[praptak]

So 7 riffles can produce every permutation equiprobably, right?

Is there a smaller number of riffles that can produce every permutation, not necessarily equiprobably?

[irontinkerer]

> equiprobably

I thought you made up that word, but you didn't! Thanks for teaching me somethign new!

> e·qui·prob·a·ble

> (of two or more things) equally likely to occur; having equal probability.

[Falling3]

Sophomore year of HS, my math teacher introduced us to the word equidistant. For at least an entire quarter, I thought he had a speech impediment and was trying to say "equally distant".

[andrewla]

I don't think the arrangements are equiprobable. Well-distributed, likely.

Heuristically, there are a finite number of outputs of a riffle shuffle (probably fairly large; basically the number of different ways that you can clump cards together, 52^20 or thereabouts). But any finite number of outputs raised to the 7th power is not going to divide 52 factorial, in terms of the number of output possibilities.