[klochner]

Sorry to be blunt, but you're confused.

The average of the sampled values will be normally distributed, but the values themselves will be uniform.

If you sample every number once from [0,100], the average is 50, but that doesn't imply that the distribution of the sampled elements is normal - it's uniform.

His question of whether "on average, does the next card come from the middle" (which it doesn't) isn't the same as "is the mean of the next sampled card in the middle" (which it is).

The language was a little misleading - he said "on average" when he intended "most frequently".

[manifold]

Ok thanks for clearing that up. I hadn't appreciated the difference between the two.