There are two boxes. Box 1 has \$60 and Box 2 has \$40. Each of you and your friend picks one of the boxes. Each of you get paid by splitting what you open collectively. For example, if both of you pick Box 2, each gets paid \$20. If one picks Box 1 and the other picks Box 2, each gets paid \$50. You two cannot communicate in any form. You two cannot pass on any objects. Both of you are rational and will follow a same strategy.
What strategy would you use?
P.S. The deterministic method will end up in \$30 for each when both pick one. There probably is a solution involving random number for each getting paid \$50. But I cannot come up with one.