–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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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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Actually, I think it’s the other way around. I believe the world population is something like 51% female and 49% male.
“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.”
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.
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.
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.
President of the Vernon Dent fan club.
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.
“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.
“For what a man had rather were true, he more readily believes” - Francis Bacon
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.
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.
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 *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”.
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:
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”.
“If A=B, B=C, and C=D, do not get a job proofreading” --Quid’s Theorem
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.
i am on a never-ending quest to eliminate capital letters
“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!!!
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.