2NT OPENING
The 2NT opening obey the same discipline of the 1NT opening and so should be balanced 4333 4432 5332 and always must have at least 3-2 in the majors. Therefore, with 5422 the hand is recommended to be open in the 5-cards suit even with 20-21 hcp.


2NT Responses to Search for Fit

After 2NT opening Responder is the captain.
Responder Opener
                   2NT     
3
<= search for major suit (Stayman/Puppet/...)
3
<= transfer to 3 - Opener bid 4 with 4 cards
3
<= transfer to 3 - Opener bid 4 with 4 cards
3
<= Stayman for minors
      Opener bids 3NT = no minors
      Opener bids 4
= 4+ cards
      Opener bids 4
= 4+ cards
3NT <= to play
4
  <= Gerber asking for Aces
4
  <= transfer to 4
4
  <= transfer to 4
4
  <= transfer to 5
4NT <= quantitative -
       Opener with 21 hcp or 5332 bid 6NT
5
  <= transfer to 5
6NT<= 13-15 hcp balanced
7NT<= 16+ hcp balanced

1-STAYMAN after 2NT
Traditional Stayman convention to search for major suit after an opening of 1NT is also used in the opening of 2NT.
The Responder bids 3
asking if Opener have a major suit and this shows that Responder has major to bid 3. Opener has only 3 answers:
Opener Responder
  2NT       3

   ?
3
=> no major suit;
3
=> 4 means 4 cards and can have also 4 cards;
3
=> 4 means 4 cards and deny 4 cards;
3NT => not use anymore, but some partnership still uses it to show both majors despite the modern understanding in transfer importance for strong hand receive the lead.
So, Responder should not try to be the declarer and after 3
if Responder bids 3NT then Opener having both majors can bid 4.

SMOLEN after Stayman
If Opener bid 3
Responder having 5-4 in the majors must bid his 4th card suit to invite Opener be the declarer in his 5th card suit if declarer has 3 cards.
Opener  Responder
   2NT       3
       
   3
           ?  
                 3
= QJxxx Kxxx xx Qx
                 3
= Qxxx Kxxxx xx xx
 
Trying Slam after a implicit fit is found:
Opener   Responder
  2NT       3
  <Stayman
 3
/3   4/4 <= bidding a minor is a cuebid showing support in the major bided by Opener and 10-11 hcp and Slam interesting.
In this case Opener must evaluate his hand:
- Opener denies good hand to Slam when rebids his suit and transfer to Responder the decision to continue;
- Opener bids another suit take the responsibility in Slam try accordingly his hand. This is a cooperative auction.

2-GAROZZO

Used by the Italian Team in 60's, this convention allow us to search for major and for a minors at same time, but not allow 5 card major in 2NT opening and need good memorization:

Opener  Responder
  2NT      3
=> ask for suit distribution
    ?
   3
=> shows 1 or 2 majors - denies minor;
   3
=> shows 4 and a minor suit;
   3
=> shows 4 and a minor suit;
 3NT => shows 1 or 2 minors suit and denies major;

After Opener's second bid Responder can sign-off the bidding in a major game / 3NT / or ask for clarify more the hand bidding a relay (next suit).

Opener  Responder
  2NT      3
=> ask suit distribution
   3
       3 => relay for clarification of distribution
    ?
   3
=> 4333 with 4;
  3NT => 3433 with 4
;
   4
=> 4423 with 4=4=2=3;
   4
=> 4432 with 4=4=3=2;

Opener  Responder
  2NT      3
=> ask suit distribution
   3
        3 => relay ask minor suit 3NT => means 4-4
   4
=> means 4-4 allow open be the declarer
 
 Opener  Responder
  2NT      3
=> ask suit distribution
   3
        4 => relay ask minor suit
   4
=> means 4-4
   4
=> means 4-4 with Ace
   4
=> means 4-4 denies Ace

 Opener  Responder
  2NT       3
=> ask suit distribution
  3NT       4
=> relay ask for the minor suit
   4
=> means 3343 with only 4
   4
=> means 2344 with 2=3=4=4;
   4
=> means 3244 with 3=2=4=4
  4NT=> means 3334 with only 4
;
   5
 => means 5332 with 5;
   5
 => means 5332 with 5.

3-PUPPET STAYMAN

An opening in 1NT or in 2NT normally don't give a simple way to Responder search for 5-cards major suit (5332). Thus, the "puppet Stayman convention" was developed to resolve this problem.

This convention was published in April/1977 in Bridge World where Christopher Woolsey and Steve W. Robinson talk about the idea of Neil Silbermann from New York in use Five Card Stayman for search 5-cards major suit after Notrump opening.

In 1978 Jeff Rubens, Bridge Word's editor, in a complementary publication used the name Puppet (doll that is manipulated by hands or strings - marionette) for this convention.

So this convention can be used after 1NT or 2NT opening but is usually used only in 2NT opening to search for a 5-cards major.

Puppet Stayman after 1NT opening
Not recommended for 2/1 system
Opener Responder
 1NT      2
<= puppet Stayman
   ?
  2
  <= 1 or 2 majors
  2
  <= has 5 
  2
  <= has 5
 2NT <= no major 15 hcp
 3NT <= no major 17 hcp
--------------------------------
Opener  Responder
 1NT      2
<= puppet Stayman
 2
          ?
             2
  <= has 4 (trf) 8-9 HCP
             2
 <= has 4 (trf) 8-9 HCP
            2NT <= has both majors  8-9 HCP
             3
  <= has 4 (trf) GF 10+ HCP
             3
  <= has 4 (trf) GF 10+ HCP
            3NT<= has both majors 10+ HCP
Note: some partnership use puppet bidding 3
GF and use 2 to find a fit for sign-off. But this loses part of level 3 that we use to bid when Responder has 4-5 or 5-5 minors suit
------------------------------------
Opener Responder
 1NT      2
<= puppet
 2
        2 <= 4 minimum
  ?
 2
 <= sign-off if Opener has 4
 2NT <= sign-off (Opener has 4
)
 4
 <= maximum 
--------------------------------------
Opener Responder
 1NT      2
<=puppet
 2
        2 <= 4 minimum
  ?
 2NT <= sign-off (Opener 4
)
 3
 <= sign-off
 4
 <= maximum
-----------------------------------

Searching for a good sign-off:
Considering Opener has only 3 bids possible (2
/2/2) Responder having a very weak hand with a distribution type: 5-4-3-1 or 5-4-3-1 or ideally 5-4-4, 6-4-3, 6-4-3 should bid Stayman and pass in Opener second bid.

Puppet Stayman after 2NT opening
recommended for 2/1 system
Opener Responder
2NT      3
<= puppet Stayman
  ?
 3
 <= 1 or 2 majors 4 cards
 3
 <= has 5
 3
 <= has 5
3NT < = denies major
--------------------------
Opener Responder
 2NT       3
<= puppet Stayman
  3
          ?
  .....        3
 <= has 4 GF
  .....        3
<= has 4 GF
  .....        4
 <= has 4+4 GF
  3NT <= denies major   

Note: Some partnerships have a convention that a non-accept of the transfer from their partner means that the Opener has the other major with 5 cards:
 Opener Responder
2NT       3
<= transfer for 3
3NT <= 5
=2=3=3
---------------------------------
Opener Responder
2NT       3
<= transfer para
3NT <= 2
=5=3=3♣ 


In principle, after the Opener clarify his hand, the captain to bid the final contract is the Responder.

MUPPET
As we see in Puppet convention there are no room to Responder shows a hand with 5-4 in the majors like in Stayman conventions where we use the Smolen convention, thus Muppet is a modern Puppet modification develop to allow Smolen:

Opener Responder
 2NT      3
<= Muppet
  ?
 3
<= one or two majors
 3
<= no majors, then Responder bids 3 to show his 5 cards asking for 3 support and If Opener bids 3NT that denies 3 support if Responder has 5-5 and knowing that Opener must have 3 cards may bid 4 with 5+ cards
 3
<= 5 cards - Responder with 3+ bids 4 or cuebid for try Slam
3NT <= 5
cards - Responder with 3+ bids 4 or cuebid for try Slam 

Note: Opening in 1NT or 2NT must have 3-2 in the major’s suit – by convention it is forbidden an opening in NT with 2245 or 2254

Example:
Opener:
Ax AJx KQJx AQ74
Responder:
Qxxxx Kxxxx xx x
Opener Responder
2NT        3
<= Muppet Stayman
  ?
 3
 <= no major
 ………… 3
ask for support of 3 cards
3NT <= doubleton in Spades
…………. 4
sign-off - Opener will receive the lead
pass

So, Muppet is recommended for regular partnership

-----------------------------
2NT AFTER RESPONSE 3 (both minors)
Considering that Opener does not know how strong is Responder we need establish a minimum strength to Responder bid 3
.

Rule#1 - Responder bidding 3 promises both minors suit with a minimum strength of 10 points (hcp + length) in the following distributions: 5-4=+1, 5-5=+2, 6-4=+2, 6-5=+3 
4
-4=> 10+ hcp;
5
-4 or 4-5=> 9+ hcp;
5
-5=> 8+ hcp;
6
-4 or 4-6=> 8+ hcp;
6
-5 or 5-6=> 7+ hcp;
All these strength are eligible to try slam.
But Opener bidding 3NT denies minor suit.
Opener Responder
 2NT      3
<= 10+ points
 3NT        ?
            pass <= less than 11 hcp
             4NT <= 11-12 invitation
             6NT <= 13-15 hcp
             7NT <= 16+ hcp                

Rule#2 – In case Opener have Ace in both majors and support with 2 top honors in a minor could Opener can take charge of the bidding asking for keycards with RKB1430 including both minors King bidding 4 with implicit agreement for Clubs / bidding 4 with implicit agreement for Diamonds:
-----------------
CLUBS AGREEMENT
Opener Responder
 2NT     
3 <= both minors
  4
<= RKB1430 for Clubs for
             6 Keycards 4A+2Kminors
.………   ?
……….  4
<= 1 Keycard
………. 4NT <= 3 Keycards

………. 
5 <= 2 Keycards no Q
……….  5
<= 2 Keycards with Q                 

After Response in
4 = 1 Keycard
Opener sign-off bidding
5 or
ask for Queen bidding 4NT
 
4NT     ?
………. 
5 <= no Q
……….  5
<= Q   
……….  5
<= Q + Q  

After Response in
4NT = 3 Keycards
Opener ask for Queens bidding 5

  5
      ?
………. 
5 <= no Queen
……….  5NT <= Q
   
……….  6
<= Q + Q  
-----------------------------
DIAMONDS AGREEMENT
Opener Responder
 2NT     
3 <= both minors
  4
<= RKB1430 for Diamonds
             6 Keycards 4A+2Kminors
.………    ?
……….  4NT <= 1 or 4 Keycards
……….  
5 <= 3 Keycards
………. 
5 <= 2 Keycards no Q
……….  5
<= 2 Keycards with Q                

After Response in
4NT = 1 Keycard
Opener sign-off bidding
5 or
ask for Queen bidding 5
 
5      ?
………. 
5 <= no Q
……….  5
<= Q   
……….  5
<= Q + Q  

After Response in 5
= 3 Keycards
Opener ask for Queens bidding 5

  5
      ?
………. 
5 <= no Q
.......  5NT <= Q

……….  6
<= Q + Q  

Rule#3 – If Opener bid 4 with 4+ cards in Diamonds, or bid 4
with 4+ cards in Clubs (could also have 4 cards in Diamonds) Responder bidding a major 4 or 4 shows a splinter and inquiry Opener if hand fits.
So, Opener may bid 4NT 1430 for minor agreed if hand fits or may sign-off bidding the agreed suit. Responder bidding agreed suit makes also a sign-off denying singleton/void.
Opener Responder
2NT
     
3 <= both minors
4
/4 <= make agreement
……….   ?
……….  4
/4
<= shorter suit
……….  5
/5 <= sign-off
……….  4NT <= RKB0314

   
                  

Rule#4 – For the very rare situations after Responder bids
3 showing both minors if Opener bids 3NT if Responder jump to 5 showing two weak minors less than 6 hcp in distribution 5-5 or 6-5 Opener must pass or correct to 5 with same length in both minors.
Opener Responder
2NT
      
3 <= both minors
3NT       5
<= pass or correct
  ?
 5
       pass
pass

 
2NT opening and Responder has 5M-(4/5)m

Rule#5 - After 2NT opening if Responder has 5Major-(4/5)minor with a minimum of 10 points 5M-4m with a minimum of 9 hcp or 5M-5m with a minimum of 8 hcp and 5M-6m with a minimum of 7 hcp) Responder should make transfer for the major and after for the minor. In case Responder has less than 7 hcp he should transfer only for the major and bid 3NT. 

Rule#6 - After 2NT opening if Responder shows 5M-(4/5)m Opener 4NT is RKB1430 including the 2 Kings of Responder’s suit.
Opener Responder
 2NT       3
/3 <= transfer
3
/3    4/4 <= 5M-(4/5)m
 4NT <= RKB1430 6 steps (4A+2K+2Q)
…………  
?
………. 
5 <= 1 or 4 Keycards
………. 
5 <= 3 Keycards
………. 
5
<= 2 Keycards no Queen
………. 
5 <= 2 Keycards + Qminor                 
………
. 5NT <= 2 Keycards + QMajor
……….  6
<= 2 Keycards + 2Queens

Rule#7 – In case Opener accept to play in the major showing 3 cards support then Responder might continue the bidding with 11+ hcp and first/second control in the other unbid suits bidding 4NT RKB0314 to try slam. Of course, the bidding may stop in the agreed major at level 5. 

 

AGAINST 6NT THE LEAD UNDER A QUEEN ISN’T NORMAL

This interesting hand occurs many years ago and was correctly interpreted. When the strong hand is playing a contract in 6NT we should avoid a lead under an honor like Queen unless the bidding shows a long suit in dummy without explicit support.
                   North       South West North East
                  
K102      2NT   pass  4NT* pass
                  
J8           6NT    all pass * quantitative 
                  
KJ83       Contract: 6NT Declarer: South
                  
K52         Lead from West: 10                  
   West                    East    
 Q86           N     9753    
 Q1095    O    E   7642
 Q76           S     854    
 Q63                    974
                   South
                  
AJ4
                  
AK3
                  
A102
                  
AJ108
Analyses: After 2NT opening (2021 hcp) North with 11 hcp may try slam. North has no Aces and the bid to search Aces after 2NT is 4
Gerber, but North has 3 Kings and so Opener should have at least 3 Aces.  Then, North makes an invitation to 6NT bidding 4NT because 6NT needs 32-33 hcp to make with his balanced hand. The invitation was accepted by South with 21 hcp and 4 Aces and 2 tens that are important middle card for finesse. If South has 20 hcp but has also a 5-card suit with 4 Aces (value 17 hcp) he should accept the invitation.

West has the 4 Queens and not has a solid lead and then chooses his best lead in
10. After 10 if dummy has J8xx normally Declarer play low hoping find a Qx with East but dummy with J8 force Declarer to play the J that for declarer surprise makes the trick. Declarer then plays Diamond to his A in second trick and another Diamond to finesse with success the Q. In trick 4 Declarer plays Clubs to his A. This is an incorrect play because when missing Q9xx the finesse should be made against East having AJ108. Against West this works only if Qxx or Qx, but Declarer was playing supposing West with 3 or 4 Queens at this moment. So, Declarer plays Q and let run to make the tricks. After play A and K both suits divide 3-3 and Declarer claims 13 tricks without the need to finesse Spades.

Understanding what is going on table is fundamental for good hand play!

 

Searching minors after 2NT – try for slam

                 North               South West North East
                
1042              2NT   pass   3*   pass
                
8                     4     pass   6 all pass 
                
KJ983               Contract: 6
                
AQ52                 Declarer: South
   West                    East       Lead from West:
Q
 Q863        N      975      * Stayman for minors
 QJ109  O      E   K7642
 76             S      Q54  
 643                    97
                 South
                
AKJ
                
A53
                
A102
                
KJ108
Analysis: After 2NT opening North with 10 hcp and a singleton consider his hand not adequate to play in NT due to his singleton that will upgrade the hand in 3 points in case a fit is minor is found. So, he asks opener for a 4-cards minor bidding 3
. South despite his 4333 can’t deny his Clubs suit and bid 4. Now North sigh-off the bidding in 6. West leads his natural Q and South was pleasure in been playing this slam.

Declarer makes the A
Q Play J and after Clubs to the A. receiving the information of trump 4-1. So, now Declarer must first establish the minors’ suit before drawing the last 2 trumps. When a fit has 9 cards like 6-3 or 5-4 probability table recommend a play for A and K in Diamonds. Culbertson in his pseudo symmetry law recommended to play for 3-1 the 9 cards fit missing the Queen always there is a singleton or void in one hand. This is the case here and Vacant Places after Clubs be 4-1 shows 12 places in East against 9 places in West to have the Q. That means 9/21 vs 12/21 or 3/7 vs 4/7 or 43% x 57% in favor of the Q finesse. So, Declarer plays low Diamond from dummy and serve the 10 making the trick to now ruff a Hearts in dummy and play 2 times trump to claim 7.       

Bottom Line: In popular conventions for searching for major suit after 2NT opening the Muppet is the modern convention used by advance players, but 98% use Stayman or Puppet. The forgotten Garozzo’s convention, like Stayman, doesn’t allow Responder to ask for 5-card major, but of course it is better than Stayman because can search all Opener’s hand. The search for slam in minors needs some agreements by partnership.