You pick up
Nice hand. You are dealer, so you open 1. Lefty (the opponent on your left) passes, and your partner bids 4. Righty (the opponent on your right) now annoyingly bids 4. You are vulnerable, they are not. It is perhaps not so obvious what to do, but you bid 5, Lefty bids 5, which is passed around to you. You double.
Ace of hearts is the obvious open lead, and dummy comes down with
Declarer ruffs the opening heart lead.
Time to count. If declarer started with zero hearts, how many hearts did your partner start with?
Declarer crosses to the K and takes a trump finesse, playing the Q. You win your K and lead your Q. Declarer wins this, and leads a trump to her A, dropping your J. That's unfortunate, you were hoping to win that too. Partner followed to both rounds of trumps.
Declarer now leads a diamond to your J, your partner showing out in diamonds.
Okay, your partner started with two diamonds. How many did declarer start with?
That is useful to know. Declarer cannot pitch any clubs on diamond winners.
At this point, your return is a no-brainer, at least from head-above-water-no-counting point of view. You have
and dummy has
Leading a heart gives declarer a sluff-and-a-ruff; one of the head-above-water principles is that you never give declarer a sluff-and-a-ruff (unless you are sure declarer has no more losers in the side suits). So you have to lead a club, and from KQx, the obvious lead is the king.
But let's count.
Counting the Distribution
I think you should figure out partner's hearts as soon as declarer showed up, and I think you should figure out declarer's diamonds as soon as she showed out. But you can usually put off counting until you have to make a decision. This is your decision time.
Can you count the spades? Declarer probably has finished drawing trump. First, declarer was trying to draw trumps. Why would she stop if one trump was still out? And how would she have known to drop your jack?
If trump are drawn, your partner started with two trump. If your partner started with two trump, how many did declarer start with?
That makes sense -- declarer would be more likely to come in at the four level holding six trump. No certainties here, but I think it's sensible to give declarer six trump. (If you have time to worry about the possibility of five, you can do that. But you won't have time on this hand.)
Eureka. The distribution in trump is the third piece of information. Even though clubs have never been played (or mentioned in the bidding), you can figure out the distribution in the club suit.
At this point, you can count declarer's hand to figure out how many clubs she has, or you can count partner's hand to figure out how many clubs he has. On this hand you will need both pieces of information.
Counting HCP and Winners
You can also try to count HCP. In one way, this is the perfect hand for counting HCP. You have seem all of the HCP in spades, hearts, and diamonds, and you can see the KQJ of clubs. The only missing honor is the A. Almost always you can place an ace from the bidding.
This hand is the exception. If there is a point range for partner's 4 bid, I don't know what it is. And partner, having 7-card heart support, might feel entitled to bend the rules anyway. Declarer too never declared a point range.
So you can't know who has the A.
The third domain of counting is counting tricks. Counting tricks is not important for this hand. But for the sake of exercise, if declarer has the A, you can and will get at least one club trick, which sets the contract one. You of course would like to try to get two club tricks. If partner has the A, then you would like to get three more club tricks to set the contract three tricks. Whether you are playing IMPs, matchpoints, or rubber bridge, your current goal on this hand is simply to maximize your number of remaining tricks.
Using the Count
Okay, on to underwater bridge. When you have counted the hand, you can often run a "scenario". Running a scenario is simply considering what will happen when you make one lead or another. Your natural lead is the king of clubs. Always start with the most intuitive plausible lead.
If your partner has the A, he will let your king win. You will then lead a small club to his ace.
Oh-oh. Your partner started with only two clubs. You know that from counting. Your partner will have to then lead a heart. Declarer will slough the losing club from her hand and trump on the board.
Now that you know that danger, you can see how to avoid the danger -- lead a small club to your partner's A. Your partner will return a club, and you win three club tricks. That is to say, this defense is no problem, ONCE YOU REALIZE PARTNER HAS TWO CLUBS and will be forced to give declarer a rough-and-sluff.
Of course, you don't know if partner has the A. So you need to run the same scenario when your partner does not have the A. If you lead a small club (the current candidate for best lead), declarer can win with the J on the board. Is that bad? Well, you have counted declarer's hand, you know that declarer has three clubs. So you still get one club trick. It would be completely silly to lead a small club if declarer had Ax; it would be equally silly to lead a small club if declarer had Axx and could pitch a club on a long diamond from the dummy. In other words, in both these situations, it is critical that you win one of the first two club tricks, and you guarantee that by leading the king of clubs.
But you know that declarer's third club is not going away. So you can lead a small club knowing that you will still get a club trick.
Can you do better than one trick my leading the king? Not really. Declarer wins your K with the A and leads a club towards the J. You get your queen of clubs, but the jack wins the third round.
So, by the analysis so far, leading a small club is always safe -- if declarer has the ace of clubs, you get one club trick no matter what you do -- and it gains a trick if partner has the ace of clubs.
You probably don't have time to think about the 10, but if you do.... If declarer has the A10x of clubs, you get only one club trick no matter what you lead. If declarer has A9x of clubs, declarer will probably win your K with your ace and lead to the J. If declarer decides to finesse instead for the 10, declarer is playing you to have led the K from K10x, which no one does. Anyway, even if declarer misguesses and finesses for the 10, losing to your partner, your partner is endplayed into giving declarer a sluff-and-a-ruff.
However, if declarer has A9x of clubs and you lead a small club, declarer might very well play you for K10x of clubs and finesse for the 10. Then you will get two club tricks. His alternative is to play you for the KQ of clubs, which makes sense on the bidding -- but very few people lead small from KQx of clubs. So leading small is actually the best chance for an extra trick even when declarer has the ace of clubs.
Let me summarize what happened on this hand. When you were in with your diamond winner, you could count the hand. Because you could count partner for only two clubs, you could become aware of the danger of partner having to give declarer a sluff-and-a-ruff. Because you could count declarer for three clubs and not being able to pitch any of them, you didn't have to worry that if you led low you would not get any club tricks.
More generally, because you could work out the distribution, you could do a scenario analysis. That analysis led to a different answer than produced by the head-above-water never-counted principles of play -- without counting, it is practically unthinkable to lead anything but the king, but the scenario analysis clearly reveals the value of leading a small club.