesassary pseudo-random number, rather than a clock cycle pick, is closer to true random.

Diceman, Bond is what the writer wants him to be....Still, he has a very good eye for odds, and is an expert cheat if he needs to be; the Original story that Moonraker was based off of (Can't remember title.) has him cheating at bridge.

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>>while contemplating the navel of the universe, I wondered, is it an innie or outie?<<

---The dragon observes

My probability professor taught us that Las Vegas casinos would make money even if the odds weren't stacked in their favor. Why? Because people dream of "breaking the bank", and generally this would meaning winning more than they have to lose. For example, you go to Vegas with $500 and promise to stop playing when you run out. (Disregard addiction for the moment.) Generally, you don't put an upper limit on winnings. Even if the odds were exactly even, you would be very likely to hit your lower limit at some point and have to stop, while you may have hit $500 in winnings earlier, but decided to keep playing.

Time for a question that I hope is not too far off-topic: In the James Bond movies, 007 always wins at gambeling. Does he cheat, or is he just really lucky?

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"I had a feeling that in Hell there would be mushrooms." -The Secret of Monkey Island

My probability professor taught us that Las Vegas casinos would make money even if the odds weren't stacked in their favor.

This is probably true. Vegas tilts the odds on the house side to protect itself against professional gamblers. These people know realistically how much they can win with a certain bankroll.

But the average gambler is a dreamer, and will eventually lose. They are the biggest contributors to the Las Vegas pot.

I find nothing wrong with it. Gambling has great entertainment value. But like anything else, it shouldn't be abused.

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¾È ³ç, ÁÖ µ¿ ÀÏ

flip a coin ten times and you might get ten heads, and that 1/2 probability kinda turns to jello. But flip a coin an infinite times (about 100+ times is sufficient), and the probability converges to 1/2.

Actually, aren't you more likely to get tails than heads, since the heads side is heavier?

Okay, now I'm curious:

The local paper prints every week what are the most commonly selected numbers. Me, I'm a random sorta girl, so I always let the computer select them. Am I being a fool? Are my odds really increased by playing the most selected numbers as reported?

Greg Charles wrote:

"My probability professor taught us that Las Vegas casinos would make money even if the odds weren't stacked in their favor. Why? Because people dream of "breaking the bank", and generally this would meaning winning more than they have to lose. For example, you go to Vegas with $500 and promise to stop playing when you run out. (Disregard addiction for the moment.) Generally, you don't put an upper limit on winnings. Even if the odds were exactly even, you would be very likely to hit your lower limit at some point and have to stop, while you may have hit $500 in winnings earlier, but decided to keep playing."

Greg, I hope your memory is faulty, because this concept is fallacious. One way to see this is to look at things from the casino's point of view. Suppose the house has no edge. Then, on any round of betting, the casino wins as much as they lose. The dice and cards and roulette wheels don't know which customer is over or under some limit. So, the casino breaks even and the customers break even (on average).

Try enother explanation: Suppose that you are betting on flips of a coin. You win or lose $1 depending on how the coin comes up. At any point in time, your expected (average) result is zero. It just doesn't matter what your stopping rule is.

A similar conundrum involves the sex of new babies. Suppose that parents in some country are partial to boys, so they continue having babies until they have at least one son. It might seem that more boys than girls would be born. However, bear in mind that each birth is a 50-50 of either sex, so in fact the same number of each sex is born. (I am ignoring the fact that babies are slightly more likely to be boys, but am assuming 50-50.)

[[Time for a question that I hope is not too far off-topic: In the James Bond movies, 007 always wins at gambeling. Does he cheat, or is he just really lucky?]]

He's lucky and he's good -- but I'd rather be the former any day.

Actually, aren't you more likely to get tails than heads, since the heads side is heavier?

--Cessandra

I never knew the heads side is heavier. But it's pretty logical to assume that a coin is not exactly equally balanced.

For practical purposes, I guess this can be negligable. But in theory, where everything goes to infinity, I suppose nothing is negligable. But also in theory, a "theoretical" coin is used, which by definition is well balanced.

Although it may very well be true the tails side could be infinitesimally more likely, I wouldn't bet my money on it.

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¾È ³ç, ÁÖ µ¿ ÀÏ

Also, there is a very slight possibility the coin could land on its edge, giving neither heads nor tails. I wouldn't bet my money on this either, though. (Unless, of course, you gave me 1 to a trillion odds.) :)

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¾È ³ç, ÁÖ µ¿ ÀÏ

(I am ignoring the fact that babies are slightly more likely to be boys, but am assuming 50-50.)

Actually, I think it's the other way around. I believe the world population is something like 51% female and 49% male.

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"Give a man a match and he'll be warm for an hour... Set him on fire and he'll be warm for the rest of his life."

Actually, I think it's the other way around. I believe the world population is something like 51% female and 49% male.Then again, women have a longer life expectancy than men, so that world population as-is tells us nothing about birth ratios.

Holger

I've heard that the odds of a newborn baby being male are > 50%, but because of higher mortality among males, females outnumber males.

When you flip a regular coin, the odds are very close to 50-50, as is demonstrated by a large series of trials. However, if you roll a penny on a flat surface, and let it fall over when it loses momentum, it will come up heads a lot more often than tails.

Statistician on a program on NOVA once put it this way.

If you stand on the top of the World Trade Center (either one) and know that someone has put a Dixie cup somewhere down below, in reach of your coin, and you toss a quarter over your shoulder off the top, your chances of hitting the Dixie cup are *TEN TIMES* greater than your chances of winning the lottery.

'nuff said, sucker?

I am no sucker, neither am I a fool. However, I may be rightfully accused of being a dreamer.

I perfectly understand that the lottery is not a good bet. Only the dimmest of us think there is a free lunch in this world. I'm very familiar with the gambling industry's closest cousin, the insurance industry. I'm not really buying a chance at gazillion dollars when I purchase my lottery ticket.

What am I really buying? I buying the opportunity to talk to my wife about what we'd do if we didn't have to worry about money anymore. What we'd do to the house. What cars we'd buy. Where we'd go. Where we'd send the children to school. How quickly we'd retire and how we'd spend our time afterwards.

We're not delusional. We know there's only the most miniscule of chances that it would ever happen. We also know there's z-e-r-o chance if you don't buy a ticket. Stranger things have happened.

But we're not really gambling with our dollar or two a week. We're buying the opportunity to fantasize. It's pure escapism. And here's a thought. Our two dollars a week for powerball is much, much cheaper than a movie a week for the two of us. It's just entertainment. Plus, it's stimulating entertainment in that it encourages us to think -- to consider what we would do with our lives if we were no longer obligated to spend the vast majority of our time working to earn money. I think it's a hell of deal for the price.

Please note, I do not condone ignorance in playing the lottery. I cringe as much as you do when I see some yap spend his paycheck on lottery tickets. Ignorance of this sort is just painful to observe. I mean, hey, now I've got 200 chances out of 40 million to win 2 million. DUH! Clearly, anybody who thinks of the lottery as a good bet is a total moron. I'm just suggesting that for many people, the lottery serves as entertainment rather than gambling.

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President of the Vernon Dent fan club.

One more thing, which just occured to me. Lotteries are run by states. Therefore, the proceeds go to state governments and are therefore used for (snicker snicker) the public good. Other gambling proceeds inure to the benefit of organized crime or other private (i.e. corporate) interests.

In my state, when the lottery was originally approved, the proceeds were supposed to go directly to the schools. Of course, it hasn't quite worked out that way, but it was a nice theory.

One more thing, which just occured to me. Lotteries are run by states. Therefore, the proceeds go to state governments and are therefore used for (snicker snicker) the public good. Other gambling proceeds inure to the benefit of organized crime or other private (i.e. corporate) interests.

In my state, when the lottery was originally approved, the proceeds were supposed to go directly to the schools. Of course, it hasn't quite worked out that way, but it was a nice theory.

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President of the Vernon Dent fan club.

One more thing, which just occured to me. Lotteries are run by states. Therefore, the proceeds go to state governments and are therefore used for (snicker snicker) the public good. Other gambling proceeds inure to the benefit of organized crime or other private (i.e. corporate) interests.

Yes, and in my state, the residents of poorest town spend more than $500 per capita per year on lottery tickets (that's every man, woman, and child), while the residents of the richest town spend about $3.

Public good, my ass.

At least casinos give you decent odds.

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"For what a man had rather were true, he more readily believes" - Francis Bacon

Regarding the OP: Although I never actually play the lottery myself, I always figured the best system to "beat" a lotto-type game would be as follows:

a) Only buy a ticket when the jackpot exceeds the odds of winning. For example, the odds of winning a pick-6 game with 46 numbers is 9.37 million to one. So only play when the jackpot is more than 9.37 million dollars. (After taxes if you really want to be anal about it.)

b) Pick a combination of numbers that someone else wont be likely to have. People tend to use birthdays and other dates as their lucky numbers, so avoid numbers 1 through 31. Also avoid a consecutive series, because a lot of other people have no imagination, as mentioned above. And maybe throw one low number into the mix, since lots of other people probably also thought of the date thing and are playing only high numbers. A combination like 11, 32, 33, 34, 37, 43 might be good.

Of course, you're still never going to win. But at least you'll have the satisfaction of knowing that, in theory at least, the odds are in your favor.

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"For what a man had rather were true, he more readily believes" - Francis Bacon

1) It is true that casinos can win in the long run even with perfectly fair odds. This can be demonstrated mathematically; the side that has a bigger bankroll to start with will, on average, bankrupt the side with a smaller bankroll. This is weighted even further by table limits, which make it impossible for the punter to bankrupt the house. It is this fact that is the solution to the "St. Petersburg paradox", and the ruin of all related "doubling" systems.

2) While most people have little imagination, they also (like the originator of this thread) have little understanding of probability. I rather fancy that bets on consecutive strings (like 1-2-3-4-5-6) are rare.

3) Slightly more boys are indeed born than girls, but the mortality rate makes up for it.

[q]While most people have little imagination, they also (like the originator of this thread) have little understanding of probability.[\q]

Hey, I take exception to that!! :). You should have said that I [i]probably[\i] have little understanding of probability. As for the consecutive strings, I think you could be in for a surprise...

P.S.: No, I don't use them.

PP.S.: Mmmmmmmm. St. Petersburg paradox, eh?

I posted the below quote in another thread but it's relevant here, with a little editing. Replace "string of letters" with "string of numbers".

I think I understand your confusion. There is a concept in information theory called "typical sequences" or "typical strings (of characters)". If you are randomly producing a stream of letters, you will usually get mush. This is because

"typical sequences" are those in which the frequency with which each letter occurs in the sequence (divided by the total letters) equals the probability that that letter will occur (according to the machine picking the letters). For example, if you flip a coin a thousand times, MOST sequences will have roughly 500 heads. That is, the frequency of heads - 500 out of a thousand - equals the probability of heads - 1/2 for a fair coin. But, as probability aces are fond of pointing out, the sequence with a thousand heads (or a thousand tails) has equal probability to each other sequence considered individually. Nevertheless, the probability that a given sequence will be such an "atypical sequence" is much less likely than the probability it will be a typical one. Atypical strings DO occur, of course. It's just that their relative rarity compared to typical sequences gives us the SENSE that random strings must necessarily be typical strings. Not true, but an easy mistake to make.

Thus, the consecutive numbers have the same probability of winning as a more "random-seeming" sequence.

But as people have pointed out the lottery isn't random. You can find a page with all of Massachusett's winning numbers for the past year; I went through it at one point and worked out the frequency of all the numbers. Some deviated CONSIDERABLY form the expected value, if you assume that every number has an equal probability of occurrence. I comprised a consensus sequence of the "best" numbers to play. I played it for a while and won ten dollars. I spent about twenty, before I stopped. I'm sure I could have lost more if it had held my interest. In the lottery, even a better chance isn't necessarily a good chance.

It was fun, though, and I learned to use the stat functions on Excel.

Mark Mal wrote:

Yes, and in my state, the residents of poorest town spend more than $500 per capita per year on lottery tickets (that's every man, woman, and child), while the residents of the richest town spend about $3.

Public good, my ass.

Which is why it has been said of state lotteries that they are a tax on stupidity.

(Yes, that's mean. Yes, I know some of you get more out of gambling than the odds. But if you're banking on the odds alone -- it ain't smart.]

BTW. Anyone with a good reference out there know the originator of the 'tax on stupidity' quote?

Peace.

This whole conversation reminds me of a T-shirt that I wish someone would make-- "The Lottery" in small type on front above the right nipple, and on the back, a black box, a creased square of paper with a black dot on it, and a rock-- with the legend "You Could Be A Winner".

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"If A=B, B=C, and C=D, do not get a job proofreading" --Quid's Theorem

quote:

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Stating the obvious - The thing that keeps them coming back is: if you don't choose any numbers at all your chances of winning are a big fat zero.

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not true---when the texas lotto first started (like 7 years ago) a guy and his kid were walking out of a conveinence store and the kid picked up a scratch-off that someone had dropped--it was un-scratched--and they won somthing like 5000 bucks.

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i am on a never-ending quest to eliminate capital letters

Ah, good point! The odds of winning Powerball are, what, 50 million to one? I figure that's only slightly better than the odds of a big bag full of cash accidently dropping out of an airplane and landing on my front lawn, so why bother spending the buck?

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"For what a man had rather were true, he more readily believes" - Francis Bacon

That's a good point, to bet only when your expected return is greater than one, but are there any 46 ball lotto games still available? In Texas, our game is 50 balls, which translates to 1 in 11.3 *billion*, so for the expected return strategy to work out, you would need one hell of a big jackpot.

I think that the record Powerball jackpot last summer was only 900 million or so, and I doubt that it will be a long time until the payout ever reaches that level. And even if it ever did, the state could just add one ball (of course they never would, they would add an even number of 5 or ten balls) and the odds get out of reach once again.

Geez, a dangling participle and vague sentence construction in that last post. Sloppy!

I forgot to include my favorite lotto analogy.

Imagine a stack of pennies 17,000 miles tall. Now pick a penny, any penny. The odds of picking any one penny are greater than winning the lottery. Pretty damn good if you ask me!!!

In Texas, our game is 50 balls, which

translates to 1 in 11.3 *billion*, so for the expected return strategy to work out, you

would need one hell of a big jackpot.

Nahhh. You're mixing up permutations with combinations. If you had to pick all six numbers and also get them in the exact order that they come up, then the odds would be 11 billion to one (and no one would ever win). But if you just pick six and the order of the numbers doesn't matter (as is usually the case), then the odds are "only" 16 million to one.

The reason the numbers don't appear to be random is that you are looking at one discrete segment of outcomes, and not at the list of all possible outcomes (a long list, in the case of the lottery.) Try flipping a coin one hundred times. It doesn't come out H-T-H-T-H-T-H-; on the contrary, you can easily get runs of four or five heads in a row. This doesn't mean that flipping a coin isn't random. Many people jump to the conclusion that the laws of probability determine the outcome of a random event, when in fact they determine the indeterminibility of the outcome of a random event. Taken to extremes, this means that there is no particular reason why the same winning lottery number can't be drawn two weeks in a row; it's just that this probably won't happen.

Oops. I always forget that!

My formula: 1/50 x 1/49 ... 1/45

The right formula: 6/50 x 5/49 ... 1/45

Thanks for bringing me back down. I always need it.

Besides which, that's a dollar now, compared to millions spead out over 10 years. I've heard that after the cash option and taxes, you only get 1/4 to 1/6 of your published amount. (Is this stat close to accurate?) So you'd need a jackpot amount of, well, lots of money for it to be a >1 proposition.

Also, state lotteries are typically about as random as you can get. This is because if there were a pattern, people would find it, and they'd use it. And it wouldn't be Sam the, mechanic, who crunches the numbers and gets a workable pattern. The lottery, after all, makes money off the little guy, picking his dog's birthday, knowing his chances are as good as anyones. So they have a vested interest in keeping it random.

-Quadell

[quote]Probability does seem kind of soft. I mean, flip a coin ten times and you might get ten heads, and that 1/2 probability kinda turns to jello.[quote]

If you flip a coin nine times, and it comes up heads each time, then the odds of the next flip being a heads in 50-50. One of of every 1024 series of 10 flips of heads in a row would be a 50% chance. Flip a coin 1033 times and see what you come up with.

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Jim Petty

A Snappy message should appear here

[quote]Probability does seem kind of soft. I mean, flip a coin ten times and you might get ten heads, and that 1/2 probability kinda turns to jello.[quote]

If you flip a coin nine times, and it comes up heads each time, then the odds of the next flip being a heads in 50-50. One of of every 1024 series of 10 flips of heads in a row would be a 50% chance. Flip a coin 1033 times and see what you come up with.

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Jim Petty

A Snappy message should appear here

[quote]Probability does seem kind of soft. I mean, flip a coin ten times and you might get ten heads, and that 1/2 probability kinda turns to jello.[quote]

If you flip a coin nine times, and it comes up heads each time, then the odds of the next flip being a heads in 50-50. One of of every 1024 series of 10 flips of heads in a row would be a 50% chance. Flip a coin 1033 times and see what you come up with.

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Jim Petty

A Snappy message should appear here

[quote]Probability does seem kind of soft. I mean, flip a coin ten times and you might get ten heads, and that 1/2 probability kinda turns to jello.[quote]

If you flip a coin nine times, and it comes up heads each time, then the odds of the next flip being a heads in 50-50. One of of every 1024 series of 10 flips of heads in a row would be a 50% chance. Flip a coin 1033 times and see what you come up with.

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Jim Petty

A Snappy message should appear here

Jimpy: What's the probability of your post appearing four times in a rowD)?

I'd say probably about the same as my mastering one day the intricacies of the smiliesD)

If you flip a coin nine times, and it comes up heads each time, then the odds of the next flip being a heads in 50-50.

But if you flip a coin 999 times and it comes up heads each time, what are the odds the next flip will come up heads?

I'd say about 100%.

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"For what a man had rather were true, he more readily believes" - Francis Bacon

Imagine a stack of pennies 17,000 miles tall. Now pick a penny, any penny. The

odds of picking any one penny are greater than winning the lottery. Pretty damn good if you ask me! Sounds to me like your chances of being crushed to death are pretty darn good, too.

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