## Friday, July 29, 2011

### Opportunity Mathematics for Declarer Play

At previous article have been studied percentage of coupled with play opportunity mathematics in case OR. And these articles we will study percentage of play in AND CaseWith same card distribution previous article, you made a success of bidding contract of grand slam 7, how much gratuity of your opportunity to fulfill contract this?

West            East
9852           AQ
A732          K86
A97            K852
J3              AK85

This Problem known as AND case because opportunity of efficacy in doing K finesse and K, both have to succeed, Success opportunity in doing K finesse is 50%, and so it is with success opportunity K finesse is 50%. Success opportunity of you is 50% x 50% = 25%.

TOTALS OPPORTUNITY AND CASE = OPPORTUNITY OF SUCCESS POSSIBILITY 1 x OPPORTUNITY OF SUCCESS POSSIBILITY 2 x OPPORTUNITY OF SUCCESS POSSIBILITY 3 and so on.

To be more sharpness let us see card distribution example which much the same to with above, like following. Taking example in effort to fulfill a contract, success opportunity depended from division of card of Heart existing on-hand fight against (3-3) and also King Finesse. What opportunity of efficacy to fulfill contract this? Data’s: Opportunity of card divided 3-3 is 36%, and success opportunity of finesse is 50. Totalizing opportunity = 36% x 50 = 18% is just, opportunity of very small efficacy

Following more complex example of:

North           South
KQ2           A63
AQ73         1042
32              AK765
KJ63          A8

West  North  East   South
1NT
Pass   2      Pass   2
Pass   3      Pass   3
Pass   3      Pass   3NT
//

West lead J. planning game of you before reading solution like hereunderOpportunity to get ninth trick very big and available in all suit except Spade, How do you play this board? Player of beginner usually will do Heart finesse. If failing, they will try A cash on the chance of J will follow to fall. If failing again, last expectation Q finesse or hope Heart suit divided to flatten. Way of playing at like this wrong is not, if calculated success opportunity is 50% (opportunity of H finesse + 4% (opportunity of J fall + 25% (opportunity of Q finesse), or equivalent by 80% success opportunity.

But there is a way of better from way of playing at like above, that is by playing small Diamond both hand. Become after opponent of lead J, take with K then play small diamond which won opponent. If opponent return to play spade, take with last Q and play diamond again. If both opponent follow diamond suit and so contract have is peaceful, even you can get additional trick (up) when position of diamond divided to flatten (3-3) both opponent hand. But when one of the opponents not follows with diamond suit second round, hence you can change over to heart suit or of suit club. Way of playing at like this will succeed with calculation of percentage like following:

Diamond divided 4-2 = 48%
Diamond divided 3-3 = 36%
Division of bad diamond = (100 – 48 : 36) x 50% (heart finesse = 8%
Heart Jack doubleton = 2%

Totals success opportunity is 96%, a way of playing at owning highest opportunity. If you chosen club finesse, its number a little lower for no additional opportunity in club suit.

To add your horizon about mathematics percentage of play, try to count highest success opportunity for cases following:

1. You have a contract; success opportunity depended thrice doing finesse
a.    Successful contract when third successful finesse
b.    Successful contract when two from three success finesse
c.    Successful contract when enough one from three success finesse
2. You play contact 2NT, West start lead with 6, how to plan you?

North           South
A72            K863
10873         A42
7532           AQ10
Q7             A83

Useful hopefully and safe try!

Previous article :

Translate from Magazine Bridge Indonesia, Opportunity Mathematics, by Syahrial Ali, 12/06