The purpose of a hold-up play is to exhaust one defender of cards in a particular suit. This is especially true at no trump. Once one opponent no longer has cards in that suit, that opponent becomes the “safe” hand and the partner is the “danger” hand. Your challenge is to develop your tricks without allowing the dangerous hand to gain the lead. The general “rule” in NT is to hold up an Ace twice if you and dummy have only 5 cards in the suit; hold up once if you and dummy and 6 cards in the suit and don’t bother to hold up if you and dummy have 7 cards in the suit. (This rule only applies with the Ace.)
If for example, you hold Axx in spades and dummy has xx, and a 4th-best spade is led, you will generally hold up twice (taking your Ace on the third round). You hope that one opponent (presumably right-hand opponent) has no more spades by then. Do not hold up when there is a more dangerous suit to which your opponent might switch. Thus, if you hold Axx in spades and xxx in dummy and a 4th-best spade is led, but you have Ax of hearts opposite 10xx, do NOT hold-up in spades. You can not afford to have a heart switch!
When there is a dangerous hand, you must tailor your play to that fact. You will try to take finesses only into the “safe” hand. If you have two possible suits to develop, you will choose to attack the one that offers the least chance that the danger hand might get the lead. When there is a dangerous hand, you want the dangerous hand to play second if you must take a finesse—NOT fourth!
When your holding is AJx in a suit, you can consider that one and one-half stoppers. How you play the suit depends on which opponent you think is likely to gain the lead next. If left-hand opponent leads the suit and right-hand opponent plays a high honor (king or queen), you should take your Ace immediately IF AND ONLY IF you believe that left-hand opponent is likely to gain the lead next. (Your Jx is still a stopper if left-hand opponent has the lead.) If, however, you think that right-hand is most likely to gain the lead next, you should hold-up for two rounds (ducking twice) and take the 3rd round of the suit—hoping that right-hand will be exhausted of the suit (no more) by then.
When does a 1½ stopper holding become a 2 stopper holding and when does it become only 1 stopper? If you hold AJx opposite xx(x), that is 1½ stoppers in the suit. If LHO leads the King (promising Queen), duck the first trick. LHO cannot continue that suit without giving you two tricks (and two stoppers in no trump). This is called the Bath Coup. If LHO leads low (promising an honor) in no trump and RHO plays the Queen (or the King), then you must assume that the other half of the royal pair is on your left. If you must take a finesse in another suit that could lose to LHO, take RHO’s sovereign with the Ace immediately. Your Jx becomes a 2nd stopper if LHO leads the suit (as you play 4th hand). If you must take a finesse in another suit that could lose to RHO, duck the sovereign. Duck the 2nd round of that suit and take the 3rd round. You are hoping to exhaust RHO of the suit that was led. Then, if your essential finesse loses, RHO will not have any of the first suit left to lead to his/her partner’s length. (Remember, your Jx is NOT a stopper if RHO leads the suit.)
Another example of a 1½ stopper combination is the KQx in a suit. If the Ace is on your right, you always have two stoppers. If the Ace is on your left, you have one stopper—or two stoppers—depending on who gets the lead next. If LHO leads that suit and RHO plays the 10 (trying to force you to play the King or Queen), assume that LHO has the Ace. If you must take a finesse in another suit that could lose to LHO, take your King immediately. Your Qx will serve as a second stopper if LHO leads that suit again (as you are playing 4th hand). If you must take a finesse in another suit that could lose to RHO, duck the 10. Play the King or Queen on the 2nd round of the suit and pray that RHO has only two cards in the suit. If so, you will exhaust RHO of that suit and, even if the finesse in the other suit loses, RHO will not be able to lead the dangerous suit to his/her partner.
These 1½ stopper combinations are also called positional stoppers. (They are two stoppers or one stopper based on the position of the opponent who leads that suit next.) Another positional stopper is AQJ opposite xx. If LHO leads low in that suit (promising an honor), RHO will play some spot card & you take the Jack. If you have two cards that you must knock out from the opponents’ hands, take the finesse in another suit that could lose into LHO’s hand first. Your AQ remaining in that first suit is two stoppers if LHO leads the suit again. It becomes only one stopper if RHO leads the suit. If you let RHO get the lead first (perhaps by knocking out an Ace), RHO eliminates your last stopper. Then, when you must finesse into LHO (the truly dangerous hand at that point), a losing finesse means losing your contract.