[JLilly]

 barmar, on 2017-March-23, 15:21, said:

I hope that the shuffles of the smaller portions of the deck make up for how clumpy my riffles are when I shuffle the whole deck. And throwing in a few overhand shuffles ensures that I don't have the same top and bottom cards each time I riffle.

Blackjack dealers in casinos use a similar procedure of shuffling small parts of the deck first and then merging them, that's where I got the idea.

Yeah, it's the topmost and bottommost cards that are the least randomized from riffle shuffling. Throwing in even one overhand shuffle (before the final couple riffle shuffles) does the trick even if you're a clumpy riffle shuffler.

If that's how casino dealers randomize the cards, then, yeah, you can bet it's reliable. I think I'm pretty smart, but I'll trust the casinos to know how to randomize a deck more than I'll trust my rudimentary logic and limited experience.

[JLilly]

Quote

Hand shuffling actually generates MILDER hands than true random shuffling.

This makes eminent sense. In bridge and other trick-taking games, you often have multiple consecutive tricks in the same suit, taken by the same side. In bridge, think of drawing trumps, or running a long suit. Or in hearts, trying to flush out the Q♠ by repeated spade leads, or someone trying to shoot the moon with repeated high heart leads. Hand shuffling, which is prone to leaving clumps of cards intact, may preserve such a clump. Say that a player led and re-led spades for two or more hands, with every other hand following. There are now eight (or more) spades all clumped together in the pile of played cards.

An especially poor hand-shuffling may keep all eight of these cards together, guaranteeing that in the next deal, nobody has fewer than two spades. A moderately poor hand shuffling may shear off four out of eight of the spades in the clump, but if four remain together, that guarantees that nobody will have a void in spades. The principle is continuous -- if there are three spades in a row, then only one hand is at all eligible to have a void in spades, and that hand must avoid a spade in all other twelve of the remaning four-card trick-subdeals.

[benlessard]

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