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
3	Pass	Pass	4
Pass	5	Pass	6
Pass	Pass	Pass

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

K and dummy comes into view:

	North
	42
	75432
	AJ9
West	AJ6	East
???		???
???		???
???		???
???	South (you)	???
	A97
	AKQ106
	K107
	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

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

Q, and if it does not, finesse one of the opponents for the

Q.

Play proceeds:

You now have to take a diamond finesse. Which opponent do you finesse for the

Q and why?

The answer is below.

No. 2

Again you are South. Partner leads the

A and you get to see dummy.

West	North	East	South
1	Double	2	Pass
3	Pass	4	Pass
Pass	Pass

	North
	???
	???
	???
West	???	East
???		J102
???		K743
???		J7
???	South (you)	A873
	Q965
	92
	108632
	K9

You play the

9 (an encouraging signal) so that partner knows that it is safe to continue spades. Partner continues with the

K and a third round of spades which declarer trumps. Declarer plays a heart to the

K and then a second round of hearts winning the

A. Partner follows to both rounds of trump playing the

Q on the second round. Declarer cashes the

A and

K and then trumps a third diamond in the dummy. Partner follows to all three rounds playing the

Q as declarer trumps in the dummy. Declarer now cashes the

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

Q) is most likely in the hand that has the most room to hold it.

West has four diamonds that could be the

Q and East only has three.

Finesse West for the

Q. Your odds of success are 4 to 3.

The complete hand:

	North
	42
	75432
	AJ9
West	AJ6	East
KQJ8653		10
9		J8
Q865		432
7	South (you)	Q1098532
	A97
	AKQ106
	K107
	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

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

K by playing it under the

A! As you can see this allows partner to win two club tricks. If partner does not hold the

Q then the contract is unbeatable.

The complete hand:

	North
	AK43
	Q5
	Q94
West	Q1062	East
87		J102
AJ1086		K743
AK5		J7
J54	South (you)	A873
	Q965
	92
	108632
	K9