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6049 clicks; posted to Main » on 13 Jul 2010 at 12:46 PM (3 years ago)   |  Favorite    |   share:    more»

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Probability experts were quoted in media reports saying the likelihood of getting eight consecutive picks right is 1/256. Sharpe said the odds of getting eight straight right was over 1/300.

Wait, so the bookie says the odds are lower?

Take 256 male and 256 female octopi. Let each group pick a team. Put winning males and winning females in one group, and losers in another group.

Then run the experiment again, and eat the ones that switched from loser to winner (and vice versa). Continue until there is one winning male, one winning female, one losing male, and one losing female. Breed winners with winners, and losers with losers.

After a few generations, your octopi will either be very lucky, or like soccer.

/Sports Illustrated, unlike CNN, is blocked at work, so I'm guessing the content of the link.

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Note: the host always opens a losing door....

/yeah I'm going there

MATH IS HARD!

impaler: /yeah I'm going there

I was told there would be no math.

If you switch, the only way to lose would be if you picked the right door on the first guess. There's a 1/3rd chance that you'll do that. So if your strategy is to switch, then your chance of winning is always 2/3.

If you always switch, you win two out of every three games. If you never switch, you win one out of every three games.

Why do I feel like I'm taking the GMAT?

math sucks

I was hoping there would be math....

Sybarite: Probability experts were quoted in media reports saying the likelihood of getting eight consecutive picks right is 1/256. Sharpe said the odds of getting eight straight right was over 1/300.

Wait, so the bookie says the odds are lower?

The first three picks for Paul were not pick-one-of-two choices, they were actually pick one of three: Paul's chosen team could have won, lost, or drawn. The group matches, unlike the knockout stages and the third-place match, could have finished in a draw.

So the real probability for Paul's correct picks was 1/3 * 1/3 * 1/3 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2, which is actually 1/864. Subby, "probability experts" AND bookie all FAIL.

Let's go shopping!

LegacyDL: Why do I feel like I'm taking the GMAT?

Because, like most most Americans, 8th grade math arithmetic intimidates you?

I KNEW someone would bring up Monty Hall.

If you switch, the only way to lose would be if you picked the right door on the first guess. There's a 1/3rd chance that you'll do that. So if your strategy is to switch, then your chance of winning is always 2/3.

If you always switch, you win two out of every three games. If you never switch, you win one out of every three games.

ouch.

LegacyDL: Why do I feel like I'm taking the GMAT?

Because you're hung over, sitting in a stifling room packed with losers, and half of them are sobbing?

They should put paul the octopus on a reality show, and he can vote off women each week based on this method of picking. and then the last one standing has to have sex with flava flav, or the octopus, they get to pick. "This fall, Tentacle of Love"

The Third Man: The first three picks for Paul were not pick-one-of-two choices, they were actually pick one of three: Paul's chosen team could have won, lost, or drawn. The group matches, unlike the knockout stages and the third-place match, could have finished in a draw.

But was there an option for tie for Paul to choose?

When I was in college my Math professor told us that a sideline of his was to be an "expert witness" in the courtroom. He said the most complicated math he was ever asked to do was to multiply out interest rates.

6% interest a year for 12 years.

1.06^12

The lawyers and judges needed a Math professor for that.

Never tell me the odds.

/in fact, never talk to me at all when I'm lit from below like this

If you switch, the only way to lose would be if you picked the right door on the first guess. There's a 1/3rd chance that you'll do that. So if your strategy is to switch, then your chance of winning is always 2/3.

If you always switch, you win two out of every three games. If you never switch, you win one out of every three games.

you dont make sense. or im just not grasbing what your saying. repeat. clearer please.

I wonder how many dolphins and horses and groundhogs were secretly being videotaped by their owners in the hopes of being a youtube celebrity.

I want to be a probability expert when I grow up.

Sybarite: Probability experts were quoted in media reports saying the likelihood of getting eight consecutive picks right is 1/256. Sharpe said the odds of getting eight straight right was over 1/300.

Wait, so the bookie says the odds are lower?

My question exactly. Why would the bookie pay out more than the odds dictate? Stupid bookie. Stupid author. Stupid.

If you switch, the only way to lose would be if you picked the right door on the first guess. There's a 1/3rd chance that you'll do that. So if your strategy is to switch, then your chance of winning is always 2/3.

If you always switch, you win two out of every three games. If you never switch, you win one out of every three games.

The odds of picking a winning door is 50-50, regardless of the number of doors. If there are three doors you have a 50-50 chance of getting it right. If there are a hundred doors you have a 50-50 chance of getting it right.

Tofu: If you switch, the only way to lose would be if you picked the right door on the first guess. There's a 1/3rd chance that you'll do that. So if your strategy is to switch, then your chance of winning is always 2/3.

If you always switch, you win two out of every three games. If you never switch, you win one out of every three games.

That part I picked up on pretty quickly (imagine it with four doors, or five, or a hundred, with only one door remaining), but what's weird to me is that the answer changes if the host picked the losing door at random, in which case it doesn't matter because the lower chance of the situation coming up if you picked the wrong door cancels with the low chance of picking the right door in the first place. It kind of goes against common sense for it to matter, doesn't it? I mean, it looks just the same.

If you switch, the only way to lose would be if you picked the right door on the first guess. There's a 1/3rd chance that you'll do that. So if your strategy is to switch, then your chance of winning is always 2/3.

If you always switch, you win two out of every three games. If you never switch, you win one out of every three games.

you dont make sense. or im just not grasbing what your saying. repeat. clearer please.

He's wrong.

The no switch is a 1/3 win. That one is pretty obvious.

But the switch is just 1/2, not 2/3. Basically, you eliminated one of the doors and then made a new selection out of the remaining two.

impaler: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Note: the host always opens a losing door....

/yeah I'm going there

Imagine the same scenario but with 1000 doors. 999 with goats. After you pick a door, the host will remove 998 other doors that have goats.

Would you switch? Obviously.

Eggheads trying to figure out how to win prizes in theory:

Actual prize winner:

Imma say Monte sexually harrassed me and win ALL the prizes in court!

Snarfangel: Take 256 male and 256 female octopi. Let each group pick a team. Put winning males and winning females in one group, and losers in another group.

Then run the experiment again, and eat the ones that switched from loser to winner (and vice versa). Continue until there is one winning male, one winning female, one losing male, and one losing female. Breed winners with winners, and losers with losers.

/Sports Illustrated, unlike CNN, is blocked at work, so I'm guessing the content of the link.

Larry Niven approves

AuntNotAnt: It kind of goes against common sense

It does. That's for sure.

"Common Sense" is stupid.

Remember that the next time you see a politician railing on about "common sense solutions."

Approves

...Except that the mathematical version of the Monty Hall problem, in isolation, ignores quotes from Monty Hall himself that he only offered the switch when switching would be bad for the contestant.

So, never switch.

If you switch, the only way to lose would be if you picked the right door on the first guess. There's a 1/3rd chance that you'll do that. So if your strategy is to switch, then your chance of winning is always 2/3.

If you always switch, you win two out of every three games. If you never switch, you win one out of every three games.

you dont make sense. or im just not grasbing what your saying. repeat. clearer please.

-you choose a door.
- The host picks a door that you didn't choose and reveals that door as being wrong (it has a goat).
- You have the choice to choose a different door, or keep the door you previously chose.

If your first pick was a goat (a), the host reveals a goat(b) and you switch, you win the car.
If your first pick was a goat (b), the host reveals a goat(a) and you switch, you win the car.
If your first pick was the car, the host reveals a goat(a/b) and you switch, you find the other goat (a/b).

If your first pick was a goat (a), the host reveals a goat(b) and you keep the door, you find a goat (a).
If your first pick was a goat (b), the host reveals a goat(a) and you keep the door you find goat(b).
If your first pick was the car, the host reveals a goat(a/b) and you switch, you win the car.

Snarfangel: Take 256 male and 256 female octopi. Let each group pick a team. Put winning males and winning females in one group, and losers in another group.

Then run the experiment again, and eat the ones that switched from loser to winner (and vice versa). Continue until there is one winning male, one winning female, one losing male, and one losing female. Breed winners with winners, and losers with losers.

After a few generations, your octopi will either be very lucky, or like soccer.

/Sports Illustrated, unlike CNN, is blocked at work, so I'm guessing the content of the link.

Approves.

/hot

impaler: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Note: the host always opens a losing door....

/yeah I'm going there

mesmer242: ...Except that the mathematical version of the Monty Hall problem, in isolation, ignores quotes from Monty Hall himself that he only offered the switch when switching would be bad for the contestant.

So, never switch.

Ahem: Note: the host always opens a losing door....

huh mock26?

imagine there are 100 doors, 1 car, and 99 goats. You pick a door, and then the host opens 98 of the other doors showing all goats. He then asks if you want to switch to the remaining door, or keep your original choice, do you do it?

You better god damn believe you should.

The Monty Hall Problem is bullshiat.

Mr.Insightful: When I was in college my Math professor told us that a sideline of his was to be an "expert witness" in the courtroom. He said the most complicated math he was ever asked to do was to multiply out interest rates.

6% interest a year for 12 years.

1.06^12

The lawyers and judges needed a Math professor for that.

Hmmm... I'd have said (e^0.06)^12? But even that is pretty tame. I'm actually hard pressed to think of when a math professor would actually be needed in a court room, unless he needed to prove his innocence...

The octopus chose whichever flag had more yellow, every time.

Really not that hard to figure out. Maybe a little bit of luck here or there.

/for the Monty Hall problem, always switch doors, assuming that the host knew what was behind the door.

There's a good explanation of the Monty Hall problem in The Curious Incident of the Dog in the Night-Time.

/Good book otherwise, too.

Statistics: how does it farkin work?

Anybody that says don't switch or doesn't matter if switch or not, just stop.

kankikr: you dont make sense. or im just not grasbing what your saying. repeat. clearer please.

Well, I first heard of this problem from a book I read years ago about an autistic kid. The title was, The Curious Incident of the Dog in the Night Time. So if you go out and read that it explains it better than I can.

At the time I read that, I didn't believe that switching gave you a 66% chance of winning, so I wrote a little perl program to play the game 1000 times and count the results (to a mathematician, I know that having to test this probably makes you laugh). Anyway, I'll dig up the code and post it if you like.

Bottom line, with three doors and one winning door, you have a 33% chance of winning if you do not switch, and a 66% chance of winning if you do. Rather than argue this mathematically, prove it to yourself by playing the game many times.

impaler: mesmer242: ...Except that the mathematical version of the Monty Hall problem, in isolation, ignores quotes from Monty Hall himself that he only offered the switch when switching would be bad for the contestant.

So, never switch.

Ahem: Note: the host always opens a losing door....

That's different from "The host always offers a switch".

I appreciate the mathematics behind the problem, but it's an awful lot of time to spend on something that never actually happened. It's a game that never actually existed in that format - it was always rigged against the contestants.

bacongood: He's wrong.

wanna bet? I'll post the code or put it online somewhere and let you play the game yourself.

mesmer242: ...Except that the mathematical version of the Monty Hall problem, in isolation, ignores quotes from Monty Hall himself that he only offered the switch when switching would be bad for the contestant.

So, never switch.

impaler: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Note: the host always opens a losing door....

/yeah I'm going there

Would choose door 3 and the goat.

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