You are a contestant on a game show. There are three curtains. Behind one of the curtains is a new car. You are asked to choose one of the curtains. Lets say that you choose curtain #1. The host of the show - who knows where the car is so as not to end the game prematurely - opens curtain #3 and of course there is no car behind it. The host now gives you a choice. You can stay with curtain #1 or you can change your choice to curtain #2. The question now is: would it be to your advantage to stay with curtain #1, or would it be to your advantage to change to curtain #2 or would there be no advantage either way?
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Simple answer. The odds are with keeping your original selection.
The home of the soul is the Open Road.
- DH Lawrence
- DH Lawrence
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LarsMac,
re: "Simple answer. The odds are with keeping your original selection."
How did you come up with the answer that it would be to your advantage to stay with your original pick?
re: "Simple answer. The odds are with keeping your original selection."
How did you come up with the answer that it would be to your advantage to stay with your original pick?
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Deleted - double post.
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Mark Aspam
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rstrats;1454071 wrote: You are a contestant on a game show. There are three curtains. Behind one of the curtains is a new car. You are asked to choose one of the curtains. Lets say that you choose curtain #1. The host of the show - who knows where the car is so as not to end the game prematurely - opens curtain #3 and of course there is no car behind it. The host now gives you a choice. You can stay with curtain #1 or you can change your choice to curtain #2. The question now is: would it be to your advantage to stay with curtain #1, or would it be to your advantage to change to curtain #2 or would there be no advantage either way?
This is the so-called "Monty Hall problem", popularized by Marilyn VosSavant in PARADE magazine quite a few years ago.
The answer is that you should switch, because if you do, the chances are 1 in 2 (50%) that you will win the car. If you do not switch, your chances remain, of course, one in three (33 1/3%), and this can easily be demonstrated with simple arithmetic.
To make it easier to visualize, let's imagine that there were FIFTY curtains. You choose curtain number one. The host than opens EVERY other curtain EXCEPT number 45. THEN would you switch?
This is the so-called "Monty Hall problem", popularized by Marilyn VosSavant in PARADE magazine quite a few years ago.
The answer is that you should switch, because if you do, the chances are 1 in 2 (50%) that you will win the car. If you do not switch, your chances remain, of course, one in three (33 1/3%), and this can easily be demonstrated with simple arithmetic.
To make it easier to visualize, let's imagine that there were FIFTY curtains. You choose curtain number one. The host than opens EVERY other curtain EXCEPT number 45. THEN would you switch?
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Mark Aspam,
re: "The answer is that you should switch, because if you do, the chances are 1 in 2 (50%) that you will win the car."
Actually, that is incorrect. Try again.
re: "The answer is that you should switch, because if you do, the chances are 1 in 2 (50%) that you will win the car."
Actually, that is incorrect. Try again.
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Mark Aspam
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- Joined: Tue Apr 15, 2008 12:00 am
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rstrats;1454098 wrote: Mark Aspam, Actually, that is incorrect.Actually actually, you are full of compost, spread it on your lawn rather than here.
Here's what you do, rst: Get three playing cards, an ace, a deuce, and a trey. With me so far?
Now get a car key. Have a friend place the car key - or even a small coin -under one of the playing cards while you turn your back (use a soft surface so that the thickness of the object doesn't give away its position).
Now you are the contestant! Pick a card, say number two. Have your friend uncover a card that he knows has no object under it, say number three.
OK so far? NOW SWITCH! In this case, to number one, your only choice.
Do it about thirty times, switching every time, and you will find that you have won the car about 15 times, more or less.
NOW do the same series of thirty tries again, but this time DON'T SWITCH! Gee, come to think of it, don't waste your time, you will obviously win the car about ten times, more or less.
QED.
Here's what you do, rst: Get three playing cards, an ace, a deuce, and a trey. With me so far?
Now get a car key. Have a friend place the car key - or even a small coin -under one of the playing cards while you turn your back (use a soft surface so that the thickness of the object doesn't give away its position).
Now you are the contestant! Pick a card, say number two. Have your friend uncover a card that he knows has no object under it, say number three.
OK so far? NOW SWITCH! In this case, to number one, your only choice.
Do it about thirty times, switching every time, and you will find that you have won the car about 15 times, more or less.
NOW do the same series of thirty tries again, but this time DON'T SWITCH! Gee, come to think of it, don't waste your time, you will obviously win the car about ten times, more or less.
QED.
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Mark Aspam,
re: "Do it about thirty times and you will find that you have won the car about 20 times, more or less."
That is correct, but it's not 50% as you said in your post #5 - it's 66 1/3%.
re: "Do it about thirty times and you will find that you have won the car about 20 times, more or less."
That is correct, but it's not 50% as you said in your post #5 - it's 66 1/3%.
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Mark Aspam
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- Joined: Tue Apr 15, 2008 12:00 am
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rstrats;1454108 wrote: Mark Aspam,
re: "Do it about thirty times and you will find that you have won the car about 20 times, more or less."
That is correct, but it's not 50% as you said in your post #5 - it's 66 1/3%.No, actually that was wrong, which is why I edited it about two minutes after posting.
The odds are 15 out of 30 if you switch, 50%.
Of course, the contestant is not going to get thirty tries, but think of 60 contestants on different days, half switching and half not. Which group will win the most cars?
ADDED LATER: The more I think about it, you may be correct about the 66 percent, but if so, I think it would be 66 2/3, not 66 1/3.
re: "Do it about thirty times and you will find that you have won the car about 20 times, more or less."
That is correct, but it's not 50% as you said in your post #5 - it's 66 1/3%.No, actually that was wrong, which is why I edited it about two minutes after posting.
The odds are 15 out of 30 if you switch, 50%.
Of course, the contestant is not going to get thirty tries, but think of 60 contestants on different days, half switching and half not. Which group will win the most cars?
ADDED LATER: The more I think about it, you may be correct about the 66 percent, but if so, I think it would be 66 2/3, not 66 1/3.
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rstrats;1454082 wrote: LarsMac,
re: "Simple answer. The odds are with keeping your original selection."
How did you come up with the answer that it would be to your advantage to stay with your original pick?
The way I see it, Either I made the right choice the first time, or I did not. Monty showing me a goat won't change that.
Statistically speaking, of course, most arguments show that you increase your odds by changing your mind. Probability Statistics are not real life.
YOU only get one shot.
re: "Simple answer. The odds are with keeping your original selection."
How did you come up with the answer that it would be to your advantage to stay with your original pick?
The way I see it, Either I made the right choice the first time, or I did not. Monty showing me a goat won't change that.
Statistically speaking, of course, most arguments show that you increase your odds by changing your mind. Probability Statistics are not real life.
YOU only get one shot.
The home of the soul is the Open Road.
- DH Lawrence
- DH Lawrence
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Mark Aspam
- Posts: 668
- Joined: Tue Apr 15, 2008 12:00 am
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LarsMac;1454114 wrote: The way I see it, Either I made the right choice the first time, or I did not. Monty showing me a goat won't change that.
Statistically speaking, of course, most arguments show that you increase your odds by changing your mind. Probability Statistics are not real life.
YOU only get one shot.But that is just the point: In this case, you actually get TWO shots.
I am still trying to wrap my mind around rst's figure of a 66 2/3% chance, which I know is correct, it still seems like it should be 50% for switching, vs. 33 1/3% for not.
HOWEVER....here is a point that I have NEVER seen come up in this matter:
The problem as stated seems to imply or assume that the host would give the contestant the opportunity to change his/her selection in any case. THAT MIGHT NOT BE TRUE.
The game show producers, and the car company, which no doubt has a stake in the matter, might very well offer the contestant the opportunity to switch ONLY if s/he has chosen the door with the car. That would get them 'off the hook' in having to part with an expensive car if the contestant chose to switch.
If, however, the contestant initially chose the goat, they might simply end the matter and send the contestant away with his/her new goat - they would still get a plug in for the car, which would return to the manufacturer or possibly be saved for a future contest.
If the contestant suspected that such was the case, then s/he might very well decide not to switch, and end up with the car.
Pretty deep waters here.
ADDED LATER: The matter is discussed in more depth in Mark Haddon's novel The Curious Incident of the Dog in the Night-Time, chapter 101.
Statistically speaking, of course, most arguments show that you increase your odds by changing your mind. Probability Statistics are not real life.
YOU only get one shot.But that is just the point: In this case, you actually get TWO shots.
I am still trying to wrap my mind around rst's figure of a 66 2/3% chance, which I know is correct, it still seems like it should be 50% for switching, vs. 33 1/3% for not.
HOWEVER....here is a point that I have NEVER seen come up in this matter:
The problem as stated seems to imply or assume that the host would give the contestant the opportunity to change his/her selection in any case. THAT MIGHT NOT BE TRUE.
The game show producers, and the car company, which no doubt has a stake in the matter, might very well offer the contestant the opportunity to switch ONLY if s/he has chosen the door with the car. That would get them 'off the hook' in having to part with an expensive car if the contestant chose to switch.
If, however, the contestant initially chose the goat, they might simply end the matter and send the contestant away with his/her new goat - they would still get a plug in for the car, which would return to the manufacturer or possibly be saved for a future contest.
If the contestant suspected that such was the case, then s/he might very well decide not to switch, and end up with the car.
Pretty deep waters here.
ADDED LATER: The matter is discussed in more depth in Mark Haddon's novel The Curious Incident of the Dog in the Night-Time, chapter 101.
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Now lets get serious here.
Are we talking about a three way guess of......lets say Find the Lady ? Played straight ?
Or are we talking about a game show or slight of hand manipulating the odds for entertainment or gain?
Are we talking about a three way guess of......lets say Find the Lady ? Played straight ?
Or are we talking about a game show or slight of hand manipulating the odds for entertainment or gain?
I thought I knew more than this until I opened my mouth
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Mark Aspam
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- Joined: Tue Apr 15, 2008 12:00 am
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Bruv;1454130 wrote: Now lets get serious here.
Are we talking about a three way guess of......lets say Find the Lady ? Played straight ?
Or are we talking about a game show or slight of hand manipulating the odds for entertainment or gain?I've never heard of "Find the Lady", I assume that it's a card game.
We're talking about an exercise in mathematics, and to a lesser extent in logic, couched in the trappings of a real American TV game show called "Let's Make A Deal".
Are we talking about a three way guess of......lets say Find the Lady ? Played straight ?
Or are we talking about a game show or slight of hand manipulating the odds for entertainment or gain?I've never heard of "Find the Lady", I assume that it's a card game.
We're talking about an exercise in mathematics, and to a lesser extent in logic, couched in the trappings of a real American TV game show called "Let's Make A Deal".
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Mark Aspam;1454140 wrote: I've never heard of "Find the Lady", I assume that it's a card game.
We're talking about an exercise in mathematics, and to a lesser extent in logic, couched in the trappings of a real American TV game show called "Let's Make A Deal".
Find the Lady or as I have just found out Three Card Monte is a gambling con where it is obvious to the onlooker where the target card is, until such time a bet is placed on the card, no one ever wins other than the card players friends in the crowd and the card manipulator.
If this all refers to a game show, I am out of here, no need to talk about it.
We're talking about an exercise in mathematics, and to a lesser extent in logic, couched in the trappings of a real American TV game show called "Let's Make A Deal".
Find the Lady or as I have just found out Three Card Monte is a gambling con where it is obvious to the onlooker where the target card is, until such time a bet is placed on the card, no one ever wins other than the card players friends in the crowd and the card manipulator.
If this all refers to a game show, I am out of here, no need to talk about it.
I thought I knew more than this until I opened my mouth