Thursday, July 28, 2011

Card Play Technique Change of Percentage

At previous article, we have studied opportunity mathematical of play bridge which consist of two especial case that is case of OR and case of AND. Nowadays, we will learn concept change of percentage after card played. But as usual before continuing with new items, let us study problem by the end of previous article.

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

Answer of problem 1
a.   This problem easy matter that is case of AND by 3 components. Its opportunity is 50% x 50% x 50 = 12,5%, very is small success opportunity.
b.   This difficult problem enough because this case composite of case of AND with of OR. Become us delay first, OK!
c.   Third problem enough easy to because this case represent case of OR by 3 component. Its opportunity is 50 + (I - 50%) x 50 + (I-50%) - (I-50%) x 50% x 50 = 50% + 25% +12.5 = 87,5%

Now, let us study problem of b which delay
a.    Success opportunity in doing first finesse is 50%. So that, this contact can reach hence one of the success finesses of second finesse or third finesse (OR Case by 2 components) with opportunity 75%. Totalizing opportunity is 50% x 75 = 37.5%.
b.    Additional opportunity: if first finesse fails hence third AND second finesse have to succeed (AND Case with two components). Its opportunity is 50% x 50% = 25%
Thereby composite among opportunity (a) and (b) is 37.5%+25 = 62.5%.

2. You play at contract 2NT, and West start lead with 6, how your plan?

North           South
A72            K863
10873         A42
7532           AQ10
Q7             A83

This example is taken away from by book “Card Play Technique" by Victor Mollo. After West of lead 6, there is no need to think of again first trick, you direct play Q in desk, because this is single opportunity of you to make two trick club suit. Now or Never. Suppose Q win, how hereinafter? Let us calculate your opportunity!

After getting extra trick of Q mean you have owned 6 sure trick and only requiring two tricks again to fulfill contract 2NT. Opportunity to get additional trick can be obtained from colour of spade when divided to flatten (3-3) and from diamond suit. If you in advance play at spade and then do K finesse, hence success opportunity is 36% (opportunity of division 3-3) multiplied 50% (opportunity of K finesse), thereby opportunity which you get only 18%. How if you fiddle around with the way of suit diamond double finesse?

Opportunity of K and also J reside in West is 50%, so that by finesse double and hope KJ reside in West , its opportunity is 25%. Opportunity addition: if first finesse diamond fails your contract still can be saved when spade divided 3-3 and also the division of club suit not too bad from division 5-3. Thereby you will only fail three trick of club, one trick of spade, and one again from unsuccessful diamond suit finesse. Total of your opportunity is 25 + 75% x 36 = 52%. A percentage of good enough opportunity.

Next article : Percentage Change after Card Played 2
Previous article : Opportunity Mathematics for Declarer Play

Translate from Magazine Bridge Indonesia, Opportunity Mathematics, by Syahrial Ali, 3/07

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