Re: Finesse or not

On Feb 6, 10:28 am, henrysun...@xxxxxxxxx wrote:
On Feb 6, 1:25 am, Andrew <agump...@xxxxxxxxx> wrote:

Andrew

P.S. Not that I need to tell them, but Charles Brenner, Eddie Grove or
any other mathematically inclined reader should feel free to explain
why I am full of it :-)

**************

Not that I'm a mathematician, nor do I play one on TV, but this whole
discussion of how the principle of vacant spaces applies when biased
information is provided is an interesting one.

Here is a hand from "The Principle of Restricted Talent" that
illustrates the point:

                              A3
                              Q62
                              KQJT9
                              762

JT753                                                 VOID
3                                                           KJT9875
A654                                                   8732
A54                                                      QT

                                KQ9864
                                 A4
                                 VOID
                                 KJ982

the narrative reads, in part, as follows;

"Here's Chthonic, West, defending 4S after East made a preemptive
double-jump overcall of three hearts.  The opening lead is the heart
three: deuce, five, ace.  Declarer plays the king of trumps and learns
of the five-zero break.  crossing to the slade ace, he leads the
diamond king and discards his losing heart....

[there now follows a discussion of how Chthonic avoided a trump
endplay and set the hand, followed by...]

"After a few seconds an older man... said in a thick accent, 'Why did
declarer lead king of diamonds?"

[After Frederick attempts to justify this line of play, Chthonic
proposes this line of play]:

"There is a superior line available.  Declarer should play East for
his actual hlding of queen-ten doubleton of clubs."

[In his attempt to prove that this line is superior, Chthonic makes
the following mathematical claim, which is the crux of this little
post:]

"East is more likely to hold a club doubleton by a ratio of five to
four," continued Chthonic.  'This is a consequence of the law of
Available Spaces."

My question is, how did Chthonic come up with that ratio? It seems as
though it is treating as unbiased information the fact that West is
5-1 majors and East is 0-7 majors, because that is the only way that
one can conclude that East is more likely to be short in clubs than
West.

But I don't have the foggiest notion as to where 5-to-4 comes from in
the computer's calculations.  As this story appeared in the Bridge
World, of which mathematician Rubens is editor, and since this story
did not appear with footnotes, I have to assume that Rubens vetted the
calculation and found it reasonable.

Anyone with any ideas as to how this calculation actually works out?

Henrysun909

There are 13 cards left, 8 diamonds and 5 clubs. We know 7 of RHO
cards. So for the remaining 6 cards the number of ways of him having 2
clubs is

(5!/2!3!)(8!/4!4!)

And of 3 clubs is

(5!/3!2!)(8!/3!5!)

and when you divide and eliminate similar terms you are left with

(3!5!)/(4!4!) which reduces to 5/4 which is what was in the book.
Believe it or not, as long as you understand combinations and
factorials (!) the calculations really aren't hard to do in you head
for a difference of one card (as in the example),

Nick France
.

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