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Tags lotteries , math puzzles , probability , probability puzzles

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Old 3rd March 2012, 05:29 AM   #201
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Originally Posted by Ladewig View Post
Let's call $10 million (after taxes) a life-changing amount of money.

If $1 buys a one in one billion chance of winning that $10 million, is it worthwhile? What if $1 buys a one in one trillion chance of winning $10 million, is that still worthwhile?
Ladewig, how many times do you expect me to explain to you what 'worthwhile' means to the common man to try to get you to understand that it has nothing to do with mathematics?!
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Old 3rd March 2012, 05:34 AM   #202
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Originally Posted by Pixel42 View Post
With the UK Premium Bond scheme you're gambling with the interest on your money, rather than the money itself. The interest is the same as with any standard savings account, it's just distributed as prizes instead of being added to your account periodically. The draw is monthly and your numbers are entered into every draw as long as you hold your bond, so you don't have to keep buying it. The prizes are not as huge as lottery prizes can get, but the biggest is big enough to be life changing for most people. You can get your money back at any time.

By any measure premium bonds are a better bet than lottery tickets. So why do any Brits buy the latter?
Because the lottery is a highly-publicised game of chance, just like any other form of gambling, sensationalised by televised draws (well it is here in Oz, and still in the UK, I believe). Premium Bond draws hardly catch the public gaze.
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Old 3rd March 2012, 05:40 AM   #203
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Originally Posted by Fast Eddie B View Post
I was not the one addressed, but since my position was referenced...

Imagine that we determine that many people are using similar schemes to select lotto numbers.

Let's say they're using Bargain Trader analysis and in large numbers choosing sets based on the 10 most and 10 least occurring numbers from past drawings.

So, we come up with a set of hopefully "unique" numbers that exclude the top and bottom 10 numbers.

Do you hold that our scheme is so clever and "unique" that no one else will have thought of it? Any algorithm to select unique numbers seems doomed as long as others are also chasing "uniqueness".

I think.

But math and number theory and probability are all far from my fields of expertise, so I'm perfectly willing to be informed here.
When I write "unique" and "uniqueness" here I'm referring to the actual numbers, not the 'system' used to select them. A set of numbers selected randomly has no guarantee of being unique, of course, although it affords a better chance than a systematised selection (unless it's a unique system!).
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Old 3rd March 2012, 05:49 AM   #204
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Originally Posted by Southwind17 View Post
When I write "unique" and "uniqueness" here I'm referring to the actual numbers, not the 'system' used to select them. A set of numbers selected randomly has no guarantee of being unique, of course, although it affords a better chance than a systematised selection (unless it's a unique system!).
I'm ignorant of many things mathematical, but...

...as soon as you put forth a set as "unique", does it not render itself "non-unique" as soon as you do so?

IOW, as a thought experiment, you come up with an algorithm or scheme which tells you that 32-37-38-41-43 is hugely unlikely to be chosen by a typical player because it has no birthdays, birth months, does not fit a sequential pattern on the card or whatever criteria you select.

That very selection is likely to have been chosen by anyone using similar logic to yours, rendering at least to some extent "non-unique". If it hit, there would be many winners who arrived at those numbers using the same or similar reasoning as yours chasing "uniqueness". Right?
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Old 3rd March 2012, 05:54 AM   #205
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Originally Posted by Fast Eddie B View Post
I'm ignorant of many things mathematical, but...

...as soon as you put forth a set as "unique", does it not render itself "non-unique" as soon as you do so?

IOW, as a thought experiment, you come up with an algorithm or scheme which tells you that 32-37-38-41-43 is hugely unlikely to be chosen by a typical player because it has no birthdays, birth months, does not fit a sequential pattern on the card or whatever criteria you select.

That very selection is likely to have been chosen by anyone using similar logic to yours, rendering at least to some extent "non-unique". If it hit, there would be many winners who arrived at those numbers using the same or similar reasoning as yours chasing "uniqueness". Right?
That's right, assuming the algorithm or system is likely to be deployed by others. Which is why a randomised system is best, such as pulling numbers out of a hat, or something similarly simple.
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Old 3rd March 2012, 05:56 AM   #206
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Worthwhiledict

I see no reference to probability theory there. I do, however, see words such as 'attention' and 'interest'.
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Old 3rd March 2012, 06:02 AM   #207
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Originally Posted by Dan O. View Post
Every possible set of numbers has exactly the same probability of being drawn. About the only thing you could count on is a lottery drawing the same set of numbers as they had drawn previously. That would be like doubly astronomically impossible.

I haven't read all the way through this thread, but the parts I have read demonstrate just about every fallacy about probability going. Dan O's is just another one of them.

The probability of getting any specified group (not sequence, which implies that the order in which the balls are drawn is significant - which it isn't) of numbers is the same, irrespective of whether it has occurred before or not. I've seen this fallacy printed in so called authoritative newspaper columns.

Probability theory is a minefield waiting forn the unwary: I've watched maths teachers screw it up.
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Old 3rd March 2012, 06:18 AM   #208
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Paul,

I think that's been stipulated repeatedly in this thread.

What's being discussed is the ability to meaningfully increase the overall payoff ratio by picking numbers that others are unlikely to home in on, thereby increasing the odds of not having to share a jackpot if you do indeed win.

BTW, Dan's contention is clearly fallacious, and reminds me of my ex-wife's inability to think clearly about probability.

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Old 3rd March 2012, 08:01 AM   #209
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Originally Posted by Southwind17 View Post
Ladewig, how many times do you expect me to explain to you what 'worthwhile' means to the common man to try to get you to understand that it has nothing to do with mathematics?!

Well, then all I can say is that I will change my original statement to "the lottery is a sucker's game designed to separate very large numbers of rubes from very trivial amounts of money."

ETA: The fact that such people consider it worthwhile is prima facie evidence that they are rubes.


MORE ETA: on those occasions when I buy a lottery ticket, I am unquestioningly acting like a rube

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Old 3rd March 2012, 08:23 AM   #210
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Originally Posted by Southwind17 View Post
I'm not claiming it's a particularly interesting question. Indeed, it was you who initially inferred the question:
You realise that there's a difference between whether it's worthwhile to play not knowing if you'll win or not, and whether it was worthwhile to play after you already won, right?


Quote:
Of course, and that proves the point I'm making: that whether something is worthwhile or not can often only be considered in the context of the class of person affected.
Look, whether or not they think it's worthwhile is different from whether it's actually worthwhile.

They get something from it. They also have to pay for the privilege. What they get is a chance at winning the prize. You need to do math to determine how valuable that chance is.

Quote:
But that misses the point of why doing the lottery is worthwhile; because it has the potential to make one wealthy. Pointing out that the odds make no sense actually misses the point. The simple fact that it has the potential to realise dreams is exactly why it's worthwhile.
That's why is may be worthwhile. That's the value it has. Now we have to compare that value to the cost. You're saying "The lottery has some positive value! Therefore it's worthwhile!" But you're both unwilling to quantify that value, and to compare it to the cost. Without doing so, you have no way to determine if it's value is greater than its cost.

Moreover, yes, it's the potential to make one wealthy that's valuable. That potential is quantifiable, and it's very small. A 1/10 chance to win $100,000 is worth only 1/10th of a 10/10 chance to win $100,000. The logic follows to a 1/100,000,000 chance to win $1,000,000.

Quote:
Change it from what to what - the mathematical proposition that the cost is real but the benefit is, essentially, zero, to the practical reality that the cost is minimal and the potential benefit could be life changing?
I never said the benefit is zero. It's not. And unlike you I'm willing to quantify exactly what the benefit is. That is the practical reality.

The benefit is potentially life changing. Which is less than certainly life changing.

Quote:
Strawman. Motivation for playing Russian Roulette for $50k isn't comparable to motivation for staking a couple dollars a week for a possible life-changing outcome.
It certainly is comparable: I made the comparison. The fact that you make the assertion that it's not comparable isn't addressing the argument.



Quote:
Even if people, like I, appreciate that the lottery odds mean that I shouldn't expect to win the jackpot, it's still a worthwhile venture. Allow me to repeat, for most the cost has no material loss of amenity, which means for all intents and purposes it's essentially free to enter.
Wait, something that costs $1 (or whatever the price is), is free?
That's pretty weird logic you have.

Quote:
What fool wouldn't enter a free lottery for a chance to become rich? Look, I see where you're coming from with the chalkboard, but that's not how people look on the lottery, and frankly your naysayer attitude is the last thing that most lottery players want to hear - they want to have fun trying to win a fortune. Leave 'em be you doom monger!
I don't care what they want to hear, or whether they play the lottery. You seem to think the fact that people play the lottery demonstrates that it's worthwhile to play the lottery.

Guess what? People can be wrong.


Quote:
Here's how to test the importance of the maths: go stand next to your local lottery ticket sales outlet, set up a billboard showing the odds and even explaining the maths, and see how many people you can convince not to buy a ticket. Many will understand and appreciate the odds, but will they be swayed? Are you a betting man, by any chance?!
So, you can't convince people not to make stupid decisions, therefore their decisions aren't stupid? Okay...


Quote:
Not at the current pricing and prize levels that most people play at, absolutely not, but I'm not going to repeat myself yet again.
Which basically proves my point.
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Old 3rd March 2012, 02:05 PM   #211
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Originally Posted by Paul W View Post
I haven't read all the way through this thread, but the parts I have read demonstrate just about every fallacy about probability going. Dan O's is just another one of them.

The probability of getting any specified group (not sequence, which implies that the order in which the balls are drawn is significant - which it isn't) of numbers is the same, irrespective of whether it has occurred before or not. I've seen this fallacy printed in so called authoritative newspaper columns.

Probability theory is a minefield waiting forn the unwary: I've watched maths teachers screw it up.
Actually, Dan O.'s statement that you can pretty much count on a previously drawn set of numbers not coming up again IS technically correct. What's fallacious is thinking that by not selecting previously drawn sets of numbers increases your chances of winning!
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Old 3rd March 2012, 02:07 PM   #212
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Originally Posted by Southwind17 View Post
Actually, Dan O.'s statement that you can pretty much count on a previously drawn set of numbers not coming up again IS technically correct. What's fallacious is thinking that by not selecting previously drawn sets of numbers increases your chances of winning!
I agree and Happy Birthday!.
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Old 3rd March 2012, 02:21 PM   #213
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Originally Posted by Ladewig View Post
Well, then all I can say is that I will change my original statement to "the lottery is a sucker's game designed to separate very large numbers of rubes from very trivial amounts of money."

ETA: The fact that such people consider it worthwhile is prima facie evidence that they are rubes.


MORE ETA: on those occasions when I buy a lottery ticket, I am unquestioningly acting like a rube
What's the difference between being a rube and just acting like a rube? I suppose you'd like to have us all believe that you have occasional and momentary lapses of reason that cause you uncontrollably to go out and buy a lottery ticket. Classic denial behaviour. You're a rube, buddy, through and through!

Actually, you're not. You just consider doing the lottery worthwhile now and then, on those rare occassions when you happen to take your mind off maths. Consider it as letting your hair down a little, if you will!

Hey but don't go off the rails now and set up a standing order. They'll have you in the assylum before you know it!
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Old 3rd March 2012, 02:21 PM   #214
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Originally Posted by Fast Eddie B View Post
Paul,

I think that's been stipulated repeatedly in this thread.

What's being discussed is the ability to meaningfully increase the overall payoff ratio by picking numbers that others are unlikely to home in on, thereby increasing the odds of not having to share a jackpot if you do indeed win.

BTW, Dan's contention is clearly fallacious, and reminds me of my ex-wife's inability to think clearly about probability.
As I said, I haven't read all the way through this thread. But yes, I go with all you say!
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Old 3rd March 2012, 02:23 PM   #215
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Originally Posted by ynot View Post
I agree and Happy Birthday!.
Why thank you ynot.
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Old 3rd March 2012, 02:25 PM   #216
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Originally Posted by Southwind17 View Post
Actually, Dan O.'s statement that you can pretty much count on a previously drawn set of numbers not coming up again IS technically correct.
Yes, but only in the sense that any specified set of numbers is unlikely to come up. It's called "random".

Sorry about sequential postings: I haven't worked out how to link them!
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Old 3rd March 2012, 02:34 PM   #217
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Forget this one!

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Old 3rd March 2012, 02:41 PM   #218
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Originally Posted by Roboramma View Post
You realise that there's a difference between whether it's worthwhile to play not knowing if you'll win or not, and whether it was worthwhile to play after you already won, right?
It's worthwhile either way. Sure, the 'worth' is different for each.

Originally Posted by Roboramma View Post
Look, whether or not they think it's worthwhile is different from whether it's actually worthwhile.
Worthwhiledict: look it up.

Originally Posted by Roboramma View Post
They get something from it. They also have to pay for the privilege. What they get is a chance at winning the prize. You need to do math to determine how valuable that chance is
Don't disagree.

Originally Posted by Roboramma View Post
That's why is may be worthwhile. That's the value it has. Now we have to compare that value to the cost. You're saying "The lottery has some positive value! Therefore it's worthwhile!" But you're both unwilling to quantify that value, and to compare it to the cost. Without doing so, you have no way to determine if it's value is greater than its cost.
Worthwhiledict: look it up again, if you're still confused.

Originally Posted by Roboramma View Post
Moreover, yes, it's the potential to make one wealthy that's valuable. That potential is quantifiable, and it's very small. A 1/10 chance to win $100,000 is worth only 1/10th of a 10/10 chance to win $100,000. The logic follows to a 1/100,000,000 chance to win $1,000,000.
Worthwhiledict: just in case

Originally Posted by Roboramma View Post
I never said the benefit is zero. It's not. And unlike you I'm willing to quantify exactly what the benefit is. That is the practical reality.
Essentiallydict You don't think 14,000,000:1 is essentially zero for all intents and purposes?

Originally Posted by Roboramma View Post
The benefit is potentially life changing. Which is less than certainly life changing.
You don't say!

Originally Posted by Roboramma View Post
It certainly is comparable: I made the comparison. The fact that you make the assertion that it's not comparable isn't addressing the argument.
Ah, I see now. By 'comparable' you mean 'contrastable'. Yes, that makes more sense now.

Are you seriously claiming that human behaviour that drives people to do the lottery would also drive people to play Russian Roulette for a $50,000 prize, and that people would consider the two equally worthwhile if the Roulette game was available to them? Seriously?! How are you translating the stakes, exactly?

Originally Posted by Roboramma View Post
Wait, something that costs $1 (or whatever the price is), is free?
That's pretty weird logic you have.
Essentiallydict (in case you missed it before).

Originally Posted by Roboramma View Post
I don't care what they want to hear, or whether they play the lottery.
And there lies your problem.

Originally Posted by Roboramma View Post
You seem to think the fact that people play the lottery demonstrates that it's worthwhile to play the lottery.
Worthwhiledict (although I'm hoping you've got it now!).

Originally Posted by Roboramma View Post
Guess what? People can be wrong.


Originally Posted by Roboramma View Post
So, you can't convince people not to make stupid decisions, therefore their decisions aren't stupid? Okay...
Worthwhiledict (last ditch attempt).

Originally Posted by Roboramma View Post
Which basically proves my point.
How so?
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Old 3rd March 2012, 02:45 PM   #219
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Originally Posted by Paul W View Post
Yes, but only in the sense that any specified set of numbers is unlikely to come up.
It's technically correct in every sense.

Originally Posted by Paul W View Post
It's called "random".
What is?
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Old 3rd March 2012, 02:48 PM   #220
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Everybody posting on this thread considers it worthwhile. Would somebody care to run the numbers on that please, just to be sure. Otherwise I'm gonna go watch sport.
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Old 3rd March 2012, 03:26 PM   #221
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Originally Posted by Southwind17 View Post
Actually, Dan O.'s statement that you can pretty much count on a previously drawn set of numbers not coming up again IS technically correct.
I would replace the word "technically" with the word "trivially".

As others have pointed out, you can pretty much count on any set of numbers not coming up. The "again" adds no add'l meaning.
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Old 3rd March 2012, 03:36 PM   #222
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Originally Posted by Southwind17 View Post
What's the difference between being a rube and just acting like a rube? I suppose you'd like to have us all believe that you have occasional and momentary lapses of reason that cause you uncontrollably to go out and buy a lottery ticket. Classic denial behavior. You're a rube, buddy, through and through!
OK, I'll own it. I am a rube because I buy lottery tickets. If it'll make you happy, I'll change my avatar title from "Hipster alien" to "turnip-truck rube"

<-----RUBE.

Quote:
Actually, you're not. You just consider doing the lottery worthwhile now and then, on those rare occasions when you happen to take your mind off maths. Consider it as letting your hair down a little, if you will!
You have it backwards. It is because I think the purchase of tickets is worthwhile that I am a rube. Believing that a game of chance with a 50ish % house advantage is worthwhile is pretty much the definition of a rube.

How odd that you mention letting one's hair down. That is one of the classic taunts that hucksters throw at rubes.

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Old 3rd March 2012, 03:48 PM   #223
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What everyone so diligently analyzing my post fail to realize is that I hadn't proofread what I had typed and left out a "not". The link was then intended to be proof that the statement itself was wrong.
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Old 3rd March 2012, 04:09 PM   #224
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Originally Posted by Undesired Walrus View Post
1,2,3,4,5,6 in the lottery

For years, I've been telling people that it's as likely for you to get the above numbers as something like 35,32,18,16, 28, 21.

People can't seem to believe it. Is this actually the case, or am I making a fool of myself?
I've just belatedly come across this thread. Strangely I bought just such a lottery ticket (1,2,3,4,5) as a potentially life-changing gift for my Secret Santee* last year.



I bought an identical one for myself in case it won and I was tempted to run off with the millions myself instead of passing them on.

Surprise! Neither of us became millionaires.



*You know who you are.
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Old 3rd March 2012, 04:57 PM   #225
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Originally Posted by Fast Eddie B View Post
I would replace the word "technically" with the word "trivially".
I disagree; it's a far from trivial point that's being made.

Originally Posted by Fast Eddie B View Post
As others have pointed out, you can pretty much count on any set of numbers not coming up.
Wrong. A set of numbers comes up most times, and there's usually a jackpot winner(s). You need to be very careful with your wording.

Originally Posted by Fast Eddie B View Post
The "again" adds no add'l meaning.
Without the "again" the point being made has no meaning. The entire point is about a winning set of numbers winning again!
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Old 3rd March 2012, 05:00 PM   #226
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Originally Posted by Ladewig View Post
How odd that you mention letting one's hair down. That is one of the classic taunts that hucksters throw at rubes.
Remind me Ladewig ... what time does the party start? I sure hope you've teed up a bouncy castle!
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Old 3rd March 2012, 05:22 PM   #227
Dan O.
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Originally Posted by 666 View Post
Surprise! Neither of us became millionaires.

Are you sure? Many people forget to check the Raffle Numbers after being disappointed in the main draw. There are still 2 outstanding £1 million prizes from December that are unclaimed.


Quote:
I bought an identical one for myself in case it won and I was tempted to run off with the millions myself instead of passing them on.
It's as if you can't throw your money away fast enough. There was a power ball lottery a few years ago that was won by an office pool. One of the participants in the pool also bought a ticket for himself using the same numbers.

Last edited by Dan O.; 3rd March 2012 at 05:30 PM.
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Old 3rd March 2012, 05:29 PM   #228
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Originally Posted by Dan O. View Post
Are you sure? Many people forget to check the Raffle Numbers after being disappointed in the main draw. There are still 2 outstanding £1 million prizes from December that are unclaimed.
Well then their best hope is that they're each semi-millionaires! That would suck!
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Old 3rd March 2012, 06:12 PM   #229
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Originally Posted by Southwind17 View Post
Wrong. A set of numbers comes up most times, and there's usually a jackpot winner(s).
Which lottery are we talking about? Because for the American inter-state lotteries (Mega Millions and Power Ball), usually there's not a jackpot winner.

Mega Millions, for instance, has two draws a week -- and exactly one of those draws has had a jackpot winner since last October.
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Old 3rd March 2012, 06:21 PM   #230
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Southwind17,

We must be talking past each other.

I just can't get the points you're trying to make.

Someone said it would be a poor bet to bet numbers that had just come up. It is a fact that those numbers would be exactly as probable as any other.

That's all I was saying, and I don't get how it's wrong.

Last edited by Fast Eddie B; 3rd March 2012 at 06:39 PM.
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Old 3rd March 2012, 06:22 PM   #231
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Originally Posted by Southwind17 View Post
Well then their best hope is that they're each semi-millionaires! That would suck!

Perhaps you didn't look it up. The raffle is not a shared prize.
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Old 3rd March 2012, 09:36 PM   #232
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Originally Posted by AvalonXQ View Post
Which lottery are we talking about? Because for the American inter-state lotteries (Mega Millions and Power Ball), usually there's not a jackpot winner.

Mega Millions, for instance, has two draws a week -- and exactly one of those draws has had a jackpot winner since last October.
I'm referring to the various Australian lotteries (in particular TattsLotto) and the UK National Lottery.
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Old 3rd March 2012, 09:45 PM   #233
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Originally Posted by Fast Eddie B View Post
Southwind17,

We must be talking past each other.

I just can't get the points you're trying to make.

Someone said it would be a poor bet to bet numbers that had just come up. It is a fact that those numbers would be exactly as probable as any other.

That's all I was saying, and I don't get how it's wrong.
This is what you actually wrote that I pointed out is wrong:
Originally Posted by Fast Eddie B View Post
As others have pointed out, you can pretty much count on any set of numbers not coming up.
That's patently wrong. A set of numbers usually does come up, at least in relation to the Australian weekly TattsLotto, as these results clearly demonstrate (Division 1 is deemed the jackpot).
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Old 3rd March 2012, 09:50 PM   #234
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Originally Posted by Dan O. View Post
Perhaps you didn't look it up. The raffle is not a shared prize.
My apologies - I failed to realise that the raffle entry numbers (and letters) are completely separate from the Euromillions entry numbers.
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Old 3rd March 2012, 11:22 PM   #235
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Originally Posted by Southwind17 View Post
This is what you actually wrote that I pointed out is wrong:That's patently wrong. A set of numbers usually does come up, at least in relation to the Australian weekly TattsLotto, as these results clearly demonstrate (Division 1 is deemed the jackpot).
It's pretty clear that he means any particular set of numbers.
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Old 4th March 2012, 05:21 AM   #236
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Originally Posted by Roboramma View Post
It's pretty clear that he means any particular set of numbers.
When I read Southwind17's response, I realized how he interpreted my statement, and that I needed to add the word "particular".

Then I scrolled down and you beat me to it. Thanks!

Of course some set of numbers will come up. That seems too obvious to state. And sometimes there will be a player who selected that set and sometimes not.

Hopefully that's straightened out - I really hate to be called "wrong" when what I'm stating is self evident. There are enough other times when I'm legitimately wrong - just ask my wife!
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Old 4th March 2012, 05:29 AM   #237
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Originally Posted by Southwind17 View Post
A set of numbers usually does come up, at least in relation to the Australian weekly TattsLotto, as these results clearly demonstrate (Division 1 is deemed the jackpot).
No, a set of numbers always does come up - nothing "usually" about it.

You're assuming an unstated premise here - that the discussion is whether any given draw will have a winner. Of course, some do and some don't.

To be clearer, you should have said, "A winning set of numbers usually does come up...". And the odds of that happening can be calculated, depending on the type of draw and number of tickets purchased.

Again, sorry if I wasn't clear. Communication is a two way street.
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Old 4th March 2012, 03:51 PM   #238
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Originally Posted by Fast Eddie B View Post
When I read Southwind17's response, I realized how he interpreted my statement, and that I needed to add the word "particular".

Then I scrolled down and you beat me to it. Thanks!

Of course some set of numbers will come up. That seems too obvious to state. And sometimes there will be a player who selected that set and sometimes not.

Hopefully that's straightened out - I really hate to be called "wrong" when what I'm stating is self evident. There are enough other times when I'm legitimately wrong - just ask my wife!
I don't mean to be harsh Fast Eddie. Call me pedantic, but it's important to be accurate when making claims about such matters as probability. I called you on it rather than assuming. The record's straight now - thanks
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Old 4th March 2012, 06:13 PM   #239
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Originally Posted by Southwind17 View Post
...thanks
WOW! What are the chances of that???

You're welcome, BTW!

Last edited by Fast Eddie B; 4th March 2012 at 06:14 PM.
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Old 4th March 2012, 07:10 PM   #240
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Originally Posted by Fast Eddie B View Post
No, a set of numbers always does come up - nothing "usually" about it.

You're assuming an unstated premise here - that the discussion is whether any given draw will have a winner. Of course, some do and some don't.

To be clearer, you should have said, "A winning set of numbers usually does come up...". And the odds of that happening can be calculated, depending on the type of draw and number of tickets purchased.

Again, sorry if I wasn't clear. Communication is a two way street.
I think the problem here is that we seem to be at cross purposes as to exactly what 'come up' means. You seem to be suggesting that you're referring to the numbers drawn, whereas I'm referring to a set of numbers selected and entered. In the context of your original statement, however, it seems clear to me that you were referring to exactly what I am, namely a set of numbers selected and entered:
Originally Posted by Fast Eddie B View Post
As others have pointed out, you can pretty much count on any set of numbers not coming up. The "again" adds no add'l meaning.
Ironically, the "again" is now critical to your meaning!
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Last edited by Southwind17; 4th March 2012 at 07:15 PM.
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