Checkback Stayman, New Minor Forcing and Fourth Suit Forcing 

Playing 2/1 system after opening at level 1 a response without jump at level 2 shows 12+ hcp and is Game Force (GF) following the principle that two hands (Opener+Responder) with strength of an opening hand should play at least game (3nt 4 4 5 5) unless misfit is found and the bidding may stop under game (3 3 4 4) - read misfit.

On the other hand if Responder bids at level 1 and Opener bids another suit at level 1 or bids 1nt we need a convention to start a GF or just to try to start a GF in the follow bidding sequences:
a) Opener Responder
     1/1   1/1
      1nt          ? <= what to bid to try GF
b) Opener Responder
     1/1    1
      1          ?  <= what to bid to try GF
c) Opener Response
      1        1
     1nt         ?   <= what to bid to try GF
d) Opener Responder
      1        1
    1/1     ?   <= what to bid to try GF       

Here we will explain 3 these conventions that are most popular by bridge players to try GF. They are:
1-Checkback Stayman (CBS)
2-New Minor Forcing (NMF)
3-Fourth Suit Forcing (FSF)

But before explain CBS / NMF / FSF let's establishe some approaches:

Supposing the bidding is without interference:
Opener Responder
 1/1   1
  1nt <= what this means?
First there are 2 classes of approaches:
- some partnerships that have 4 cards but distribution 4333/4432 prefer to inform partner that his distribution is flat bypassing the possible 1 to permit a view of shape's hand, what is very important;
- there are partnerships that prefer to bid 1 even with 4333/4432 hand.

So we use the approach that the priority is to find a fit. We should avoid bid 1nt with 4 cards in this sequence because partner could also has 4 cards and he may pass in 1nt when 2 is a more confortable contract, or worst, opponents may reopen the bidding and we missed spades fit. 
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Opener Responder
 1        1 
 1nt <= what this means?
Here there are 2 classes of approaches:
- there are partnership that bids up the line and with 4 and a major they bidding Diamonds before the major suit;
- there are partnership that follow Walsh's principle that the priority is to bid the major 4 cards even having 5+ when Responder's hand is limited up to 11 hcp, but with 12+ hcp then bids first the long Diamonds suit and after reverse bidding the major suit at level 2.
So we assume that Walsh's principle is our approach and then 1nt here may have one or two majors or no major.
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Opener Responder
   1        1 
 1/1  <= in Walsh principle this means long Clubs <=5-4 or 5-4
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Opener Responder
  1        1 major
  1nt       2 <= 4+ with 6-9 hcp - sign-off
Opener Responder
  1        1 major
  1nt       3 <= 4+ with 10-11 - invitation to game
Opener Responder
  1        1 major
  1nt       2 <= this depends on what convention we play:
                      if checkback then this searches the hand
                      if NMF this also searches the hand
                      if Responder is a passed hand this means 5+ sign-off
Opener Responder
  1        1 major
  1nt       2 <= this depends on what convention we play:
                      if checkback then this search the hand
                      if NMF this is 4+ cards  6-9 hcp and sign-off
Opener Responder
  1        1 major
  1nt       3 <= 4 cards major and 5+ Walsh with 6-9 hcp - sign-off
Opener                  Responder
  1                         1 major
  1nt                        2 <= checkback
  2/2/2/2nt      3 <= sign-off 5+ and 6-9 hcp
  pass                                 this is the way to sign-off in Clubs
Opener                  Responder
  1                         1 major
  1nt                        2     <= checkback
  3/3/3nt            4 <= sign-off 5+ and 6-9 hcp
                                          this difficult in Clubs's sign-off is the
                                          drawback of checkback to use NMF
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Opener   Responder
  1         1 major
  1nt        4 <= this shows 16+ hcp and strong Clubs support
                          asking to Opener bid his ace up the line or 5
Opener    Responder
  1          1 major
  1nt         4 <= this shows 16+ hcp and strong Diamonds support
                           asking to Opener bid his ace up the line or 5
 
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Note: When Opener supports Responder's suit with 3 cards we will use the notation: Hxx for a top honor (A/K/Q) and xxx for low cards 

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1-CheckBack Stayman is a conventions like 2 Stayman after 1nt opening that calls for 3-cards support and wheter the Opener has the other major.

Most partnerships use simple responses in checkback like:

Opener Responder
 1/1   1
  1nt       2 <= checkback searching for 3 cards or 4 cards
    ?
 2 <= denies 3 support and 4 cards with minimum
 2 <= 4 cards and denies 3 support
 2 <= shows 3 support and may also have 4 cards
2nt <= shows stoppers in unbid suits with maximum (14 hcp)
So if you will play checkback with a new partner probable this is the way he will use checkback - ask him about his checkback

Checkback convention with extension

If you have a regular partner and want to play a more eficient checkback convention with information about minimum and maximum of Opener's hand and also knowing if Opener has other major or stopper in the other major then read below:

Opener Responder
 1        1
 1nt       2 <= search for 3 cards and 4 cards - must have 10+ hcp
    ?
Opener answers are:
 2 <= 4 cards and 3 cards support - minimum 12-13 hcp
            Responder may sign-off in 2 or bidding 3 asks for Hxx to 4
            Responder bids 3 GF asking for more explanation
              Opener bids 3 with A and Hxx, bids 3 with Hxx or 3nt xxx
            Responder bids 4 is GF 16+ hcp asking for Diamond cuebid or 4
              Opener bids 4 with A or bids 4 and Responder decide
 2 <= 4 cards and denies 3 cards - 12-14 hcp
            Responder may sign-off in 2 or 2nt or 3
            Responder bidding 3 is GF asking for more explanation
              Opener bids 3nt with stoppers in Diamonds, bids 3 with Hx
              and bids 4 with 5 cards  
            Responder bidding 4 is GF 16 hcp asking for cuebid or 5
              Opener bids 4 with A or bids 4 and Responder decide
 2 <= 3 cards and denies 4 cards - minimum 12-13 hcp
            Responder may pass or bidding 3 asks for Hxx to 4
2nt <= denies 4 cards and 3 cards - shows stopper in Hearts 12-14 hcp
            Responder may pass or sign-off in 3 or 3  
            Responder bidding 4 is GF 16+ hcp asking for Ace cuebid or 5
 3 <= 5 cards and denies stopper in Hearts
 3 <= 4 + 3 - maximum 14 hcp with Hxx
 3 <= 3 with Hxx - maximum 14 hcp - denies 4 cards
3nt <= 14-15 hcp with atoppers in and possible singleton's Spades
    
Opener Responder
  1        1
  1nt       2 <= search for 3 cards or 4 cards - must have 10+ hcp
    ?
Opener answers are:
  2 <= 4 cards and 3 cards support - minimum 12-13 hcp
             Responder may sign-off in 2 or bidding 3 asks for Hxx for 4
             Responser bidding 3 is GF asking for more explanation
              Opener bids 3 with A and Hxx, bids 3 with Hxx or 3nt xxx
             Responder bidding 4 is GF 16+ hcp asking for cuebid or 5
  2 <= 4 cards and denies 3 cards - 12-14 hcp
             Responder may sign-off in 2 or 2nt or 3
             Responser bidding 3 is GF asking for more explanation
               Opener bids 3nt with stoppers in Clubs, bids 3 with Hx
               and bids 4 with 5 cards  
             Responder bidding 4 is GF 16+ hcp asking for cuebid or 5
  2 <= 3 cards and denies Hearts suit - minimum 12-13 hcp
             Responder decide and bidding 3 asks for Hxx to 4
 2nt <= denies 4 cards and 3 cards - shows Hearts stopper 12-14 hcp
             Responder may pass or sign-off in 3 or 3  
             Responder bidding 4 is GF 16+ hcp asking for Ace cuebid or 5
  3 <= 4 + 3 - maximum 14 hcp with Hxx
  3 <= 3 - maximum 14 hcp with Hxx - denies 4
 3nt <= 14-15 hcp with stoppers in and - possible singleton in Spades

Opener Responder
  1        1
  1nt       2 <= search 3 cards - must have 10+ hcp
    ?
Opener answers are:
  2 <= 3 cards with Hxx support - minimum 12-13 hcp
             Responder may sign-off in 2 - any other bid is GF cuebid
  2 <= 3 cards xxx support denies top honor - minimum 12-13 hcp
             Responder may pass with 10-11 hcp - any other bid is GF cuebid
  2 <= shows stopper in Spades and denies Diamonds stopper 12-14 hcp
             Responder bidding 4 is GF 16+ hcp asking for cuebid or 5
 2nt <= denies 3 cards and 12-14 hcp with Diamonds stopper
             Responder pass or sign-off in 3 or 3 asking for Hxx for 4   
             Responder bidding 4 is GF 16+ hcp asking for Ace cuebid or 5
  3 <= cuebid A with maximum 14 hcp and Hxx
  3 <= cuebid A with maximum 14 hcp and Hxx denies A
  3 <= cuebid A with maximum 14 hcp and Hxx denies A and A
 3nt <= 14-15 hcp with possible singleton in Hearts

Opener Responder
  1        1
  1nt       2 <= search 3 cards - must have 10+ hcp
    ?
Opener answers are:
  2 <= 3 cards Hxx support - minimum 12-13 hcp
             Responder may sign-off in 2 - any other bid is GF cuebid
  2 <= 3 cards xxx support no top honor - minimum 12-13 hcp
             Responser may pass with 10-11 hcpr any other bid is GF cuebid
  2 <= shows stopper in Spades and denies Diamonds stopper 12-14 hcp
             Responder bidding 4 is GF asking for cuebid or 5
 2nt <= denies 3 cards with 12-14 hcp with shows Diamonds stopper
             Responder may pass or sign-off in 3 or 3  
             Responder bidding 4 is GF asking for Ace cuebid or 5
  3 <= cuebid A with maximum 14 hcp and Hxx
  3 <= cuebid A with maximum 14 hcp and Hxx denies A
  3 <= cuebid A with maximum 14 hcp and Hxx denies A and A
 3nt <= 14-15 hcp with possible singleton in Hearts


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2- New Minor Forcing is a conventions like 2 checkback that asks for support of 3 cards and prioritarilly asks if Opener has the other major. If the opening is made in 1 then 2 search the hand and if the opening is made in 1 then 2 search the hand (the other minor search the hand).

Most partnerships use simple responses in NMF like:

Opener Responder
  1        1
  1nt       2 <= search for 3 cards or 4 cards - must have 10+ hcp
    ?
  2     <= shows 4 cards and denies 3 cards support
  2     <= shows 3 cards support and may also have 4 cards
  2nt    <= denies 4 and 3 cards

  1        1
  1nt       2 <= search 3 cards support - must have 10+ hcp
    ?
  2     <= shows 3 cards support
  2nt    <= denies 3 support

Opener Responder
  1        1
  1nt       2 <= search for 3 cards or 4 cards - must have 10+ hcp
    ?
  2     <= shows 4 cards and denies 3 cards support
  2     <= shows 3 cards support and may also have 4 cards
  2nt    <= denies 4 and 3

Opener Responder
  1        1
  1nt       2 <= search 3 cards - must have 10+ hcp
    ?
  2     <= shows 3 cards support
  2nt    <= denies 3 support

To read NMF extension use this link here

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FOURTH SUIT FORCING - FSF

The 4th Suit Forcing is on for sequences where Responder with 11+ hcp bids the 4th suit asking for more explanation:

a) Opener Responder          b) Opener Responder
     1         1                           1         1
     1         2 <= 4th suit        1         2 <= 4th suit

c) Opener Responder           d) Opener Responder
     1         1                            1         1
     1         2 <= 4th suit         1         2 <= 4th suit

FSF obey the follow priorities:
1- bidding responder's suit with 3 cards support;
2- bidding NT to show stopper in the 4th suit;
3- bidding the 4th suit with 4 cards in that suit/
4- bidding any natural rebid when lacking any of the above priorities.

Let's show some examples based in the bidding sequence above:

a)       Opener: K1074 532 5 AKQ105
     Responder: Q4 AK1098 Q1032 84
and the bidding is (a), so after 2 (4th suit) Opener bids 2 to show his minimum with 3 cards support and now Responder decide for a prudent trial bid in 3 and then Opener with singleton in Diamonds bids 4 with great chance in success.

b)       Opener: KQ94 102 A1098 KQ10
     Responder: 104 AK983 KJ2 84
and the bidding is (b), so after 2 (4th suit) Opener without support in Responder's suit but having good stoppers in Clubs and 14 hcp jumps to 3nt. Of course if Opener has 12 hcp with only one black Queen then Opener bids only 2nt that is passable if Responder is only 11 hcp.

c)       Opener: AJ74 2 K85 KQ1052
     Responder: Q4 A98 AQJ32 84
and the bidding is (c), so after 2 (4th suit) Opener shows 3 cards support in Diamonds. Consider that we play Walsh convention that says after 1 opening and response 1 a rebid by Opener in a major shows 5 cards the Opener's hand after support in Diamonds should be 5431 with singleton in Hearts. Conclusion Responder then jumps to 5 with great chances of success.

c)       Opener: 4 K2 KQ1095 KQ1095
     Responder: Q64 A9873 J7 A84
and the bidding is (d), so after 2 (4th suit) Opener shows his 5-5 in the minors bidding 3. Responder make a invitation with 4 that is accepted by Opener valuing this K in partner suit with great chance of success.

The exception: Bidding the 4th suit at level 1, by agreement, many partership do not consider in this sequence a GF bid but a natural bid and  just one-round force
      Opener: K1032 KQ72 5 AQ109
Responder: 9864 73 AKJ876 4
Opener Responder                  
 1         1                               
 1         1 <= natural
 2       pass             

Here the 4th suit is GF
Opener: K9 A1092 95 AQ1095
Responder: Q84 73 AKQJ87 84
Opener Responder
 1         1
 1         2 <= 4th suit GF
2nt <= shows Spades stoppers
             3nt
pass

Opener bidding the 4th suit shows a suit
Opener: 94 AJ109 9 AQ10985
Responder: KQJ4 73 AKJ8 J4
Opener Responder
 1         1
 1         2 <= forcing artificial bid - may have 4
                         because bidding 2 is not forcing
 2 <= 5+4 
             3nt
pass


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