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December 17, 2000
Counting, Counting, and More Counting

Counting, Counting, and More Counting

I do not know what made me think of counting .... but here are a couple of hands with a counting theme!

No. 1

West North East South
3spade.gif (842 bytes) Pass Pass 4heart.gif (841 bytes)
Pass 5heart.gif (841 bytes) Pass 6heart.gif (841 bytes)
Pass Pass Pass

You are South.

South

spade.gif (842 bytes)A97
heart.gif (841 bytes)AKQ106
diamond.gif (837 bytes)K107
club.gif (841 bytes)K4

Was the bidding very scientific? No, but it frequently is not when the opposing sides starts things off with a preempt.

The opening lead is the spade.gif (842 bytes)K and dummy comes into view:

North
spade.gif (842 bytes)42
heart.gif (841 bytes)75432
diamond.gif (837 bytes)AJ9
West club.gif (841 bytes)AJ6 East
spade.gif (842 bytes)??? spade.gif (842 bytes)???
heart.gif (841 bytes)??? heart.gif (841 bytes)???
diamond.gif (837 bytes)??? diamond.gif (837 bytes)???
club.gif (841 bytes)??? South (you) club.gif (841 bytes)???
spade.gif (842 bytes)A97
heart.gif (841 bytes)AKQ106
diamond.gif (837 bytes)K107
club.gif (841 bytes)K4

You have ten top tricks (1 spade, 5 hearts, 2 diamonds, and 2 clubs). An eleventh trick is easy by way of trumping a spade. To do that you will have to lose a spade trick first. Alternatively you could trump a club in the South hand but that would still leave you with a spade loser.

It looks as though there are a few possibilities for a twelfth trick:

The best line would be to try to combine as many of these various chances as possible. So the proper line is to win the spade.gif (842 bytes)A, pull trump, concede a spade trick, win the return, trump a spade in the North, cash the top two clubs to see if the club.gif (841 bytes)Q, and if it does not, finesse one of the opponents for the diamond.gif (837 bytes)Q.

Play proceeds:

You now have to take a diamond finesse. Which opponent do you finesse for the diamond.gif (837 bytes)Q and why?

The answer is below.

No. 2

Again you are South. Partner leads the spade.gif (842 bytes)A and you get to see dummy.

West North East South
1heart.gif (841 bytes) Double 2heart.gif (841 bytes) Pass
3heart.gif (841 bytes) Pass 4heart.gif (841 bytes) Pass
Pass Pass
North
spade.gif (842 bytes)???
heart.gif (841 bytes)???
diamond.gif (837 bytes)???
West club.gif (841 bytes)??? East
spade.gif (842 bytes)??? spade.gif (842 bytes)J102
heart.gif (841 bytes)??? heart.gif (841 bytes)K743
diamond.gif (837 bytes)??? diamond.gif (837 bytes)J7
club.gif (841 bytes)??? South (you) club.gif (841 bytes)A873
spade.gif (842 bytes)Q965
heart.gif (841 bytes)92
diamond.gif (837 bytes)108632
club.gif (841 bytes)K9

You play the spade.gif (842 bytes)9 (an encouraging signal) so that partner knows that it is safe to continue spades. Partner continues with the spade.gif (842 bytes)K and a third round of spades which declarer trumps. Declarer plays a heart to the heart.gif (841 bytes)K and then a second round of hearts winning the heart.gif (841 bytes)A. Partner follows to both rounds of trump playing the heart.gif (841 bytes)Q on the second round. Declarer cashes the diamond.gif (837 bytes)A and diamond.gif (837 bytes)K and then trumps a third diamond in the dummy. Partner follows to all three rounds playing the diamond.gif (837 bytes)Q as declarer trumps in the dummy. Declarer now cashes the club.gif (841 bytes)A.

Can you defeat the contract. If so, how?

The answers:

No. 1

You know that each player started with 13 cards. From the play to the first six tricks you know that West started with 7 spades (East showed out on the second round), 1 heart (West had two), and 1 club (West showed out on the second round of clubs). West therefore holds exactly four diamonds. That leaves exactly three diamonds for the East hand. The rule is that any specific card (such as the diamond.gif (837 bytes)Q) is most likely in the hand that has the most room to hold it.

West has four diamonds that could be the diamond.gif (837 bytes)Q and East only has three.

Finesse West for the diamond.gif (837 bytes)Q. Your odds of success are 4 to 3.

The complete hand:

North
spade.gif (842 bytes)42
heart.gif (841 bytes)75432
diamond.gif (837 bytes)AJ9
West club.gif (841 bytes)AJ6 East
spade.gif (842 bytes)KQJ8653 spade.gif (842 bytes)10
heart.gif (841 bytes)9 heart.gif (841 bytes)J8
diamond.gif (837 bytes)Q865 diamond.gif (837 bytes)432
club.gif (841 bytes)7 South (you) club.gif (841 bytes)Q1098532
spade.gif (842 bytes)A97
heart.gif (841 bytes)AKQ106
diamond.gif (837 bytes)K107
club.gif (841 bytes)K4

No. 2

Declarer is marked from the play with 2 spades, 5 hearts, 3 diamonds, and therefore exactly 3 clubs. Declarer has lost two tricks (2 spades). You must take two club tricks if you are going to defeat this contract. Declarer has cashed the club.gif (841 bytes)A and if you do not do something about it you will win the second round of clubs and be forced to lead a spade or diamond. Either will give declarer a ruff-sluff and the contract.

What is the answer? Avoid winning the club.gif (841 bytes)K by playing it under the club.gif (841 bytes)A! As you can see this allows partner to win two club tricks. If partner does not hold the club.gif (841 bytes)Q then the contract is unbeatable.

The complete hand:

North
spade.gif (842 bytes)AK43
heart.gif (841 bytes)Q5
diamond.gif (837 bytes)Q94
West club.gif (841 bytes)Q1062 East
spade.gif (842 bytes)87 spade.gif (842 bytes)J102
heart.gif (841 bytes)AJ1086 heart.gif (841 bytes)K743
diamond.gif (837 bytes)AK5 diamond.gif (837 bytes)J7
club.gif (841 bytes)J54 South (you) club.gif (841 bytes)A873
spade.gif (842 bytes)Q965
heart.gif (841 bytes)92
diamond.gif (837 bytes)108632
club.gif (841 bytes)K9

Thanks!
Gary King

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