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October 28, 2000
Giving Yourself the Best Chance

Giving Yourself the Best Chance

This brief is an excerpt from an article that first appeared in Issue #22 (Jan/Feb 1998) of The Bridge Companion.

Play of the hand is a matter of choosing from among the alternatives available to you on any one specific hand. Many times, the best line of play is a combination of these alternatives. Alternative A can be tried and, if unsuccessful, Alternative B can be then be tried. The following hand is such a case. Can you find the proper combination of plays that lets you have the greatest chance of bringing home your contract?

West	North	East	South
			1
Pass	2	Pass	3NT
Pass	6NT	Pass	Pass
Pass

	North
	Q42
	AJ10
	J6
West	AQ1084	East
???		???
???		???
???		???
???	South	???
	AK7
	Q64
	AQ93
	KJ9

You open with 1 and make a jump rebid in no trump, showing 19-21 points and a balanced hand. Note that after partner responds at the two level you must rebid 3NT. A 2NT rebid would be 13-15 points and a balanced hand. Holding a 15 point hand (14 HCP plus 1 for the club length) partner gets right to slam (partner knows the combined assets are 34-36 points. There is no chance of missing two aces.

As with every hand you play you should make a plan:

(1) What is your objective?

12 tricks

(2) How many sure winners?

10 sure winners (3 spades, 1 heart, 1 diamond, and 5 clubs)

(3) Which suits offer the possibility of developing additional tricks?

No additional tricks are available in spades or clubs, but both hearts and diamonds have potential.

(4) Play the first card from dummy.

Let us look more closely at the potential of the red suits. What combination of plays offers the best opportunity?

In the heart suit a repeated successful finesse will produce the extra two tricks you need. If you try nothing but the heart finesse you will make 6NT 50% of the time (half of the time the K will be favorably located). Even if you take the heart finesse and it loses (when the K is with East), you will always promote one additional heart trick.

In the diamond suit you also have the potential for a simple finesse. Just like in the heart suit, if the finesse fails, you will also promote one additional winner. Unlike the heart suit you do not hold the 10.

First plan - Take a heart finesse. If it wins (50%), repeat it to get the two needed tricks. If it loses (50%), take the diamond finesse which will also win 50% of the time.

Chance of success:
Heart finesse = 50%
(when the heart loses) Diamond finesse = 50% of 50% = 25%
Total = 50% + 25% = 75%

Not bad but can you do better? Is there a way to take advantage of the 9? Given an opportunity, the 10 might fall under the diamond honors and eliminate the need for a heart finesse altogether!

Second plan - Take the diamond finesse (low to the Q) first. If it succeeds, abandon the diamond suit and take the heart finesse. Irrespective of whether it wins or loses you will have 12 tricks (3 spades, 2 hearts, 2 diamonds, and 5 clubs). If the diamond finesse fails (your Q loses to the K), then cash the remaining two diamond honors (A and J) to see if the 10 falls. The 10 will fall whenever it is singleton, doubleton, or tripleton. If it does drop, then there is no need to risk the heart finesse at all. If no 10 appears, then take the heart finesse.

Chance of success:
Drop 10 singleton = 1/7 of all of the 6-1 breaks = 1/7 of 7% = 1%
Drop the 10 doubleton = 2/7 of all of the 5-2 breaks = 2/7 of 31% = 9%
Drop the 10 tripleton = 3/7 of all of the 4-3 breaks = 3/7 of 62% = 27%
Diamond finesse = 50% of 63% = 32%
Heart finesse = 50% of remainder = 50% of 31% = 15%
Total =1%+9%+27%+32%+15% = 84%

Do you see the problem? If you lead a diamond to the Q and it loses, East will lead a heart! You will now be forced to choose between the remaining alternatives. Either play for the drop of the 10 or play for the K to be onside. You will not be able to do both! That reduces your chances back to 75%. Can you arrange it so that you can try both plays?

Third plan - You must remember the definition of a finesse (lead a small card towards a card with which you hope to win the trick). Is there another way to finesse in the diamond suit? Lead a small diamond towards the J! What can happen? If West has the K and plays it, then you have two additional diamond winners (J and Q) and twelve tricks. If West has the K and does not play it, then you will win the J. With one additional diamond trick in hand you can now take the heart finesse and guarantee the contract. If East has the K and captures your J, then she is unable to lead a heart and force you to choose between the remaining alternatives. You will be able to play the A and Q to check to see if the 10 drops (making the 9 a winner). If no 10 appears, only then do you take the heart finesse. This allows you to take advantage of all the alternatives in a serial way. You can try each alternative in turn moving on only if unsuccessful. I wish all my slams had a 84% chance of success.

The complete hand:

	North
	Q42
	AJ10
	J6
West	AQ1084	East
10986		J53
753		K982
K1072		854
75	South	632
	AK7
	Q64
	AQ93
	KJ9

Thanks!
Gary King

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