Some OD&D house rules make use of "roll 2d6, take the lower result" and "roll 2d6, take the higher result." Obviously that would skew the chances of each possible result away from the flat 16.66% chance of each number coming up with a typical roll. But I wanted to see how much that skew would be, so I did the math real quickfast.
Here's the same idea, but using 3d6 and only keeping the result of one die.
But the real interest possibility with throwing three dice is the possibility of keeping the middle result. If you define the middle result to include any roll of doubles (e.g. 3,5,5, is a 5 result) then that spread looks like this:
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