Posted by SteveB in another thread:

Suppose that Monty Hall (on TV's Let's Make a Deal) asks you to choose between three doors: #1, #2, and #3. Behind a random door is a new Rolls Royce. Behind each of the other two doors is a goat. Let's assume that you would prefer a Rolls Royce to a goat. You choose a door. Now, Monty, who knows which door hides the Rolls Royce, shows you a goat behind one of the two doors that you did not choose. He then gives you the opportunity to change your choice. Assume that Monty always does this, regardless of your guess. Should you change your choice?The moment you pick your door, you have a chance of 33% picking the door with the TV behind it, and the chance that one of the other doors have a TV is 66%. Those chances remain the same after what's behind one of the other doors is revealed.

So your best bet is to change your choice and pick the other door, and have a 66% chance of getting your jewtube.

A way to feeling that is correct is imagining there are a thousand doors and after you pick one, Monte opens the other 998 ones.

Posted by SteveB in another thread:

The moment you pick your door, you have a chance of 33% picking the door with the TV behind it, and the change that one of the other doors have a TV is 66%. Those chances remain the same after what's behind one of the other doors is revealed.

So your best bet is to change your choice and pick the other door, and have a 66% chance of getting your jewtube.

A way to feeling that is correct is imagining there are a thousand doors and after you pick one, Monte opens the other 998 ones.

The choice is between a TV & 2 goats, all three behind their respective doors.

Once I make my initial pick I have a 1/3 chance of being correct. If Monty reveals a goat behind one of the two doors that I DID NOT PICK, then I have a 1/2 chance of being correct. A coin toss, if you will

Since, I had a reason to pick the door that I originally picked, I am not dissuaded from my choice because I now see 1 goat revealed.

It's a 50:50 proposition, but I stick with my choice. My odds have improved from before & I'll let the chips fall where they may.

That's strange, yes, the jewess wrote Rolls Royces but I went on to write about TVs! I immediately associate jews with TV, not with a Rolls Royce. :D

Ok, I understand your reasoning, but now assume there are a thousand doors with one TV and 999 goats and after you pick one, Monte opens the other 998 ones and reveals the goats.

That's strange, yes, the jewess wrote Rolls Royces but I went on to write about TVs! I immediately associate jews with TV, not with a Rolls Royce. :D

Ok, I understand your reasoning, but now assume there are a thousand doors with one TV and 999 goats and after you pick one, Monte opens the other 998 ones and reveals the goats.

Again 2 doors are unrevealed. 1 hides a Rolls or tv :D & the other hides a goat.

2 doors 1 goat 1 tv. 50% chance of the tv being picked & 50% chance of the goat being picked.

Here is why I haven't responded to this, even though I have a degree in mathematics.

1. I hate these games.

2. I know this particular puzzle. I have discussed it with mathematicians countless times, sober and drunk.

3. When first presented with the puzzle, I got the wrong answer.

4. I've been brow beaten by "real good" mathematicians until I will pretend I believe the correct answer.

5. I still think the wrong answer is the right answer.

6. Enough said! Having discussed this thing for too many damned hours, I won't discuss it any more.

Enkidu

I still think the wrong answer is the right answer. I guess I'm just not smart enough.

Here is why I haven't responded to this, even though I have a degree in mathematics.

1. I hate these games.

2. I know this particular puzzle. I have discussed it with mathematicians countless times, sober and drunk.

3. When first presented with the puzzle, I got the wrong answer.

4. I've been brow beaten by "real good" mathematicians until I will pretend I believe the correct answer.

5. I still think the wrong answer is the right answer.

6. Enough said! Having discussed this thing for too many damned hours, I won't discuss it any more.

Enkidu

I still think the wrong answer is the right answer. I guess I'm just not smart enough.I maintain that 50/50 are the odds regardless of whether or not you switch. Turning the problem into a half page equation might make someone feel smart, but it doesn't change the fact that a choice between 2 possible outcomes means a 50/50 chance of either being correct.

I once saw a a half page equation that definitively proved 2 and 3 are equal. Numbers never lie, but when the human hand gets involved...mistakes occur. No matter how intelligently they are covered.

Changing your choice will not improve your odds.

If there were 1000 doors, and Monty Hall opened 998 of them, showing 998 goats, with two doors remaining closed, there's still a 50-50 chance of your having already picked the door with the Rolls Royce.

Frankly, though, I'd bargain for 999 goats and let Hall keep the Rolls. The fancy car guzzles gas, which you must pay for. The goats eat grass and produce meat and milk, and you can make cheese and butter, and as long as you have enough grass to feed the herd you can eventually get more profit than the car ever will. Even if you managed to sell it right away to Bill Gates.

Jerry Abbott

Changing your choice will not improve your odds.

If there were 1000 doors, and Monty Hall opened 998 of them, showing 998 goats, with two doors remaining closed, there's still a 50-50 chance of your having already picked the door with the Rolls Royce.


Jerry Abbott

I maintain that 50/50 are the odds regardless of whether or not you switch. Turning the problem into a half page equation might make someone feel smart, but it doesn't change the fact that a choice between 2 possible outcomes means a 50/50 chance of either being correct.

Sorry Jenab and Odin but I believe you are wrong, here's why.

1)You have a 1 in 3 chance of guessing the Rolls Royce door the first time. Not very good odds.

2) You have a 2 in 3 chance of not guessing the Rolls Royce door the first time. Much better odds.

Lets say for the sake of argument that you are going to switch doors no matter what.

Scenario 1: You picked the right door the first time.(1/3) Then you switch, you lose. Chances of you winning were 1 in 3.

(Lets keep in mind the contestant doesn't know if he has picked the Rolls Royce door or not.)

Scenario 2: You picked the wrong door the first time(2/3) then you switch to the only remaining door. You win, chances of you winning were 2 in 3.

So, it is not a 50/50 chance after Monty shows you the goat door it is a 66/34 chance in your favor because every time you guessed wrong the first time(which the odds say you will), you switch to the correct door, and win.

http://www.jimloy.com/puzz/monty.htm

I maintain that 50/50 are the odds regardless of whether or not you switch. Turning the problem into a half page equation might make someone feel smart, but it doesn't change the fact that a choice between 2 possible outcomes means a 50/50 chance of either being correct.

I once saw a a half page equation that definitively proved 2 and 3 are equal. Numbers never lie, but when the human hand gets involved...mistakes occur. No matter how intelligently they are covered.

Thank God.

Yes 2 outcomes ( 1 goat, 1 Rolls) REMAIN.

Divide 1 choice by 2 outcomes =
1/2 = .50
.50= 50%
50% chance of picking a goat & 50% chance of picking a Rolls.

finit
.

http://planettom.home.mindspring.com/vossavant.htm

This link allows you to try for yourself. Supposedly random placement of the goats.

At our local pawnshop or second hand store, I can buy a nice television for $50.00. being that this area is mountainous and difficult to keep clear a goat is the perfect hillside lawn mower. A good healthy goat can bring as much as $250.00. If the choice is between a goat that will save me 20 hours working with a weed eater a week or a television that I may watch 2 hours a week, I would stick with my original choice. Besides a week before Christmas Wal-mart sells 19 inch Emerson televisions for $99.00 so a goat is worth 2 televisions here.

After further consideration, I admit my mistake. In the 3 door scenario, the odds of my picking the correct door are 1 in 3. The odds of the correct door being one of the remaining two are 2 in 3. When one of the doors I did not choose is opened to reveal a goat, that does not change the original odds of the game. There is still a 2 in 3 chance that the prize is behind one of the two doors I did not pick. Since one of those doors has been revealed as incorrect, the odds are now 1 in 3 that my original choice is correct, but 2 in 3 that the other door is correct.

My mistake was in creating a new scenario, with new odds, when one door was revealed. The odds will only be 50/50 if one door is revealed, the two remaining doors are shuffled, and I am asked to choose again between those two.

So, if I start by choosing door one, it looks like this...

Start of Game

Door 1............................. Doors 2 & 3
1/3 odds............................ 2/3 odds to
to win ...............................win

When a door (containing a goat) is opened, it looks like this:

After One Goat is Revealed

Door 1..............................Door 2 & a Goat
Still 1/3 odds........................Still 2/3 odds to
to win.................................win

Here is why I haven't responded to this, even though I have a degree in mathematics.

1. I hate these games.

2. I know this particular puzzle. I have discussed it with mathematicians countless times, sober and drunk.

3. When first presented with the puzzle, I got the wrong answer.

4. I've been brow beaten by "real good" mathematicians until I will pretend I believe the correct answer.

5. I still think the wrong answer is the right answer.

6. Enough said! Having discussed this thing for too many damned hours, I won't discuss it any more.

Enkidu

I still think the wrong answer is the right answer. I guess I'm just not smart enough.

For some reason, on this particular puzzle, the smart ones get it wrong. I'm not sure why. Maybe they are trying too hard or over analyzing the numbers or maybe they think it is a "trick" puzzle, I donno.

Instead of looking at the problem as a mathematician trying to find the correct solution, try looking at the problem as a professional gambler playing the odds.

My math skills are next to zero and yet I easily found the correct answer by reducing it into simplest terms, in my pretty 'lil head, in about 60 seconds. Here's how.

You have 3 doors, 2 doors have goats behind them and 1 has a Rolls Royce.

Say you choose door number 1. The odds that you have picked the door with the RR is not good, 1 in 3. No successful pro gambler in his right mind would bet on these odds. Not when there are better ones coming.

Monty opens up door number 2 and lo and behold a goat. Monty then asks you if you want to switch your door number 1 for the remaining door number 3.

Hmmm, what to do. Your door number 1 is a suckers bet. According to the laws of probability you didn't pick the correct door the first time, 1 in 3 chance, remember? So, door number 1 is most likely the wrong door.

Door number 2 is definitely the wrong door and has been eliminated, baa.

Do you switch your door number 1 for door number 3? Fuck yeah you do! Simple logic and common sense...plus some greed! :p

Steve_B,

Actually, I eventually did get it right. But it took weeks of my insisting that there was no advantage to switching. I even got somewhat angry at my "stupid" wizbo friends who insisted that it was better to switch.

I don't know what the mental crossover was, but one morning I was sitting in my Barcalounger, drinking my morning coffee, and I started thinking "What if there were 100 damn doors? Of course it is advantageous to switch. In fact, with 100 doors you have a 99 times better chance if you switch.

The only complication is if you are psychic. Psychics get the door correct with their first choice, and are screwed if they switch, regardless of the odds.

Enkidu

I don't know what the mental crossover was, but one morning I was sitting in my Barcalounger, drinking my morning coffee, and I started thinking "What if there were 100 damn doors? Of course it is advantageous to switch. In fact, with 100 doors you have a 99 times better chance if you switch.I thought about a deck of cards. What if someone asked me to pick the three of diamonds from a deck of cards (without seeing the card faces). After I pick one card, what if they then looked at the card faces, threw out 50 of the remaining cards and said ONE of the two remaining cards (either the one I had picked, or the one remaining from the deck) was the three of diamonds. Which is more likely to be the three of diamonds? The one I originally picked (a 1 in 52 chance) or the one that was kept from the deck? It makes perfect sense then, and is easily extrapolated downward to the three door scenario.

Goats are more useful than TV's. Maybe not a Rolls, since you can sell one of those for some serious clams. To get a herd of goats.

But if you've got 1 tv, I'd rather have the goat. Buy some land, get a ninny, and breed goats. Their cheese alone is big bucks if managed correctly.

TV's are fucking useless, except for the occasional playstation game and a rented movie of your choice. Otherwise all they're good for is importing stupid advertisements into your brain.

Goat Milk is $3.75 a quart here and the only place it can be purchased is Wal-mart.


But if you've got 1 tv, I'd rather have the goat. Buy some land, get a ninny, and breed goats. Their cheese alone is big bucks if managed correctly.

Dammit people, you caused me to wreck my brain trying to solve the same problem, assuming you want to win a goat! :D

The answer there is that in that case your best tactic is to stick to your choice, and that gives you a 2/3 chance of winning a goat.

Steve_B,

Actually, I eventually did get it right. But it took weeks of my insisting that there was no advantage to switching. I even got somewhat angry at my "stupid" wizbo friends who insisted that it was better to switch.

I don't know what the mental crossover was, but one morning I was sitting in my Barcalounger, drinking my morning coffee, and I started thinking "What if there were 100 damn doors? Of course it is advantageous to switch. In fact, with 100 doors you have a 99 times better chance if you switch.

The only complication is if you are psychic. Psychics get the door correct with their first choice, and are screwed if they switch, regardless of the odds.

Enkidu

Don't feel bad, E. I only brought up the 3 doors teaser because it was one of the few I ever got right. For some reason it just clicked in my mind. This one, on the other hand, stumped me to no end. And it's supposed to be an easy one.

Weigh this fish.

"What is the weight of a fish if it weighs 10 pounds, plus half its weight?"

Don't feel bad, E. I only brought up the 3 doors teaser because it was one of the few I ever got right. For some reason it just clicked in my mind. This one, on the other hand, stumped me to no end. And it's supposed to be an easy one.

"Weigh this fish.

"What is the weight of a fish if it weighs 10 pounds, plus half its weight?""

I've redeemed myself. I did this in my head in about 20 seconds. You weigh 20 lbs. That is 10 lbs + 1/2 of (total weight, 1/2 of 20 lbs -> 10 lbs ) all for your weight of 20 lbs.

Ha!! and this after an emergency root canal this morning about 11 AM. I am on my third (prescribed) Vicodin and barely able to focus my eyes. Probably my last too. If the pain doesn't come back in the next two hours, I'll gut it out, without the drugs. [You, the fish, something weighs 20 lbs.]

Enkidu

I tried it by taking 3 cards numbered 1,2,3 and flipping them over with something underneath. In EVERY instance except the two she picked right the first time, the winner was under the opposite card she picked. It was accurate 100% of the time. Unreal, and she argued me that there could be no advantage. It took 10 times before she would switch and when she switched it was correct every time.

Don't feel bad, E. I only brought up the 3 doors teaser because it was one of the few I ever got right.

LOL well the expectancy is to be correct 2 out of 3 times if you switch.

I have a better game.

Three doors - behind one is a jew, behind another is a black and behind the other is a mexican.

Whichever door you choose, that person gets shipped back to his respective country of origin.

There's a game where you win 100% of the time

AM :D