Are It True?
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Joined: Oct 2003
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From: city
I was thinking about this, and came up with a better example.
I am thinking of a number. You guess it, and I will give you a cash prize. If you are wrong, I will give you a smaller cash prize.
You write the number 7 on a piece of paper. Then you scratch it out and write the number 4, and hand me the paper.
Did you increase your chances of winning by taking a second guess? No. The odds of your winning remain the same, no matter how many times you change your mind. You derive no benefit from changing your guess, regardless of how many numbers you have to pick from, and regardless of the values of the individual prizes. Does that make sense?
In your two-envelopes game, you are just making the original guess more complicated. If you use your logic, by first picking envelope A, you are really selecting envelope B, since you advise swapping envelopes no matter what. Why not just mentally pick envelope A, and then mentally swap it with envelope B, and really pick up envelope B? The end result is the same, whether you physically touch one or two envelopes. Even simpler, just drop the pretense of swapping envelopes, and pick envelope B in the first place, if that is the one you really want.
I am thinking of a number. You guess it, and I will give you a cash prize. If you are wrong, I will give you a smaller cash prize.
You write the number 7 on a piece of paper. Then you scratch it out and write the number 4, and hand me the paper.
Did you increase your chances of winning by taking a second guess? No. The odds of your winning remain the same, no matter how many times you change your mind. You derive no benefit from changing your guess, regardless of how many numbers you have to pick from, and regardless of the values of the individual prizes. Does that make sense?
In your two-envelopes game, you are just making the original guess more complicated. If you use your logic, by first picking envelope A, you are really selecting envelope B, since you advise swapping envelopes no matter what. Why not just mentally pick envelope A, and then mentally swap it with envelope B, and really pick up envelope B? The end result is the same, whether you physically touch one or two envelopes. Even simpler, just drop the pretense of swapping envelopes, and pick envelope B in the first place, if that is the one you really want.
Thread Starter
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Joined: Jul 2001
Posts: 6,592
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From: Yorba Linda, CA
Originally posted by EvoVII
lol, we had a similar situation in our math class just recently.. it dealt with a gameshow back in the day, forgot the name, but basically, here was the situation: You have 3 doors to choose from, and one door contains the prize. You choose a door, but then the gameshow host elects to take one door away that doesn't have the prize in it. Would you stick with your original selection or switch to the other door? Does it make a difference? Why?
lol, we had a similar situation in our math class just recently.. it dealt with a gameshow back in the day, forgot the name, but basically, here was the situation: You have 3 doors to choose from, and one door contains the prize. You choose a door, but then the gameshow host elects to take one door away that doesn't have the prize in it. Would you stick with your original selection or switch to the other door? Does it make a difference? Why?
