Second Hand Low I

Second hand low means you go low though you could do otherwise as the second hand to play to a trick. The advisability of doing so as a general principle (though exceptions will be given) is based on a fairly elementary though pervasive principle that also underlies the finesse, the throw-in, the squeeze and a few other plays, to wit: when the honors are scattered and not solid for either side, you want to make the other side commit itself from a hand with honors before you do, insofar as you can. With that in mind, here more specifically are the reasons for going low second hand:

1. To put declarer to a guess:
K J 8 5
A 10 3 Q 7 6 4
9 2

This is a very common situation: declarer has a doubleton opposite K J. Maybe he puts the finesse off till near the end of the hand, hoping the defense will solve his problem for him and maybe he hits it quickly at trick 2 before the defense has a good grasp of his distribution. Now he leads low and . . .if West hops up, obviously declarer cannot go wrong. You must go low and put declarer to a guess, unless . . .
Yes, of course there are exceptions, and you don't want to go low mechanically. If, for instance, your ace would represent the setting trick, then you'll almost surely want to go up, lest on a duck, declarer hops up and you never get your ace. Could that lead be a singleton? Even if it is, not a few defenders have come out smelling like a rose on a duck as declarer finesses into their partner's queen and never establishes the K as a winner. In any event, there's nothing absolute here. It may be costly to go up, it may be costly to duck, but by and large you'll do well to duck and put declarer to a guess rather than solve the decision for him. And while we're on the divided A and Q in defenders' hands, we might look at this situation:

K J 8 5
A 4 3 Q 7
10 9 6 2

Here there's no right guess if the suit goes to the third round and West ducks twice. There is only the possibility that declarer will delay losing a trick in the suit one round if you duck. In trump, you can't be skunked out of your ace and would do well to duck twice. In a side suit, that is possible, of course, but if declarer hops up first round and subsequently leads toward the J, the only question is, does he have any outside winners in dummy on which to pitch the queen? If not, then either your partner has the queen and you'd do well to duck, or declarer has it and you'll get it in a trick or two.
In trump, you're safer as to whether you'll lose a good card or not:

A 8 5
J 3 K 6 4
Q 10 9 7 2

Declarer goes to his ace of trump and comes back. Going up makes sure he has only one trump loser. Go low and put him to the guess.

Here is a series of situations, in each of which going high second hand will allow declarer to bring home the entire trump suit losing only to the ace, while going low is bound to induce some wrong guesses, with the exception of Case F where there is no right guess available.

A.

5
8 6 A J 3
K Q 10 9 7 4 2

If you go low and declarer plays a high honor, he will have no more cards to lead through your jack, and hence will be forced to lead into the A J tenace. But suppose he finesses the 10 on the first round? You can only say he's made a fine play or a good guess. Going low hasn't helped you, but then it hasn't hurt you either. More important, if declarer likes to finesse the 10 on the first round, he's bound to run into cases (B) and (C) on occasion, not to mention a stiff jack, giving your side the two tricks you want.
B.
5
J 6 A 8 3
K Q 10 9 7 4 2

C.

5
J 8 3 A 6
K Q 10 9 7 4 2

In each case, you will note, declarer has a right guess open to him, much like finessing the 10 first round with Case A. In case B, declarer can go up with the K first round and play the Q, smothering the J. Which doesn't work too well with Case C, where declarer's right guess consists of going up with the K first round, and then leading a low spade to pick up East's ace. But you're putting him to a lot of guessing and one need hardly say that he's going to go wrong a fair percentage of the time.

D.

5
J 10 A 8 6
K Q 9 7 4 3 2

E.

5
J 10 3 A 6
K Q 9 8 7 4 2

D and E are complementary, much like B and C. Declarer has a right guess in each case, going up first round with the K and then either smothering the J or finding his RHO with a now bare ace. But there is one qualification here. In case E, West must falsecard with an honor, or declarer can hardly go wrong.

And lastly, in case F, there's no right guess open to declarer. Go up second hand and you hand him the whole trump suit aside from the A. Go low and he must lose two tricks:

F.

5
10 3 A J 6
K Q 9 8 7 4 2

2. You will often go low so as to preserve your honor for capturing one of declarer's honors. Here is a very common situation at the bridge table:

K 7 5
A 8 6 J 10 4 3
Q 9 2

When declarer leads toward the king, obviously he'll get by with only one loser if West hops up. But if those spot cards are low enough and West holds off, the defense stands to pick up two tricks in the suit. When the king is showing, you have to be mindful of a possible singleton and of winners in dummy in another suit, and for that matter, if dummy has trump, of an established suit in the closed hand. Nobody's asking you to follow all rules blindly. But in the long run, you're going to lose far more seeing a singleton on these leads toward a king and popping up than you will in going low and occasionally falling prey to that possibility.
But if the queen is showing and there are no established winners in dummy, there is little excuse for going up with the ace. If your partner doesn't have the king, then declarer must and that cannot be a singleton.
Sometimes going low so as to capture an honor will coincide with putting declarer to a guess:

K 9 5
A J 6 8 4 3 2
Q 10 7

With a two-way finesse for the jack, declarer might guess right and hold himself to one loser in the suit, and surely will sometimes against you. But he's got to go wrong sometimes also, playing the king on the first round, leaving you with A J sitting over the queen.

Often there will be no guess on the matter. Your partner will hold the cards that force the high honor, leaving you with that tenace over declarer's other honor if you will only go low:

K 9 5
A J 6 10 8 3 2
Q 7 4

Sometimes it is second hand low plus a lack of entries that does declarer in:

9 5 2
J 7 6 A 8 4
K Q 10 3

Obviously with two entries to dummy, declarer can pick up the whole suit, losing only to the ace, on a right guess. But if declarer has only one entry to dummy, the defense can assure itself of two tricks in the suit if East goes low on that one lead.
And note this ambiguous situation, which might exemplify either reason thus far given for going low, depending on how declarer plays the suit:

K 9 5 2
A 10 6 J
Q 8 7 4 3

If declarer leads toward his king, West must go low, assuring the defense of two tricks in the suit. The jack forces the king and West now has A 10, a literal tenace, over the queen. But if declarer leads toward the queen, picking up the jack, West winning the trick, of course, then declarer has a potential for finessing the 9 on the way back, picking up the suit except for the ace.

Going low to protect an honor for better things can assume any of a number of configurations. Here is one from play:

Q 3
9 K 10 5
A J 8 7 6 4 2

When declarer leads low from dummy, if East goes low, there is no right guess that will allow declarer to avoid a loser in the suit. Obviously he'll have to play the jack to win the trick, leaving East with the K 10 tenace over the queen. But in actual play, East, evidently with his eye on that queen, went up with the ten! Declarer played the jack and when the 9 fell, he had no problem picking up the whole suit without loss.
Declarer did have a means of picking up the suit without loss, i.e., by smothering the nine with the lead of the queen and then coming back to finesse through the 10 with the 8 or 7. But when he led low, East should certainly go low and save his 10. It might be a matter of a guess, and it might be a matter where your partner forces out a high enough card to make your holding worth a trick. But it's a poor practice to hand declarer a valuable card like a 10 when you're not taking anything with it.

Here is a situation observed from time to time:

K 10 7 5
J 4 Q 8 3
A 9 6 2

Declarer leads low from the closed hand and West goes up "to force out the king." But the queen is already doing that and it should be clear that the jack's most valuable function will be to force out the ace on the next round, making East's queen a winner. Actually, I just saw an illustration of something close to that by the computer. In the post-mortem, I wondered how declarer had avoided a heart loser, where my partner, sitting East, had J low, and I had the queen with 3 guards, dummy showing K 10 7 6. Well, my partner hadn't gone high second hand, so this is a little off topic. But what he had done was to blank his jack of hearts to save some very high diamonds which he couldn't run without getting the lead, which he had no chance of doing. That danged computer took advantage of it, dropping the jack first round and then finessing the 10.
You might note that in addition to possibly giving up a sure trick above, the retained jack might be worth a trick on this layout:

K 10 7 5
J 4 A 8 3
Q 9 6 2

Declarer could lose the king to the ace, and then come back finessing the 9.