Woman wins millions in lottery 4 times!

[Balthamael]

Well, I assumed there's only a few people who've won twice, let's call it x, so the odds of one of them winning twice are approximately 16 million squared divided by x.

 

But you can't just go and factor probabilities like that. That just tells you the odds for two particular tickets both winning, like for example winning in consecutive weeks. Here we have a situation where someone has won several times over a long period of time. That requires a somewhat more complex calculation. Not to mention that you are forgetting completely that we would be having exactly this same discussion if she had won five times, or six or seven. You have to account for those events as well.

[Meshugger]

It was magic.

[Wrath of Dagon]

I'm calculating orders of magnitude, not exact numbers. So for a specific person to win 4 times over a period of time in which she spent an amount of money y playing would be approximately 16 million to the fourth power divided by y. The chance of someone winning once we know is 1. The chance of someone winning twice has also been calculated previously and it amounts to someone winning every few years, and that's where the y divisor comes in. So now that only leaves the 16 million squared term, which is what I used. I'm willing to concede I could be off somewhat in this reasoning, but in any case it comes out to a huge number against anyone in the world winning 4 times.

[Pidesco]

I don't see why this is so hard to understand. It just boggles the mind, that the debate wasn't over in the first few posts.

[Humodour]

Oh god, I'm having flashbacks to trying to explain the "Monty Hall problem" back on BIS...

 

To be fair, a lot of mathematicians and statisticians are utterly clueless when it comes to the Monty Hall problem/fallacy. It's awesome.

[Wrath of Dagon]

Are you talking about the gambler's fallacy? What mathematicians and statistians are clueless about it?

[Amentep]

Oh god, I'm having flashbacks to trying to explain the "Monty Hall problem" back on BIS...

 

To be fair, a lot of mathematicians and statisticians are utterly clueless when it comes to the Monty Hall problem/fallacy. It's awesome.

 

Yes, yes it is awesome.

 

That doesn't help that reading through this thread reminded me of that long lost, grand time.

[Amentep]

Are you talking about the gambler's fallacy? What mathematicians and statistians are clueless about it?

 

Unambiguous Monty Hall Problem:

"Suppose you're on a game show and you're given the choice of three doors [and will win what is behind the chosen door]. Behind one door is a car; behind the others, goats [unwanted booby prizes]. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one [uniformly] at random. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?"

 

The answer is "yes, it is to your advantage to change your choice"

[Gfted1]

The answer is "yes, it is to your advantage to change your choice"

 

Its not a 50/50 chance at that point?

[Amentep]

The answer is "yes, it is to your advantage to change your choice"

 

Its not a 50/50 chance at that point?

 

Nope.

 

The way its set up each door has a 1/3 chance to have a car.

 

When the player picks a door their door has a 1/3 chance of having the car, as do the other two.

 

So the player's door has a 1/3 chance to have the car, while the remaining doors have 2/3.

 

When Monty Hall reveals the door with the goat amid the other two, it means that the 2/3 chance the other two have are now with the door that didn't have a goat and that the player didn't pick.

 

So the player will win a car by switching 2/3 of the time, compared to the 1/3 if he stays.

[Balthamael]

Oh dear, it begins.

 

Counterintuitive as it may seem, no, it is not 50/50. You picked a door when you had 1/3 odds to be correct. By showing you the empty door, Monty Hall changed nothing. You still have the same odds. Thus, you should switch, there is 2/3 chance that the car is behind the remaining door.

 

The thing may be easier to visualise if you imagine being offered this option hundred times. So you make your initial choices, statistics suggest that you will have chosen 33 correct doors, and 67 empty ones. Now, when Monty Hall opens hundred empty doors, surely that doesn't change the amount of cars you have picked. You still have 33. 17 sports cars didn't just materialize out of emptiness, right? So, you should switch all your choices. There are 67 cars behind the 100 remaining closed doors, and 33 cars behind the doors you have chosen.

 

Edit. Ahh, beaten by Amentep.

Edited July 15, 2010 by Balthamael

[Amentep]

Oh dear, it begins.

 

I hate myself already.

[Gfted1]

@Tep and Balth: Thanks, that makes sense.

[Humodour]

Are you talking about the gambler's fallacy? What mathematicians and statistians are clueless about it?

 

The gambler's fallacy is nothing compared to the Monty Hall problem.

[Serrano]

I don't see why this is so hard to understand. It just boggles the mind, that the debate wasn't over in the first few posts.

 

Welcome to the internet

Edited July 15, 2010 by Serrano

[Wrath of Dagon]

OK, what the MH problem illustrates is that people are used to thinking about probabilities of random independent events. They get confused because in this case the events (which door has what) are not independent since MH knows which doors have the goats and acts accordingly.

 

Edit: A simple way to explain it is that MH not opening your door tells you nothing, since he's not allowed to open the door you picked. However, his not opening the other door makes it more likely that the car is behind that door, since he's also not allowed to open the door with the car, so that's the door you should pick.

Edited July 15, 2010 by Wrath of Dagon

[Gorth]

Math makes my head hurts. I prefer Monty Haul. Brain it with an axe and grab 100% of the loot.

[Oblarg]

Math makes my head hurts. I prefer Monty Haul. Brain it with an axe and grab 100% of the loot.

 

Here's a *really* easy way to think of it. Same problem, different numbers

 

There are 100 doors. One door has the prize.

 

You are allowed to pick one door. Then, Monty Hall reveals 98 doors that have no prize, leaving one other door. You can either switch or not switch.

 

Now it should be very obvious that you should switch doors.

 

This is the exact same situation.

Edited July 16, 2010 by Oblarg

[Tigranes]

Funnily enough, Amentep's one post was enough - I understand the Monty Hall thing, now it's very obvious to me that he should switch his choice (the 2/3 doesn't disappear when Monty Hall closes the door, etc). But I still don't quite get the initial stuff about the lottery. To me, there still hasn't been an explanation I can grasp about why there is no difference in probability between a person winning a lottery 4 times, and the same person winning it 4 times?

 

I mean, this is not surprising, as I'm, again, rubbish at maths...

 

Also, I swear we had this exact same maths discussion ~2 years ago here.

[Wrath of Dagon]

Actually what you said are the same thing. It's actually the difference between a pre-selected person winning and anyone in the world winning. Let's say you and your 9 friends have to pull out a correct card. You each have 1/5 chance of success. The chances that any one of you gets the correct card are a lot higher than that it's specifically you that gets the correct card.

[Tigranes]

That's what I meant, yeah. I know what you're saying, I just don't quite get the other argument.

[Deadly_Nightshade]

Except that this does nothing to change the individual odds of each person, you all have the same chance of drawing the card as you you would if you were the only person - the difference is that, in your situation, you would win if anyone in your party drew the correct card and that is what raised the odds of that happening. The lottery, unless you go in as a group, does not function that way and thus your example is flawed.

 

EDIT:

And you still have yet to support your claim that things with extremely bad odds cannot happen in nature.

Edited July 16, 2010 by Deadly_Nightshade

[Wrath of Dagon]

I didn't say you would win in this situation. I'm trying to illustrate that the odds of a specific person winning are less than the odds of someone in the group winning.

 

Edit: What I'm trying to say is that for all practical purposes they can't happen. To repeat once again, if something can only happen once in a trillion years, you're will not ever see it happen. If you don't believe that, there's nothing more I can say to you.

Edited July 16, 2010 by Wrath of Dagon

[Deadly_Nightshade]

What I'm trying to say is that for all practical purposes they can't happen.

 

Sure, but they do happen - exceptionally improbable events happen regardless of how improbable they are. Also, just because the odds say something is likely to occur, to use your example, once in the trillion years does not mean that they cannot occur more than once in that time-frame.

 

 

To repeat once again, if something can only happen once in a trillion years, you're will not ever see it happen.

 

Except when you do see it happen.

 

If you don't believe that, there's nothing more I can say to you.

 

Fine, but that doesn't change the fact that you're utterly and completely incorrect about this.

 

 

EDIT:

 

I just happen to be talking to a friend who has a physics degree, with mathematics and computer science minors, and he agrees that you're mistaken - just tossing that out there since you seem so focused on proving that you're so good with the maths.

Edited July 16, 2010 by Deadly_Nightshade

[Wrath of Dagon]

Name me another even that happened that had 100 trillion to one odds. But regardless, whatever makes you feel better.