[quote]Affliction wrote:
It is hard for me to elucidate exactly what I mean when trying to disprove your wall example, and we never stipulated certain things that would have a big effect on the outcome of that particular exercise. Basically, if the host comes to the second person behind the wall and says, “I’ve got two doors, one with a car behind it, one without, pick one,” then the odds are 50/50. But you are eliminating the variable change aspect to the exercise, thus rendering it useless. There has to be a first pick, and then an elimination of X amount of doors, and then another pick opportunity for this to work.
Still, I’m going to stick to my guns and ask you to disprove the 1,000 door example. I know it’s impossible.[/quote]
The confusing part about the wall example is that there is still a 2/3 probability that the car is behind one door, but since the guy on the wrong side does not have the prior knowledge to know this, his chances of winning are only 50%.
[quote]pookie wrote:
LIFTICVSMAXIMVS wrote:
The host then eliminates one incorrect choice and tells the other guy separated by the wall, with no knowledge of what choice the other guy made, to pick one out of the two remaining.
The odds are: 1/2 right + 1/2 wrong = 1
That’s where you’re wrong. The odds at that point are 1/3 + 2/3 = 1. The second guy simply has no way of knowing which is which.
If he picks the same door as the first guy picked, he’ll win 33% of the time and if he picks the remaining door, he’ll win 67% of the time. Just because he’s late to the game doesn’t mean the odds for each door have changed.
If you go see a boxing match between two boxers you’ve never heard of before, that doesn’t suddenly make their odds of winning 50/50. Your ignorance of the actual odds doesn’t affect them in any way.
[/quote]
Gosh. What does boxing have to to with picking something?
Do you not understand that only the second pick matters? Both trys are independent of each other. This whole thing is a hoax and you are falling for it.
[quote]LIFTICVSMAXIMVS wrote:
Do you not understand that only the second pick matters? Both trys are independent of each other. This whole thing is a hoax and you are falling for it.[/quote]
No. The second pick matters, sure. Given the specific set of circumstances that yielded the opportunity for the second pick, I will change my second pick, every time.
You are ignoring the context. If the host offers a choice between two doors and clarifies that one contains a car, and one does not, then you are correct. That is not the case with this example.
Would you really cling to your pick with initial odds of 1/million when the alternative is an opportunity to change your pick, and subsequently your odds, to 999,999/million? interestingly enough, I can continue to do this with increasingly large numbers if need be… LOL.
This is my last post defending my stance to you. I will continue to discuss with others the finer points of probability exercises like this because they are indeed enjoyable, but I think we’ve made it overwhelmingly clear that you are incorrect.
Maybe this will help. Pick your strategy for playing the game before it starts. Switch or don’t. Now there is no “change of state” going on. You have no more essential information after the goat door is revealed than you had before the game started. Winning or losing depends only on your chosen strategy and your initial choice of door.
[quote]LIFTICVSMAXIMVS wrote:
Gosh. What does boxing have to to with picking something?[/quote]
It is an attempt to illustrate that you cannot “wish away” the history that lead to the current odds. You can stubbornly ignore that history and reduce your chances of winning, but there’s no amount of tantrum that will change the 1/3+2/3 odds of the doors for those who know the entire history of the situation.
Well, if it’s a hoax, why won’t you play it for money? Tedro made you a 100:1 payoff offer. According to your “theory”, you should make and average of $49.50 every time you play the game.
Thank you. You are just confusing people with stuff that isn’t really so complicated you need a computer program to figure it out.
Garbage in, garbage out.
If you start with incorrect theory your solutions will always be incorrect.[/quote]
Are you saying my code is garbage? Please point to the line(s) that are incorrect for this game. The game is a simple one to code, and involves no probabilities. Where is the incorrect theory?
[quote]johnnytang24 wrote:
Are you saying my code is garbage? Please point to the line(s) that are incorrect for this game. The game is a simple one to code, and involves no probabilities. Where is the incorrect theory?[/quote]
Last try and then I am done. Either you are an idiot or you are just too stubborn to read the posts and consider that you may be wrong.
Let’s change the game just a bit and pretend there are 2 contestants. Contestant A gets to pick a door. Contestant B gets both of the other doors. A has 1/3 chance of winning the car. B has 2/3 chance of winning. After contestant A picks a door, the host still opens one of Contestant B’s doors to show a goat.
This event does not change the probabilities of A or B winning at all. Would you stick with your door if you were A? Or would you switch doors with B, essentially giving yourself 2 chances?
Thank you. You are just confusing people with stuff that isn’t really so complicated you need a computer program to figure it out.
Garbage in, garbage out.
If you start with incorrect theory your solutions will always be incorrect.
Are you saying my code is garbage? Please point to the line(s) that are incorrect for this game. The game is a simple one to code, and involves no probabilities. Where is the incorrect theory?[/quote]
Your code does not throw away the first pick.
Since each pick is independent of each other you have to start over.
The odds that you are correct is always 1/2 because you essentially will always have ONLY two choices. That is the tricky part that you do not realize. It is a mind game and all of you are falling for it.
Since each pick is independent of each other you have to start over.
The odds that you are correct is always 1/2 because you essentially will always have ONLY two choices. That is the tricky part that you do not realize. It is a mind game and all of you are falling for it.
Are there any statisticians in the house?[/quote]
You still haven’t answered my question. Which line(s) are incorrect?
Thank you. You are just confusing people with stuff that isn’t really so complicated you need a computer program to figure it out.
Garbage in, garbage out.
If you start with incorrect theory your solutions will always be incorrect.
Are you saying my code is garbage? Please point to the line(s) that are incorrect for this game. The game is a simple one to code, and involves no probabilities. Where is the incorrect theory?
Your code does not throw away the first pick.
Since each pick is independent of each other you have to start over.
The odds that you are correct is always 1/2 because you essentially will always have ONLY two choices. That is the tricky part that you do not realize. It is a mind game and all of you are falling for it.
Are there any statisticians in the house?[/quote]
Of course there are only two choices, this does not mean that each choice has equal probability.
Come on, let’s play. We’ll just play with three doors. You get $1.50 everytime you win, I only get $1.
[quote]tedro wrote:
Last try and then I am done. Either you are an idiot or you are just too stubborn to read the posts and consider that you may be wrong.
Let’s change the game just a bit and pretend there are 2 contestants. Contestant A gets to pick a door. Contestant B gets both of the other doors. A has 1/3 chance of winning the car. B has 2/3 chance of winning. After contestant A picks a door, the host still opens one of Contestant B’s doors to show a goat.
This event does not change the probabilities of A or B winning at all. Would you stick with your door if you were A? Or would you switch doors with B, essentially giving yourself 2 chances?[/quote]
It doesn’t matter what I do. I do not know which one is correct all I know is that my odds are always the same because the host always throws away one bad choice for me.
The first pick does not matter. The second one is the only pick.
What if the host tells you to pick a door but don’t tell him what it is. He then throws away one bad door.
Thank you. You are just confusing people with stuff that isn’t really so complicated you need a computer program to figure it out.
Garbage in, garbage out.
If you start with incorrect theory your solutions will always be incorrect.
Are you saying my code is garbage? Please point to the line(s) that are incorrect for this game. The game is a simple one to code, and involves no probabilities. Where is the incorrect theory?
Your code does not throw away the first pick.
Since each pick is independent of each other you have to start over.
The odds that you are correct is always 1/2 because you essentially will always have ONLY two choices. That is the tricky part that you do not realize. It is a mind game and all of you are falling for it.
Are there any statisticians in the house?[/quote]
I’m studying engineering, with a heavy focus on statistics. While I’m not a statistician, I do have quite a bit of experience as do some of the other posters who are trying to explain to you where you are wrong time and time again.
You seem to think that the two choices are not linked.
This graphical link should show effectively that if you stick to your guns, you will lose 66.66667% of the time.
The first pick does not matter. The second one is the only pick.
What are your new odds?[/quote]
Actually, this is where your misunderstanding comes in. The first pick is all that matters. Whether you win or lose depends then on your chosen strategy. There is no real second choice.
[quote]Sick Rick wrote:
Sounds like bullshit to me. I’d stick with what my gut’d tell me at the time.[/quote]
Unfortunately, you’d be wrong.
"When first presented with the Monty Hall problem an overwhelming majority of people assume that each door has an equal probability and conclude that switching does not matter (Mueser and Granberg, 1999). Out of 228 subjects in one study, only 13% chose to switch (Granberg and Brown, 1995:713). In her book The Power of Logical Thinking, vos Savant (1996:15) quotes cognitive psychologist Massimo Piattelli-Palmarini as saying “… no other statistical puzzle comes so close to fooling all the people all the time” and “that even Nobel physicists systematically give the wrong answer, and that they insist on it, and they are ready to berate in print those who propose the right answer.”
[quote]Sick Rick wrote:
The 1/3-2/3 chance reflects back to all three doors being shut. One is open, but it doesn’t affect the amount of options you have?[/quote]
You have two options: Switch or don’t switch. That doesn’t make it 50/50.
Tomorrow it may rain or not rain. That does not mean that everyday has a 50% chance of rain.