Thursday, July 28, 2011

Opportunity Mathematics - Or Case

At last article we have studied percentage of division of holded card opponent. Nowadays we will join percentage of division of card with simple mathematics science so that deal which we play highest percentage value. But before us study these items; beforehand let us see problem previous article.

North                    South
9852                    AQ
A732                    K86
A97                      K852
J3                        AK85

West     North    South    East
Pass       1       Pass      2NT
Pass       3NT       //
Bidding System: Standard American

West of Lead 6, North of 8, East of 10. How to play at which you do?
Some ways able to be done like following:
·         Hoping Diamond divided to flatten,
·         Hope Heart divided to flatten, or
·         Hope Q in West.

Do you make special note that opportunity at suit of Diamond will get extra trick more than Heart suit? Just taking example is Diamond divided 4-2 with QJ, or Q10 of J10 doubleton, hence you'd get third trick this suit. Thereby opportunity to get three trick bigger than 36%, if division 3-3 or 4-2 with condition of like above, Opportunity Heart suit? Yes, 36%, hereinafter how opportunity Club suit? Where Q reside in, West or East? For no information about offer of opponent, hence opportunities of ♣Q reside in West or East are 50-50. So, how to play owning biggest percentage? Way of playing Club suit, playing small Club of South up at J in North.

Mathematics Opportunity
Taking example you reach contract of slam in Diamond suit with distribution hold of card like hereunder:

North                     South
532                       AQ
A73                       K8
AJ97                      Q10652
1032                     AKQ5

Contract 6 by South, West of Lead Q. At this card distribution, contract depended from position of K with K. How many opportunity you earn to fulfill this contract? Opportunity of K resides in West is 50%, while opportunity of K in the East also 50%. Becoming how much is totalizing your opportunity?

How to play? Like this, to fulfill contract only requiring once successful finesse, hence totalizing your opportunity is: 50% (for example opportunity of K reside in West) and if finesse fail, you still have opportunity for the finesse of K (50%* from 50 %**) that is 25%. Becoming is total opportunity is 50%+25% = 75%. High enough! Note: Sign * it’s meaning 50% from unsuccessful first opportunity, and sign ** opportunity of second finesse.

Case above referred as “Or Case” with formula like following:


To be more sharpness come on a kit see example of following.
Taking example to fulfill its opportunity contract depended to the division of card of Hear 3-3 residing in hand fight against or succeed finesse of trump King. How many gratuity of opportunity contract this can reach? Data’s: opportunity of division of card 3-3 is 36%, and successful opportunity finesse is 50%.

Totals opportunity = 36% + (100-36) x 50% = 68% or
Totals opportunity = 50% + (100 – 50) x 36% = 68% with result of same.

The above is true this article, hopefully with a few follow the example of like have been elaborated above can add knowledge how to calculate totally percentage in OR CASE.

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Translated from Magazine Bridge Indonesia, Opportunity Mathematics, by. Syahrial Ali, 12/02

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