[NBLUG/talk] Request for help--how to program shuffling

[Steve Zimmerman]

On Wednesday 21 May 2003 05:07 pm, you wrote:
> It seems to me that your proof breaks with reality at 2B.  A royal flush is
> just as probable as any given bust.  It's just that there are so many more
> busts than roayal flushes.  To define as non-random any combination of
> cards which has value in poker may prove something but not about shuffling.
>
> > -----Original Message-----
> > From: talk-admin at nblug.org [mailto:talk-admin at nblug.org]On Behalf Of
> > Steve Zimmerman
> > Sent: Tuesday, May 20, 2003 9:01 PM
> > To: talk at nblug.org
> > Subject: Re: [NBLUG/talk] Request for help--how to program shuffling
> >
> > On Tuesday 20 May 2003 07:35 pm, you wrote:
> > > On Tue, 20 May 2003, Steve Zimmerman wrote:
> > > [snip]
> > >
> > > > Therefore, *a truly random shuffle would prevent the
> > > > programmer from ordering the cards in any way whatsoever,
> > > > either randomly or non-randomly!*
> >
> > I amend the above statement as follows:
> >
> > 	"A true shuffle is not random."
> >
> > Proof of the statement "A true shuffle is not random.":
> >
> > [Ground rules for the proof ]:
> >
> > 	1.  Notation involved in proof:
> > 	         a.  Face cards
> > 		A=Ace, K=King, Q=Queen,
> >                    	J=Jack
> > 	         b.  Numbered cards
> >                              2=2, 3=3, 4=4, etc.
> > 	         b.  Suits
> > 		s=spades, c=clubs, h=hearts,
> >                   	d=diamonds
> >
> > 	2.  Meta-logic to be used in proof:
> > 	        a.  Definition of "normative poker values":
> >
> > 		i.     pair
> >                             ii.    pairs
> >                             iii.   three of a kind
> >                             iv.   straight
> >                             v.    flush
> >                             vi.   full house
> >                             vii.  four of a kind
> >                             viii. straight flush
> >
> > 	        b.  Definition of "random hand":
> >                             A poker hand which contains no
> >                            "normative poker values"
> >
> > 	        c.  Definition of the perceptual primitive:
> >
> >                            The"perceptual primitive" is the
> >                            fact that perception is non-amenable
> >                            to proof, i.e., no one "proves" that
> >                            blue is blue.  Blue is blue by
> >                            concatenation of a certain sense
> >                            datum (the first "Blue" in the sentence,
> >                            'Blue is blue.') with a certain word (the
> >                             second "blue" in the sentence, 'Blue
> >                             is blue.').  No proof is involved, hence
> >                             the word, "primitive."  Sense data is
> >                             involved, hence the word "perceptual."
> >
> >
> > [Proof proper of the statement,
> > "A 'true shuffle' is not random." ]:
> >
> > Hand #1:  As 4d 7s 8s 9h
> >
> > Hand #1 is a random hand, according to
> > the definition of randomness.
> >
> >
> > Hand #2: 4d 4h 9c Jc Ad
> >
> > Hand #2 is not a random hand, according to
> > the definition of randomness.
> >
> > By the perceptual primitive I know that the
> > distribution of a shuffle will produce both
> > random and non-random hands.  Hence,
> > a true shuffle is not random.
> >
> > I don't want randomness in my shuffle
> > function.  I want a computer
> > simulation of a true shuffle.
> >
> > [End of proof]
> >
> > I will try to read the recommended Knuth passages,
> > but I must say, he's not a personal favorite of mine.
> > My heroes are Ritchie and Torvalds.
> >
> > : )
> >
> > Thank you for reading this.
> >
> > : )
> >
> > All responses except flames are welcome.
> >
> > : )

Your point is well taken.

This discussion reminds me of something in classical music called 
"atonality."  

In the mid-twentieth century, Arnold Schoenberg invented a system for 
creating music in which each of the twelve musical tones had to be used in a 
"tone row" which had strict rules for the ordering of tones.

This system was supposed to give equal weighting to all 12 tones, so that the 
traditinal concept of a "key" in music--one tone around which all the others 
are centered--was eliminated.

The resulting compositional system was dubbed "atonality," 
a word which etymologically means "without tone."

Later on, some musicologist noted that Schoenberg's 
system wasn't "atonal" at all--it still involved tones.

I suppose this musicologist could be accused of 
stating the obvious; in a sense, I'm trying to make 
a similar point viv-a-vis "randomness," which, 
please note, could correctly be called "aorder."

I.e., atonality is to tonality as aorder is to order.

I.e., random means "without order" 
as atonality means "without tone."

Is there such a thing as randomness?

Does an honest throw of two dice produce a random number?  

I suppose it depends on the context.  If there is no context within which to 
judge whether or not the dice are ordered, then the throw is random.  

If a craps game is in progress (i.e., if there is "context"), then no throw 
of the dice is ever random, because every throw will fit into the 
pre-arranged schema of craps, i.e.,

	1. A throw that immediately wins (7 or 11);

	2. A throw that immediately loses (1, 2, or 12);

	3. The point;

	4. A roll that matches the point;

	5. A roll that doesn't match the point.
                 
There are no other possibilites.  There is no randomness.

However, if there is no context within which to judge a series 
of dice throws, then they are indeed random.  

Thus, the same series of throws that are non-random 
within the context of a craps game are indeed random 
outside of any context.

Therefore, I venture a hypothesis, open to debate:

"In any system in which there is context, and with context
a system of order within which to judge any mathematical
series or sequence whatsoever, there is by 
definition no randomness."

The musicologist who said that no matter how hard
you try to create an arbitrary sytem of tones, you're still
going to have tonality...

is the same as I am, in this respect:

No matter how hard you try to create randomness, 
you're still going to have order, because your very 
efforts to create randomness are creating "context"
within which to judge whether a series is random or not,
and in so doing, you are destroying randomness.

Put more mildly, I would say that the search for 
randomness is a holy grail that will never be reached
and that is unecessary in the first place, because, as
I have pointed out, no real-life card game, dice game,
or any game has any randomness in it.

: )
In conclusion,

#define FLAMUS_NON_RERUM  "No flames allowed \
              ,but honest debate is welcomed."
.
.
.
	printf("%s\n", FLAMUS_NON_RERUM);

	return 0;
}

: )