I think I heard this story in a statistics class in Berkeley in 1955. Fishing boats would spend weeks at sea and do some processing immediately after the fish were caught. The livers were especially valuable and were promptly extracted, put into cans and frozen. Liver quality varied and the buyers of the frozen liver needed to sample the quality without thawing the livers. The cans were cylindrical. They would sample by drilling a thin hole thru from one rim to the opposite point on the other rim of the can, passing thru the center of the can.

This sampling was done in view of the sellers. The buyers discovered that the samples were assaying higher than the thawed livers and that they were thus paying too much. Closer examination of the content of the cans revealed that for extreme values of z and small values of r, or mid values of z and large values of r, the quality was poor. Elsewhere it was good. The samples went thru the good stuff. Testing was changed a few times and each time, after the new testing was understood, the same problem arose.

Finally a bit of continuous game theory was invoked resulting in the follow testing procedure: Choose r1 and r2 randomly from the uniform distribution between 0 and the can’s radius. Choose a random φ between 0 and 2π. Drill a sample parallel to the can’s axis thru a point in the can’s top whose polar coordinates are <max(r1, r2), φ>. The resulting sample covers any point in the can with the same density.

The game was over and the samplers had won, but not without some applied probability theory. The fishers lost not because they were uneducated, which they were, but because this is the game theoretical outcome.