gold mountain [ Atwood's machine ] [ bag of marbles ] [ balance moon stone ] [ ball up/down ] [ bead parabola accelerometer ] [ boat anchor lake ] [ boat time ] [ bobbin on incline ] [ bosun's chair ] [ bouncing ball ] [ bowling ball rolling ] [ bug on band ] [ bursting shell ] [ falling chain ] [ Feynman's restaurant problem ] [ five pills ] [ flying cable ] [ forced pendulum ] [ gold mountain ] [ half pills ] [ hallway pole ] [ impelled rod ] [ inelastic relativistic collision ] [ infinite pulleys ] [ mass on an incline ] [ maximum angle of deflection ] [ packs of shirts ] [ particle in bowl ] [ particle in cone ] [ particle on sphere ] [ particle points parabola ] [ pile of bricks ] [ pion muon neutrino ] [ piston ramp spring ] [ plank weight trough ] [ rocket vs. jet ] [ roll without slipping ] [ rough inclined plane ] [ shooting marbles ] [ speedometer test ] [ three balls ] [ three logs ] [ turntable cart ] [ two rolling balls ] [ wheel and block ] [ whirling pendulum ] [ worlds fair ornament ]

This is a variant, invented by Michael Gottlieb, of the famous "Monty Hall" problem.

Suppose there were a mountain of volume M that has in it a (Poisson) distribution of mine-able gold having total volume G, and you are given a mine claim that includes a total mine-able volume V of the mountain. While you are deliberating as to whether or not to invest in the (considerable!) expense of gold-mining, someone else works a claim, mining out a volume of the mountain R that yields a volume Rg of gold. If you were then given the opportunity to trade your mine for another (unworked) mine of equal volume V, anywhere else on the mountain, what should you do? How much can you expect to win if you keep your mine? And if you trade for another one?