When partner opens a major and we have an opening bid with four card support, a popular gadget is the Jacoby 2NT raise. This is aimed at discovering whether we may have slam. Two types of hands do not employ Jacoby: with only three card support, bid a suit before supporting partner -- the fourth trump can be crucial for slam. With a (small) side singleton and about 11-14 hip, make a splinter raise.
Over 2NT, opener typically shows a (small) singleton, if any; or rebids 4 of the major, 3NT, or 3 of the major with hands of increasing strength. The four bid suggest 11-13 hcp; 3NT suggests 14 to 15 or a good 13, and three of the major suggests 16+ or a good 15 with extra playing strength.
Examples:
1H-2NT KQ6 KJ9754 83 K5 rebid 4H, minimum with no singleton
1H-2NT A106 KJ1097 3 K532 rebid 3D, showing the singleton
1S-2NT KQ9732 A63 86 A63 good 13, rebid 3NT
1S-2NT AQ985 AJ J872 A5 16+, rebid 3S
As responder, you have the following hands; after responding 2NT, what is your rebid? (You may want to cover the comments which follow while you select your bid.)
(A) 1H-2NT; 3D-? 985 AQ62 A10765 A
(B) 1S-2NT; 3S-? J742 K8 AKQ10 K103
(C) 1H-2NT; 3S-? A6 Q763 KJ742 A3
(D) 1H-2NT; 4H-? K102 J873 K53 AK2
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(A) Excellent singleton! Bid 3H, hoping partner can control-bid 3S. After that you can use 4NT.
(B) 16+16+big fit should be slam; 4NT will reveal all. But you actually have a poor hand to be asking; perhaps a better plan would be to control-bid 4D. You know partner has no control there; covering that suit might prompt 4NT from the proper side. If not, you can fall back on 4NT yourself.
(C) Partner's singleton only covers one loser, but you still have a fairly good hand. Keep the ball rolling with 3NT. Given the known 9 card major fit, this is not a suggestion to stop there, it merely suggests the singleton wasn't wonderful but if partner has extras you have some useful cards for slam.
(D) Pass.
Complete pairs of hands and possible auctions:
A106 985
KJ1097 AQ62
3 A10765
K532 A
1H 2NT
3D 3H
3S 4NT
5H* 6H *2 key cards no queen; or 5D = 1 ace
AQ985 J742
AJ K8
J872 AKQ10
A5 K103
1S 2NT
3S 4D
4NT 5D* * 1 or 4 key cards; or 1 ace; 1430 bid 5C
6S
5 A6
AJ8542 Q763
A65 KJ742
K54 A3
1H 2NT
3S 3NT
4H pass
QJ9 K102
KQ964 J873
A92 K53
103 AK2
1H 2NT
4H pass
