CONVENTIONS TO SEARCH SUITS AFTER 2NT OPEN

After 2nt opening (20-21 hcp balanced) Responder is the captain.
Opener Responder
 2nt       3 <= search for major suit (Stayman/Puppet/Muppet/...)
             3 <= transfer to 3 - Opener bids 4 with 4+ cards
             3 <= transfer to 3 - Opener bids 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=0/4. 4=1, 4=2, 4nt=3)
            4  <= transfer to 4
            4  <= transfer to 4
            4  <= transfer to 5
            4nt <= quantitative - Opener with 21 hcp or 5 cards suit bids Slam
            5  <= transfer to 5

1-STAYMAN
Tradicional Stayman convention to search major suit after 1nt open is also used in 2nt open.
The Responder bids 3 asking if Opener have a major suit and is he must have a 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 denies 4 cards in ;
3nt => not use anymore, but some partnership still use it to show both majors despite the modern understanding in transfer importance for strong hand receive the lead. So, Responder should not be the declarer and after 3 if Responder bid 3nt then Opener having both majors can bid 4.

SMOLEN
If Opener bid 3 Responder having 5-4 in the majors must bid his 4th card suit to invite Operner 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 bidded 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 responsability in Slam try accordingly his hand. This is a cooperative auction.

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2-BARON

This is a old natural way to search for a fit in major and minor suits. After 3 from the Responder the Opener bid his first suit in a ascending hierarchy and after Responder do the same if it is possible.

Opener  Responder
   2ST          3
3 => shows  4 (or 5) suit and can have another suit;
3 => deny 4, shows 4 and can have another suit;
3 => deny 4 and 4, shows 4 suit and can also have 4;
3ST=> shows only 4 (or 5) suit.

Opener  Responder
   2ST          3
   3            ?   3 => shows 4 suit;
                                      if Opener bid 3 then Responder com bid 3nt or 4;
                                      if Opener bid 3nt then Responder can pass or try Slam.
                         3 => deny 4 and shows 4;
                                      if Opener bid 3nt then Responder can pass or try Slam.
                        3nt => deny majors and shows 4+ and Slam interesting
                                      if Opener have also 4 - without Slam interesting
                                      the Responder don't bid 3 and bid 3nt;
                         4 => 5+ and want play 5 or 6;
                         4 => set the fit to try Slam;
                         4nt => ask for aces considering the suit.
  3             ?   3 => denies 4 and shows 4;      
                         3nt => to play - deny 4.
  3             ?   3nt => to play;
                         4 /4/4 => are cuebids - shows Slam interesting
                         4 => to play;
                         4nt => ask for aces considering the suit.
 3nt             ?   pass;
                         4 => fit in Clubs and Slam interesting;
                         4/4/4 => are cuebids and showing Slam interesting;
                         5 => to play;
                         4nt => ask for aces considering as the suit.

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3-GAROZZO

Used by the Italian Team in 60's, this convention allow to search for major and for a minors at same time, but need some 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;
 3ST => 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 clarification of 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;
  3ST => 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; 
  4ST=> means 3334 with only 4;
   5 => means 5332 with 5;
   5 => means 5332 with 5.

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4-PUPPET STAYMAN

Opener  Responder  1ST      2 <= puppet Stayman    ?  2  <= 1 or 2  majors  2  <= has 5   2  <= has 5  3nt <= no major ...... ......

Opener  Responder  1ST      2 <= puppet Stayman  2         ?  2 <= has 4 (transfer) 8-9 HCP  2 <= has 4 (transfer) 8-9 HCP 2nt <= has both majors  8-9 HCP 3 <= has 4 (transfer) GF 10+ HCP 3 <= has 4 (transfer) GF 10+ HCP 3ST<= has both majors 10+ HCP Note: some partnership use puppet with 3 GF and use 2 to find a fit for sign-off.

Opener  Responder  1ST      2 <= puppet Stayman  2        2 <= 4 mínimo   ?  2   <= sign-off  2ST <= sign-off (Opener 4)  4   <= maximum

Opener  Responder  1ST       2 <=puppet stayman  2         2 <= 4 mínimum   ?  2ST <= 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) the 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 2ST Open

Opener  Responder 2ST        3 <= puppet stayman   ?  3  <= 1 or 2 majors 4 cards  3  <= has 5  3  <= has 5 3nt  < = denies major

Opener  Responder  2ST        3 <= puppet stayman   3          ?   .....        3  <= has 4 GF   .....        3  <= has 4 GF   .....        4  <= has 4+4 GF   .....        3nt <= denies major

Note: Some partnership adopt that a non accept transfer from his partner means that the Opener have a 5th card major in the other major suit:

Opener  Responder 2ST         3 <= transfer for 3ST   <= 5=2=3=3

Opener  Responder 2ST         3 <= transfer para 3ST   <= 2=5=3=3

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

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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 we use the Smolen convention, thus Muppet is a modern Puppet modification develop to allow Smolen:

Opener Responder
 2nt       3 <= Mupet
  ?
 3 <= one or two majors
 3 <= no majors,
            then Responder bids 3 to show his 5 cards asking for 3 and
            If Opener bids 3nt that denies 3 support now Responder knowing
            that Opener has 3 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 

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