statistics problem

[bobbywithani 0]

It seems like it would be 50-50 at first, but once it is made clear that the host deliberatly picks the door with the goat and you can see that swithching is the only option.

[Pupsta 0]

Thats me , Think about it this way though. Say your on the show "Who wants to be a millionaire". Your on a questions where your options are A,B,C. You use a life line to eliminate 1 wrong answer. Now we all can agree this is a 50/50 choice assuming that we know absolutly nothing about the question and its a pure guess. Ok now substitute A,B,C and replace it with the 3 doors. What im saying is by guessing door A B or C it doesnt matter, you are essentially taking a life line and reducing the problem down to 2 doors. Why is this so? This is true because as said earlier even if your pick is indeed a goat the host will still eliminate the other "1"wrong answer leaving me with 2 possible choices. Now I dont know that my guess was right or wrong because because the host would reveal a wrong answer if i guessed wrong or right. So Im sure we can all agree on the first part being 50/50, so how can you not see the second one also being 50/50

respond to my question above please.

[Pupsta 0]

Thats me , Think about it this way though. Say your on the show "Who wants to be a millionaire". Your on a questions where your options are A,B,C. You use a life line to eliminate 1 wrong answer. Now we all can agree this is a 50/50 choice assuming that we know absolutly nothing about the question and its a pure guess. Ok now substitute A,B,C and replace it with the 3 doors. What im saying is by guessing door A B or C it doesnt matter, you are essentially taking a life line and reducing the problem down to 2 doors. Why is this so? This is true because as said earlier even if your pick is indeed a goat the host will still eliminate the other "1"wrong answer leaving me with 2 possible choices. Now I dont know that my guess was right or wrong because the host wouldnt reveal a wrong answer if i guessed wrong or right. So Im sure we can all agree on the first part being 50/50, so how can you not see the second one also being 50/50

the first part is 50/50 because you are eliminating and THEN choosing.if you say "i choose A, but eliminate either B or C for me", and they eliminate B, you have a 33 percent chance of beig right, and it's 66% that c is right.

[Sh0rtstack 0]

Thats me , Think about it this way though. Say your on the show "Who wants to be a millionaire". Your on a questions where your options are A,B,C. You use a life line to eliminate 1 wrong answer. Now we all can agree this is a 50/50 choice assuming that we know absolutly nothing about the question and its a pure guess. Ok now substitute A,B,C and replace it with the 3 doors. What im saying is by guessing door A B or C it doesnt matter, you are essentially taking a life line and reducing the problem down to 2 doors. Why is this so? This is true because as said earlier even if your pick is indeed a goat the host will still eliminate the other "1"wrong answer leaving me with 2 possible choices. Now I dont know that my guess was right or wrong because because the host would reveal a wrong answer if i guessed wrong or right. So Im sure we can all agree on the first part being 50/50, so how can you not see the second one also being 50/50

respond to my question above please.

I see what your saying but the original posted said that the host will keep eliminating doors until there is only 2 left. He said nothing about 2 guess and thats it. He said the game will end when there is 2 doors left and you pick either the right or wrong door

[Pupsta 0]

Thats me , Think about it this way though. Say your on the show "Who wants to be a millionaire". Your on a questions where your options are A,B,C. You use a life line to eliminate 1 wrong answer. Now we all can agree this is a 50/50 choice assuming that we know absolutly nothing about the question and its a pure guess. Ok now substitute A,B,C and replace it with the 3 doors. What im saying is by guessing door A B or C it doesnt matter, you are essentially taking a life line and reducing the problem down to 2 doors. Why is this so? This is true because as said earlier even if your pick is indeed a goat the host will still eliminate the other "1"wrong answer leaving me with 2 possible choices. Now I dont know that my guess was right or wrong because because the host would reveal a wrong answer if i guessed wrong or right. So Im sure we can all agree on the first part being 50/50, so how can you not see the second one also being 50/50

respond to my question above please.

I see what your saying but the original posted said that the host will keep eliminating doors until there is only 2 left. He said nothing about 2 guess and thats it. He said the game will end when there is 2 doors left and you pick either the right or wrong door

do you not realize that it's the SAME THING?whether he opens 98 incorrect ones or whether he says "there are at least 98 incorrect ones" or whether he doesn't say anything at all (it is implied that there are at least 98 incorrect ones) DOES NOT CHANGE THE MATHEMATICAL ODDS.

[Sh0rtstack 0]

Thats me , Think about it this way though. Say your on the show "Who wants to be a millionaire". Your on a questions where your options are A,B,C. You use a life line to eliminate 1 wrong answer. Now we all can agree this is a 50/50 choice assuming that we know absolutly nothing about the question and its a pure guess. Ok now substitute A,B,C and replace it with the 3 doors. What im saying is by guessing door A B or C it doesnt matter, you are essentially taking a life line and reducing the problem down to 2 doors. Why is this so? This is true because as said earlier even if your pick is indeed a goat the host will still eliminate the other "1"wrong answer leaving me with 2 possible choices. Now I dont know that my guess was right or wrong because the host wouldnt reveal a wrong answer if i guessed wrong or right. So Im sure we can all agree on the first part being 50/50, so how can you not see the second one also being 50/50

the first part is 50/50 because you are eliminating and THEN choosing.if you say "i choose A, but eliminate either B or C for me", and they eliminate B, you have a 33 percent chance of beig right, and it's 66% that c is right.

Yes but what you dont realize is the first pick is irrelevant. Either by picking something or saying eliminate something either way its getting reduced to the right or wrong answer and u will still have a choice between 2 options.

[Guest Anonymous]

The three doors dilemmaSo you think you understand gambling odds, eh? Well, try this...Imagine you're on a game show, and you're given the choice of three doors. Behind one door is a car; behind each of the other two, a goat. You pick a door, say No. 1, and the host opens one of the remaining two doors, say No. 3, to reveal a goat. He says to you, "Do you want to stick with the door you've chosen, or do you want to change your mind and go for door No. 2 instead?"Question: Is it to your advantage to switch your choice of doors?

You should always switch your choice.Do you see why?Calculate the odds of hitting a flush in hold'em, when you have 4 to a flush after the flop.The math is the same.

[Sh0rtstack 0]

Well im really off this time, but its been fun, i could careless right or wrong i just enjoy the debate. See you all around..

[Pupsta 0]

Thats me , Think about it this way though. Say your on the show "Who wants to be a millionaire". Your on a questions where your options are A,B,C. You use a life line to eliminate 1 wrong answer. Now we all can agree this is a 50/50 choice assuming that we know absolutly nothing about the question and its a pure guess. Ok now substitute A,B,C and replace it with the 3 doors. What im saying is by guessing door A B or C it doesnt matter, you are essentially taking a life line and reducing the problem down to 2 doors. Why is this so? This is true because as said earlier even if your pick is indeed a goat the host will still eliminate the other "1"wrong answer leaving me with 2 possible choices. Now I dont know that my guess was right or wrong because the host wouldnt reveal a wrong answer if i guessed wrong or right. So Im sure we can all agree on the first part being 50/50, so how can you not see the second one also being 50/50

the first part is 50/50 because you are eliminating and THEN choosing.if you say "i choose A, but eliminate either B or C for me", and they eliminate B, you have a 33 percent chance of beig right, and it's 66% that c is right.

Yes but what you dont realize is the first pick is irrelevant. Either by picking something or saying eliminate something either way its getting reduced to the right or wrong answer and u will still have a choice between 2 options.

no.it makes a difference.by picking one, they will never eliminate the one you picked as an option. if they only eliminate one of the incorrect other ones (since there is always at least one incorrect on the other side), it never changes the odds of your choice being correct.if they eliminate before you choose, it's 50/50.

[Guest Anonymous]

Yes but what you dont realize is the first pick is irrelevant. Either by picking something or saying eliminate something either way its getting reduced to the right or wrong answer and u will still have a choice between 2 options.

Your first choice is not irrelevant. With your first choice you have a 1 in 3 chance of being right.So there is always a 2/3 chance that the car is behind one of the other two doors.The host will always be able to show you a goat, regardless of what door you picked.So after he shows you a goat, there is a 2/3 chance that the car is behind the other door.If you always switch, you will be wrong 1/3 of the time. Not half the time.Always switching is +EV.To emphasize this, imagine there are 5 doors, and after you pick one, the host shows you 3 goats. Do you switch now?

[mx957 0]

Thats me , Think about it this way though. Say your on the show "Who wants to be a millionaire". Your on a questions where your options are A,B,C. You use a life line to eliminate 1 wrong answer. Now we all can agree this is a 50/50 choice assuming that we know absolutly nothing about the question and its a pure guess. Ok now substitute A,B,C and replace it with the 3 doors. What im saying is by guessing door A B or C it doesnt matter, you are essentially taking a life line and reducing the problem down to 2 doors. Why is this so? This is true because as said earlier even if your pick is indeed a goat the host will still eliminate the other "1"wrong answer leaving me with 2 possible choices. Now I dont know that my guess was right or wrong because the host wouldnt reveal a wrong answer if i guessed wrong or right. So Im sure we can all agree on the first part being 50/50, so how can you not see the second one also being 50/50

the first part is 50/50 because you are eliminating and THEN choosing.if you say "i choose A, but eliminate either B or C for me", and they eliminate B, you have a 33 percent chance of beig right, and it's 66% that c is right.

Yes but what you dont realize is the first pick is irrelevant. Either by picking something or saying eliminate something either way its getting reduced to the right or wrong answer and u will still have a choice between 2 options.

Now you are getting close, you have the choice between 2 options...option 1 pick set A which contains 2 items or pick set B which contains 1 item.

[smiley 0]

Monty Hall: The SolutionYOU are the contestant--------------------------------------------------------------------------------For the moment, we will make the simplifying assumption that The Contestant always begins by choosing Door #1. (As we will see, this assumption does not affect the answer.) First we will examine all the possible games in which The Contestant does not trade doors when given a choice. As we will see this will ensure that the contestant will win 1 out of 3 times. Now, there are three possible games: Possible Game 1: The prize was originally behind Door #1: The Host then opens one of the other doors (which doesn't matter): Since The Contestant does not switch doors when given the choice: ==>YOU WIN!!<==Possible Game 2: The prize was originally behind Door #2: The Host then opens Door #3. Since The Contestant does not switch doors when given the choice: ==>YOU LOSE!!<==Possible Game 3: The prize was originally behind Door #3: The Host then opens Door #2. Since The Contestant does not switch doors when given the choice: ==>YOU LOSE!!<==Summarizing we have the three cases: Game 1: ==>YOU WIN!! Game 2: ==>YOU LOSE!! Game 3: ==>YOU LOSE!! As we can see: If The Contestant does not change doors he will win one of the three possible games. That is, in this case --if The Contestant does not change doors-- the chance of winning is 1/3. Now, we will examine all the possible games in which The Contestant does trade doors when given a choice. As we will see this time, the contestant will win 2 out of 3 times. As before, in this case there are three possible games: Possible Game 1: The prize was originally behind Door #1: The Host then opens one of the other doors (which doesn't matter): The Contestant now switches to the remaining unopened door: The resulting situation is: ==>YOU LOSE!!<==Possible Game 2: The prize was originally behind Door #2: The Host then opens Door #3. The Contestant now switches to the remaining unopened door: The resulting situation is: ==>YOU WIN!!<==Possible Game 3: The prize was originally behind Door #3: The Host then opens Door #2. The Contestant now switches to the remaining unopened door: The resulting situation is: ==>YOU WIN!!<==Again, summarizing we have three cases: Game 1: ==>YOU LOSE!! Game 2: ==>YOU WIN!! Game 3: ==>YOU WIN!! As we can see: If The Contestant does change doors he will win two of the three possible games. That is, in this case --if the Contestant does change doors-- the chance of winning is 2/3. --------------------------------------------------------------------------------This, then, is the final answer. A Contestant who does not switch doors (i.e. who keeps the originally chosen door) has only a 1/3 chance of winning. A Contestant who switches doors, however, has a 2/3 chance of winning. In short, although it may contradict "common sense", The Contestant will double their chance of winning by switching doors. THANK YOU GOOGLEhttp://www.sover.net/~nichael/puzzles/mont...y/solution.html

[LongLiveYorke 38]

The above was the best reply yet. If anyone still doesn't think switching is a good idea, please read it again. Do this until you understand.

[sholden 0]

Thats me , Think about it this way though. Say your on the show "Who wants to be a millionaire". Your on a questions where your options are A,B,C. You use a life line to eliminate 1 wrong answer. Now we all can agree this is a 50/50 choice assuming that we know absolutly nothing about the question and its a pure guess. Ok now substitute A,B,C and replace it with the 3 doors. What im saying is by guessing door A B or C it doesnt matter, you are essentially taking a life line and reducing the problem down to 2 doors. Why is this so? This is true because as said earlier even if your pick is indeed a goat the host will still eliminate the other "1"wrong answer leaving me with 2 possible choices. Now I dont know that my guess was right or wrong because the host wouldnt reveal a wrong answer if i guessed wrong or right. So Im sure we can all agree on the first part being 50/50, so how can you not see the second one also being 50/50

It's been explained over and over again. That you are clearly functionaly retarded and can't see that being able to pick 2 doors gives you more chances than 1 is your problem.Clearly you refuse to try and understand the math, so lets gamble then.I'm serious lets play this game a few thousand times. You stay. I switch. I pay your $10 every time you pick the winning door. You pay me $7.50 every time I switch to the winning door.If it's 50/50 how can you turn down this clearly +EV offer.I'll bring $5k to game. And I'll play until you either win it all or I double up.We can even do it over the damn internet. We'll both go to a play money table at a poker site that both of us are comfortable the other isn't able to influence the cards at. I'm sure some other FCPers will be willing to fill up the remaining the seats so that no one else comes and slows the game down. To make things fast we will both pick the same door (two games at once essentially) - I'm happy with always picking door 1, but if you want you can call out the door number. Then the next hand we see the flop and it decides the winning door, is door 1, is door 2, is door 3, if it's a do the same with the second card, then the third. If the flop is all :spade:s then we wait for the next flop (everyone will be folding on the flop to speed things up - play money remember...). Since we both choose the same door, if that door is the winner then we just say the host opens the next door, if the door we choose isn't the winner then the host has to open the other non-winning door. I switch, you stay. An observer can keep score, and we can transfer funds in multiples of $100 (whenever one player is $100 up the other transfers $100).Don't let the obviousness of me winning on two suits and you winning on one stop you from sticking to your 50:50 belief...I'm serious about this. I'm happy to play for smaller stakes too.

[Swift_Psycho 1]

If anyone still doesn't think switching is a good idea, please read it again. Do this until you understand.

[pokerloser 0]

I didn't read the whole thread, because each post was redundent.Didn't anyone else up here watch this on the TV show Numbers? The question asked the exact same way. Oh I guess the original poster watched the show, didn't you.It's all explained, and far more clearly than any post I read up here.

[kdogg 0]

Imagine you're on a game show, and you're given the choice of 1,000,000 doors. Behind one door is a car; behind each of the others, a goat.You pick a door and the host opens all but one of the remaining 999,999 to reveal goats. He says to you, "Do you want to stick with the door you've chosen, or do you want to change your mind and go for the other remaining door instead?

[mobius481 0]

Thats me , Think about it this way though. Say your on the show "Who wants to be a millionaire". Your on a questions where your options are A,B,C. You use a life line to eliminate 1 wrong answer. Now we all can agree this is a 50/50 choice assuming that we know absolutly nothing about the question and its a pure guess. Ok now substitute A,B,C and replace it with the 3 doors. What im saying is by guessing door A B or C it doesnt matter, you are essentially taking a life line and reducing the problem down to 2 doors. Why is this so? This is true because as said earlier even if your pick is indeed a goat the host will still eliminate the other "1"wrong answer leaving me with 2 possible choices. Now I dont know that my guess was right or wrong because the host wouldnt reveal a wrong answer if i guessed wrong or right. So Im sure we can all agree on the first part being 50/50, so how can you not see the second one also being 50/50

The difference is that in this situation with you taking a completely random guess at three answers there is also the possibility that your life line will eliminate the answer you chose. So you're correct, in this scenario, if he knows for 100% certainty that one answer is wrong, then this one will be 50/50. But it is a different problem than the three doors.

[Vman96 0]

I tried to explain this problem to my g/f and we got into an argument about it....trying to explain this problem to people who suck at math is pointless.Switch people! lol

[Fooditty 0]

Door ~~~~ case A B C ~~~~ 1 bad bad good 2 bad good bad 3 good bad badImagine you choose Door A. You have a 1/3 chance of being right. Now in case 1 and 2 respectively B and C are removed. In both of these switching will give you the good door.Only in case 3 where you got it right to begin with, does staying give you the correct door.This is a really good explanation. And if you dont understand, dont listen to people who say you are dumb. Mathematicians disagreed with this answer when it was first presented.

[howdyo 0]

What yall make a simple question complicated?I say kill the fucking goats, grill them and eat them, kick the host's ass, screw his assistants, then drive the car away.Problem solved.

[smiley 0]

The above was the best reply yet. If anyone still doesn't think switching is a good idea, please read it again. Do this until you understand.

or if you are a "Visual Learner" the LINK has pretty pictures too:http://www.sover.net/~nichael/puzzles/mont...y/solution.html

[mcpickl 0]

Do the same experiment with a 1000 doors now instead of 3. Does that clear it up are will you say your 1 in 1000 chance changes to 50/50 when it gets down to your door and the last one the host didn't open?

yes

[Whatever 1]

So if you replicate that 100 times you would expect your 1 in 100 chance to be successful 50 times? Wow. :shock:

[smiley 0]

Thats me ,  Think about it this way though. Say your on the show "Who wants to be a millionaire".  Your on a questions where your options are A,B,C. You use a life line to eliminate 1 wrong answer. Now we all can agree this is a 50/50 choice assuming that we know absolutly nothing about the question and its a pure guess.      Ok now substitute A,B,C and replace it with the 3 doors. What im saying is by guessing door A B or C it doesnt matter, you are essentially taking a life line and reducing the problem down to 2 doors. Why is this so? This is true because as said earlier even if your pick is indeed a goat the host will still eliminate the other "1"wrong answer leaving me with 2 possible choices. Now I dont know that my guess was right or wrong because the host wouldnt reveal a wrong answer if i guessed wrong or right. So Im sure we can all agree on the first part being 50/50, so how can you not see the second one also being 50/50

The difference is that in this situation with you taking a completely random guess at three answers there is also the possibility that your life line will eliminate the answer you chose. So you're correct, in this scenario, if he knows for 100% certainty that one answer is wrong, then this one will be 50/50. But it is a different problem than the three doors.

this "should" helpImagine that there were a million doors. Monty knows which door conceals the prize, so he then opens 999 998 losing doors. You are now confronted with two doors, the one you chose initially and the one Monty has left. Do they each have a 50% chance of concealing the prize?so in the beginning you had a 1 in 1,000,000 chance of picking the door that concealed the car... he narrows it down to the one you chose and the one he chose (by process of elimination)... are you sure you want to stay w/the one you chose out of a Million. you still feel like its a 50/50 shot.?!