SECOND BID FROM RESPONDER AFTER 1NT

Opener Responder in a free auction (no interference)
1/1    1/1
  1nt           ?

After 1nt Opener's second bid in 1nt limits his hand in a range of 12-15 hcp, and the possible distribution are:  4333  4432  5431 (also 5422), so now Responder must show his strength between:
1- biding sign-off having 5-9 hcp;
2- make a invitation with 10-11 hcp;
3- start a Game Force (GF) with 12+ hcp.

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1- sequences of sign-off:
1.1. The rebid of Responder suit is 100% sign-off and could be done with 5-9 hcp.
Opener Responder  Opener Responder  
 1/1     1             1/1    1
   1nt          2              1nt        2
  pass                          pass

1.2. A second bid in a less hierarquical suit could be not NMF or a search for support but just a sign-off
Opener Responder  Opener Responder     
 1/1   1               1        1                        
   1nt       2*             1nt        2 (5+ cards-not NMF) 
  pass                         pass
* If Responder was interested in game he should bid new minor forcing (NMF) so 2 could be bided with 5-9 hcp and Opener must choise in pass or correct to 2 and with 3-2 in major Opener can pass if don't has honor in Spades - there is a chance that Responder have also 5 cards.
Note1: In the sequence 1 - 1 - 1nt - 2 is NMF but 2 is sign-off showing 5+ cards, so here Opener has no preference for Spades unless Opener has singleton in Diamonds.  

1.3. simple raise in Opener suit shows a sign-off and shows 5-9 hcp in Responder's hand.
Opener Responder Opener Responder  
   1       1             1          1
   1nt       2             1nt         2
  pass                    pass  

Opener Responder Opener Responder  
   1        1            1          1
  1nt         2            1nt         2
 pass                        pass

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2- Invitations sequences:
2.1. When Responders's rebid in jump to level 3 shows a 6th suit with 10-11 hcp and ask for support or pass from Opener. So Opener pass with minimum or only 2 blank cards. Opener bid of 3nt could be a disaster if has only 2 cards and minimum. Opener with good 13 hcp or 14 hcp and 3 cards or honor second must bid game.
Opener Responder Opener Responder  
 1/1   1             1/1    1
  1nt        3               1nt        3
     ?                             ?
Now is the Opener that decide if goes to game or pass:
2.1.1 pass with singleton always
2.1.2 pass with dubleton and minimum 12-13 hcp
2.1.3 bid 3nt with honor second and 14/15 hcp
2.1.4 support Responder's suit with 3 cards and 13-14 hcp.
Note2: in this avaliation it is important A or K to decide for game, hands with many Queens and Jack is danger for bid game with 23-24 hcp.

2.2. The jump in level 3 in a less hierarquical suit shows 5-5 hand with 10-11 hcp in 2/1 system but is GF in SAYC, so to be GF
Opener  Resp   Opener Resp   Opener Resp 
 1/1   1       1       1        1       1
   1nt       3       1nt       3        1ST      3
     ?                      ?                       ? 
Opener Resp or Opener Resp   
  1        1          1        1
 1ST       3          1ST       3
   ?                         ?
Now Opener decide if goes to game or pass or sign-off in first suit:
2.2.1 pass with 3 cards and minimum 12/13 hcp - bad support
2.2.2 simple preference with minimum and bad support
2.2.3 bid game in level 4 or game in level 5 with honors good support
2.3.4 support minor in level 4 is invitation
2.3.5 bid 3nt with maximum 14/15 in hand 5422 and honors in Responder suits.

2.3 jump at level 3 in Opener suit shows 10-11 hcp with 4+ cards
Opener Responder      Opener Responder 
   1      1                     1        1
  1nt      3 invitation     1nt        3 <= 10-11 hcp
    ?                                    ?  

Opener Responder      Opener Responder
   1      1                     1        1
  1nt      2 invitation     1nt       3 <= 10-11 hcp
    ?                                ?

2.4 raise to 2nt showing 11 hcp
Opener Responder      Opener Responder   
1/1   1                    1/1   1
 1nt      2nt invitation     1nt      2nt invitation 11 hcp
   ?        with 11 hcp        ? 

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3- Sequences that can be FG / Slam:
3.1 The New Minor Forcing (NMF) need 10+ hcp and the major can be 5th or 6th asking for 3 cards support. It is fundamental read NMF.
Opener Responder     Opener Responder   
  1      1                    1         1
 1nt      2 => NMF      1nt        2 => NMF
   ?                                 ?  

Opener Responder    Opener Responder   
  1        1                 1         1
 1nt        2 => NMF   1nt        2 => NMF
  ?                                ?

3.2 The Responder's second bid in reverse is GF:
Opener Responder or Opener Responder   
  1       1                    1         1
 1nt       2 => GF         1nt        2 => GF
   ?                                  ?  

3.3 The raise to Opener minor at level 4 ask to Openr cuebid and shows strong support and Slam interesting:
Opener Responder  Opener Responder   
  1        1                 1         1
 1nt        4 => GF      1nt        4 => GF
   ?                                 ?  

Opener Responder  Opener Responder   
  1        1                   1        1
 1nt        4 => GF         1nt        4 => GF
   ?                                  ?
 
Note3: If the Opener's second bid at level 1 is other suit then the 4th suit bid by Responder is FG, include 1 after 1 pass 1 pass 1 now the 1 not shows 4 cards but ask for stopper in Spades or support in Diamonds so Opener whitout stopper or support must rebid his Clubs suit. 
Thus, Responder to show 4 cards in Spades need bid 2 that's also a GF!
Opener Responder      Opener Responder   
  1        1                     1        1
  1        1 => GF          1        2 => reverse 5-4-x-x
   ?                4th suit       ?
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