Second Hand High and Third Hand Low (to Prevent Entries to Dummy)
You Already Know...
If you were going to learn only two rules for second-hand play, they would be "Second hand low" and "Cover an honor with an honor." These rules are designed to maximize the number of tricks that you take in a suit. For example, suppose declarer is leading towards Qx in dummy, and you have the ace. Perhaps it will not matter whether or not you play your ace. For example, declarer might have Kx. But if it does matter, and your only goal is to take as many tricks in this suit as possible, you should play low. For example, declarer might have Kxx.
Sometimes, though, your goal is to minimize entries to the third hand. For example, declarer might have a long suit set up in dummy and need an entry to dummy. Or declarer needs two entries to dummy, one to set up a long suit and a second to cash the winners in that long suit.
When the only goal is minimizing entries to the third hand, the two rules for second-hand play are completely reversed. If an honor is led, you play small; if a small card is led, you play an honor.
Two-card Combinations in Declarer's hand
I will assume in all my examples that declarer is leading, you are playing second, and you want minimize entries to dummy. First, suppose declarer has Kx of a suit and dummy has Qx(x). If declarer plays the king, you play low -- don't cover an honor with an honor. That one is probably easy to see. If declarer plays small, you play your ace -- play an honor on a small card. Then declarer has no entry to dummy in this suit.
If declarer has Qx doubleton and dummy has AJ(x) and you have the king, you can't stop the ace from being an entry. If declarer leads the queen and you do not cover, declarer might get three tricks in this suit, but declarer will have only one entry to the dummy. (However, declarer will get only one trick in this suit if declarer finesses the second round and your partner has the king, so the second finesse is dangerous.) And if declarer plays small from hand, then you have to insert your honor to prevent two entries to dummy.
Of course, if the situation is Qxx opposite AJx, then you give up a trick when you play your king on a small card or when you do not cover the queen. That is the whole reason for the standard rules -- second hand low and cover and honor with an honor usually maximizes the number of tricks you can take in a suit. When you reverse the rules, you might be giving up a trick, but you are always preventing all of the entries that you can.
Finally, suppose declarer has Jx in declarer's hand and K10(x) on the board. You have the queen. If declarer leads the jack, you play low, and if declarer plays low, you insert the queen. Declarer wins one trick but does have an entry to dummy.
Upon reflection, the reason for reversing the rules can be seen. On the last combination, the king is not an entry to board because partner has the ace; the real threat is the 10. But declarer can lead the suit only twice. The 10 cannot win the trick when declarer plays the jack, and if you play the queen on the other trick, the 10 cannot win that trick either. You in a sense are using declarer's jack, together with your queen, to stop the 10 from winning a trick.
Your efforts will not work if the threat on the board is larger than the honor in declarer's hand. If declarer leads small towards AJx, you can insert your king and hope declarer has Qx. But if declarer leads small towards AQx, you accomplish nothing by playing your king. Or suppose declarer has Qx in hand and Kxx on the board. Declarer could lead the queen, hoping that the defenders will win their ace. But declarer's only straightforward play is to lead towards the king hoping the ace is onside. If declarer actually has Qxx opposite Kxx, you are simply giving up a trick when you don't take the queen with your ace.
If declarer is leading to Kx(x) and you have the queen, don't reverse the rules. The only threat on the board is the king. You can't stop the king from winning, that's up to partner. You reverse the rules only to smother the threats on the board that are smaller than your card.
Three card positions (and even four-card positions) follow the same reversed rules -- to minimize entries to third hand, second hand ducks an honor and plays an honor when a small card is led. For example, this position came up for my partner recently. My partner had Q10x sitting in front of the dummy's K9x. A suit was ready to run in dummy. Partner had to hope I had the ace, and in fact I did. Declarer led the Jack, and now all the relevant cards are known, the only problem is knowing what to do. Holding both the queen and the 10, it was natural for my partner to cover the jack. Declarer, holding Jxx of the suit, now had an entry to dummy in the nine. My partner should perhaps have laboriously worked out the position. But he could have also followed my very simple principle and not covered the jack.
What if declarer had led a small diamond? Playing low is a knee-jerk response, so most players will not stop to work out the full position. But my partner knew that the goal was to prevent an entry to the dummy. Knowing my rules, that should at least suggest the thought of playing the 10. (Or if he is not going to play the 10, at least stop to laboriously verify that that is the right play.)
There are too many three-card positions to try to list. As far as I know, reversing the rules can sometimes cost a trick but always minimizes entries to third hand. Suppse declarer has A10x on the board and you have Qxx(x). If declarer has Jxx and leads the jack, you lose a trick if you do not cover. But assuming your partner does not win the jack with the king, the board still has just its one entry. And if declarer leads low from Jxx, inserting the queen costs a trick but not an entry. However, suppose declarer has KJx and intends to finesse you for the queen. Now, reversing the play of your queen -- not covering the jack and inserting the queen when declarer leads a small card -- does not cost a trick, but it prevents a second entry to dummy.
It's a little more obvious if you have KQx(x) in front of dummy's A10x and declarer leads the jack -- don't cover. If declarer leads small, you have to play the queen if declarer has Jxx. If dummy has A108, declarer has Jxx, and you are sitting in front of dummy with Q9x(x), declarer can always get two tricks but you can hold dummy to one entry by not covering the jack and by inserting your queen when declarer leads a small card.
Putting this into Practice
How do you know if declarer needs entries to dummy? One clue that dummy doesn't have entries in other suits. The other clue is a need to be in dummy. Perhaps declarer wants extra entries in dummy to take successful finesses; sometimes declarer wants to get to dummy to ruff a suit in hand in preparation for a trump coup. The problem in those situations is balancing the need to reduce entries to dummy with a desire not to give away extra tricks by reversing the rules.
But anyone can tell when there is a long suit in dummy and declarer desperately needs entries to set up the suit and/or just cash the winners. If there is a potential threat in dummy that you might be able to smother with the help of declarer's high cards, then simply reverse the rules for second hand play.