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Sacks
22 Answers
After Socks and Sex here's the last one from me for a while as work beckons. (and I need to buy some new light bulbs and socks and knock on doors to see whether a boy or girl answers)
I have two sacks, and inside each I have put some money. In fact, one sack contains twice as much money as the other.
I'll blindfold you and let you select one sack, which you can have after the game is over. But as soon as you select one, I offer you the option to switch sacks. Should you switch?
You reason as follows: My sack has $x, and with probability 1/2 the other sack has either $x/2 or $2x dollars. Thus the expected value of the other sack is (1/2)($x/2) + (1/2)($2x) which is $1.25x. This is greater than the $x in my current sack. Therefore I should switch sacks...
But if you do switch, a similar argument would instruct you to switch back... and therefore keep switching! What's going on here? Is there a flaw in the reasoning?
I have two sacks, and inside each I have put some money. In fact, one sack contains twice as much money as the other.
I'll blindfold you and let you select one sack, which you can have after the game is over. But as soon as you select one, I offer you the option to switch sacks. Should you switch?
You reason as follows: My sack has $x, and with probability 1/2 the other sack has either $x/2 or $2x dollars. Thus the expected value of the other sack is (1/2)($x/2) + (1/2)($2x) which is $1.25x. This is greater than the $x in my current sack. Therefore I should switch sacks...
But if you do switch, a similar argument would instruct you to switch back... and therefore keep switching! What's going on here? Is there a flaw in the reasoning?
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