29 Mar '07 02:323 edits

Two envelopes, connected by a string, are in a box. One envelope contains $1 and the other one $10. Now a coin is tossed. If the result is "head" another pair of envelopes is put into the box, this time with $10 and $100; otherwise the experiment is stopped.

If the experiment was not stopped, again a coin is tossed. If the result is "head" another pair of envelopes is put into the box, this time with $100 and $1000; otherwise the experiment is stopped.

If the experiment was not stopped, again a coin is tossed. If the result is "head" another pair of envelopes is put into the box, this time with $1000 and $10000; otherwise the experiment is stopped.

And so on, until we get a "tail".

You don't know how many envelopes there are in the box. You take a connected pair of envelopes without looking into the box, and open one envelope. Inside you see x dollars. Now you are given the choice to take the x dollars, or take the sum in the other envelope. What do you do?

If your answer is "always swap envelopes", then why not take the other envelope in the first place?

If the experiment was not stopped, again a coin is tossed. If the result is "head" another pair of envelopes is put into the box, this time with $100 and $1000; otherwise the experiment is stopped.

If the experiment was not stopped, again a coin is tossed. If the result is "head" another pair of envelopes is put into the box, this time with $1000 and $10000; otherwise the experiment is stopped.

And so on, until we get a "tail".

You don't know how many envelopes there are in the box. You take a connected pair of envelopes without looking into the box, and open one envelope. Inside you see x dollars. Now you are given the choice to take the x dollars, or take the sum in the other envelope. What do you do?

If your answer is "always swap envelopes", then why not take the other envelope in the first place?