Re: [FWP] Shufflebug

["Bernie Cosell" <bernie@fantasyfarm.com>]

On 18 Jul 00, at 11:23, Ira Joseph Woodhead wrote:

> I just want to point out that studies show even humans with
  ... physical decks have to shuffle 7 times to produce a fair deck. 

Actually, this is probably a reference to Persi Diaconis's work.  The 
limitation isn't so much "humans" as "using a riffle shuffle" --- 
interesting, a *machine* doing a riffle shuffle doesn't really 
shuffle the deck hardly at all... it is only the randomness 
introduced by tthe realities of having people in the loop that makes 
a 'riffle' be a shuffle *at*all*.

Persi was under contract from the ACBL [amer contract bridge league] 
to investigate fair-shuffling for tournaments and the 'seven 
shuffles" was his result.

The anecdote that goes along with this is a bit amusing: he 
discovered that when he analyzed the play of the top bridge players, 
they occasionally made "probabilistically incorrect" plays...  to his 
surprise, the difference in probability was very close to being the 
difference between a 'typical' shuffle and a perfect one... it shows 
that the really great bridge players learned "the odds" *NOT* by 
studying math, but by playing bridge!  [now think about *how*much* 
bridge you have to play to _infer_ the statistics for finesses, suit 
splits, etc... whew!!  no wonder I s*cked at bridge]

> ...In physical cards it's the proximity of positions that
>  have to be overcome by multiple shufflings.

Not quite: for bridge, you only have to randomize the position *mod*4 
-- this is actually a lesser constraint than having to have a shuffle 
that can generate all 52! [or whatever it is] shuffles with equal 
probability.  That is, you don't care that card A's *position* is 
indpendent of its position in the pre-shuffled deck, but rather that 
*the*hand*that*gets*it* is independent of that...  alas, I can't 
offhand come up with an algorithm that I can defend that just makes a 
"random deal" [rather than a randomly shuffled deck] but my intution 
says we ought to be able to come up with one...

  /Bernie\

-- 
Bernie Cosell                     Fantasy Farm Fibers
mailto:bernie@fantasyfarm.com     Pearisburg, VA
    -->  Too many people, too few sheep  <--          

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