Consider the following game. We have a probability distribution on
the following countably infinite deck of cards.
Card # front back probability
------ ----- ---- -----------
1 1 3 1/2
2 3 9 1/4
3 9 27 1/8
... ... ... ...
A card is selected according to this distribution, and you are shown,
at random, one of its two sides. (Let's say that the number you see
is X, and the one on the other side is Y). You may now decide to
"keep" or
"flip". If you decide "keep", you gain X-Y. If you decide "flip",
then you gain Y-X.
What to do?
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