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Diaconis on Randomness

Posted By: Timothy Chow
Date: Friday, 24 May 2013, at 3:07 a.m.

In Response To: Diaconis on Randomness (Douglas Zare)

Doug wrote:

At least, that's the explanation I've heard. It's also possible that there was no real difference, but when there was some potential difference people started noticing the hands with extreme distributions and suspected that there was a problem, much the way people complain about the dice on every single backgammon server.

I've wondered the same thing myself. A web search turned up one secondhand report of an actual empirical test of bridge shuffling. If we take this report at face value, it suggests that there is no hard evidence that ordinary hand-shuffling produces detectably bad distributions.

On the other hand, I have heard one bridge player who is a mathematician arguing that one should expect more voids with truly random shuffling. If tricks are thrown into the middle of the table as they are in some informal settings, then I can see getting lots of runs of four cards of the same suit, which then get evenly dealt to the four players in the next hand if the shuffling is poor. Or, if people place their cards in a row in front of them as they are played, then it's still possible to get runs since it's not uncommon for a player to play several cards from the same suit in succession if they are winning the tricks. But I'm still not convinced that any humanly-detectable bias would show through after normal shuffling.

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