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How better is a hand than another one? Damned Statistics!

 Authors: Delfí Querol, Francesc Bofill

 ..........

In connection with some discussion on one of our articles, we arrived to the following.

 

1.-Suppose you are given 

x QJTxxx KQJx xx.

Which hand would u prefer to find in front

Qxxxx AK A Jxxxx

or

AKQxx  xx  Jxxxx?

 

2.- Change sides, before the auction, which hand would you prefer to be given

Qxxxx AK A Jxxxx

or

AKQxx xx A Jxxxx?

 

This is a somehow biased example (not as much, in some sense, as we might think) but the important question in connection to what we are now concerned is:

Why do we prefer that that we prefer?  We must be careful because in our answer we risk to

fall in devils arms... if probability were to be considered a diabolic emanation.

For instance if we said

Answer: ... "because in the long run we will get more tricks with that we chose" we would fall in a probabilistic and statistical paradigm.

 

We found this mephistophelic enhancing of the previous answer

Enhanced answer: because with hand   AKQxx xx A Jxxxx, we will make in average 9.8 tricks per deal, (nice coincidence with the gravitational constant)

whereas with  Qxxxx AK A Jxxxx we will make "only" _____. Can u guess the missing value?  (We show it at almost the end.)

 

We give some statistics.

In the link

https://goo.gl/yYPZ7H

you will find

1.- The blocks: "Honors in shorts", "Honors in longs" which contain a sample of 1000 deals each, West hand is always  Qxxxx AK A Jxxxx in the first and " AKQxx xx A Jxxxx in the second. No conditions on the other 3 hands of each deal.

2.- A spreadsheet called "Comparacio dos cassos" that resumes the number of tricks available to West in his partnership best trump or no trump for both previous blocks. And the comparison of results corresponding to each of the two hands.

Sincerely ourselves believed the missing value to be quite smaller, but... it is 9.5. Three tricks less each ten deals. Also with the "weaker hand" opps will be more reluctant to compete. Thus this "weaker hand" is yet less weak than appreciated till now.

 

.................

A more difficult question. What would be better to be dealt in front of a 15-17 (or other (it doesn't mind much (as we believe))) passed 1nt opening from partner?

QJx  xx  xxxx   KQxx  (concentrated honors) or  QJx  xx   Qxxxx  Kxx (a longer suit)?

How could we now do a personal feelings independent evaluation? Statistically we know, but else...?

 

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