The average 3d6 dice roll is 10.5 (because [1+2+3+4+5+6]/6 = 3.5 )
The average 1d20 roll is also 10.5 ( [1+2+3...20] / 20 = 10.5 )

I undoubtedly knew this full well a long time ago, but I re-realized it today. Why is it interesting, because the odds of rolling "close to average" are higher on 3d6 than on 1d20. The outcome probability distribution is flat for the d20 bar-chart, vs. a "normal curve" (high in the middle, falling off symmetrically) for 3d6.