AFTER 1NT OPENING RESPONSES AT LEVEL 3 IS RESERVED TO SHOW 2 MINORS SUITS WITH 10-14 HCP HAVING DISTRIBUTION 5431 OR 5521 


CONSIDERATIONS: When partner opens in 1nt 15-17 hcp and we have both minors in 5422 (no singleton) with a limited hand of 10-14 hcp the chances for Slam are few. So, unless we have cards in sequence in both suit making it solid (KQJ108 or AQJ109), it is recommended that we bid directly 3nt to sign-off the bidding and not try to find a better contract in a minor suit at level 5 that also could help opponents find the best lead for defense.

Even when our partnership has no stopper in a specific major the chances of this suit be divided 4-4 (33%) is significant. Thus only when there is a singleton in a major that is a threat for our 3nt contract and so we should inform partner about our singleton. On the other hand out singleton, like in a splinter, may improve the chances for a Slam with less high cards points needed.

So when Responder's hand is 5521 or 5431 with 10-14 hcp Opener should be inform by Responder about his shorter major suit. However the information about what minor is 4 cards or 5 cards it is not so revelant than the information of what is the singleton suit.

Rule#1: After 1nt opening in any position all suit bidded by Responder at level 3 shows a singleton major with minors 5-4 or 5-5:
Opener Responder
 1nt       3
  <= 31??  <= 54 or 54 with singleton Hearts
             3  <=
13??  <= 54 or 54 with singleton Spades
             3
  <= 2155 <= singleton Hearts
             3
  <= 1255 <= singleton Spades 

Note: If Responder is a passed hand his range must be 10-11 hcp, but if he is not passed then his range should be 10-14 hcp.

Let's establish some bids conventions to search more information in  Responder's hand making to Opener the principal captain of the final contract.

Opener should first observe if hands fits (Axx - x  or Jxx - x). In case there are wasted honors like in KQx - x in Responder's singleton and the 1nt opening is minimum it is the case to stop the bidding in a partial score of
4/4. But if hands fits and Opener has good 4 cards support for one of Responder's minor then Opener it is the case that Opener should take charge and search Responder's hand for maximum or minimum. But what is a maximum? Can we establish a criterion to help our decision? Let's propose 2 ways to search Responder's hand:

Rule#2: The singleton suit can't have A or K as singleton card. If it has a Ace or King singleton then this hand should not be use to jump to level 3 to show his singleton.

A) When distribution is 5521 (and hands fits) we may count
A=2 controls and K=1 control to search hand's strength. Then if Responder's hand has 5+ controls (2A+1K or 1A+3K) we may consider his hand as maximum else as minimum. Of course Queens are very important and together with jacks they make the hand more solid, but here we are limited only in emphasize the possession of the Aces and Kings.

Opener also may avaliate his hand by this criterious and for a maximum hand we should consider 7 controls (3A+1K or 2A+3K or 4A). But as we restricted the range of Responder's it is more easy to Opener search Responder hand than the oposite.

Opener controls examples:
a)
Axx Kx AJx AJ98x  = 3 A + 1 K = 7 controls => maximum
b)
AJx Qx Kxxx AKxx = 2 A + 2 K = 6 controls => minimum
c)
AKx 9xxx Kx AKxx = 2 A + 3 K = 7 controls => maximum
d)
KJx KJx KJx KQxx  = 0 A + 4 K = 4 controls => minimum
e)
Ax Axxx Axx Axxx = 4 A + 0 K = 8 controls => maximum
f)
QJ09 QJx KQx AQx = 1 A + 1 K = 3 controls => minimum
g)
KJ10 AJx AJx Qxxx = 2 A + 1 K = 5 controls => minimum 

Responder controls examples:
h)
Ax x K10xxx KQJxx = 4 controls => minimum
i)
Jx x KJxxx AK9xx     = 1 A + 2 K = 4 controls => minimum
j)
xx x KQxxx KQJxx    = 0 A + 2 K = 2 controls => minimum
k)
x Qx AKJxx K9xxx   = 1 A + 2 K = 4 controls => minimum
l)
x Kx AJ9xx AQxxx    = 2 A + 1 K = 5 controls => maximum
m)
x Qx KQxxx AQJxx  = 1 A + 1 K = 3 controls => minimum
n)
x Axx AJ10xx Kxxxx = 2 A + 1 K = 5 controls => maximum 

Rule#3: When Responder distribution is 5521, and hands fits, we use the artificial bid of 4
to search for controls in Responder's hand, but we assume that in the major 2 cards can have only A or K never both, and each minor may have 3 controls (A+K). Considering that range is limited to 10-14 hcp then maximum controls are 2A+2K = 14 hcp and let's assume a minimum of 3 controls (A+K) or (3K) for make a mental evaluation of Responder's hand when searching for controls.
Opener Responder
 1nt       3 or 3  <= shows distribution 5521
 4 <= asking for controls in 3 suits (excluding the singleton suit)
 .........   ?
 .........  4nt  <= 3 controls (1A+1K) or (3K) (rarely less)
 .........   5  <=
4 controls (2A) or (1A+2K)
 .........   5
  <= 5 controls (2A+1K) or (1A+3K)
 .........   5  <= 6 controls (3A) or (2A+2K)


Of course if Opener has both majors aces after 5
or 5 probably he will be able to bid Slam based in this simple information. So a disciplined response bid to show 5521 controls is very important for a partnership know what they are bidding.
suppose Opener =
 
Axx Axx K3 KJxxx
 and Responder =
 
Kx x AJ1083 A10xxx
Opener Responder
  1nt      3
<= singleton Heart (so hands fits)
   4
      5 <= 5 controls (partnership has all controls)
   7      pass 
Hands fits and with a 10 cards fit and all controls we bid Grand Slam.
Note that when we have a 10 cards fit the trump's Queen has only 22% in be third against 52% in be second and 26% in be singleton.


B) by searching keycards and Queens in the minors in steps. The minors suits together have 4 keycards (A
A K K) and 2 Queens (Q Q) so now we build a list or relationship of steps assuming that Responder's hand needs 10-14 hcp and a minimum of 2 keycards in the minors.

Rule#4: When distribution is 5431 Opener search for honors in the 3 cards major bidding a relais (next suit) and the responses are:
Opener Responder                      .... Opener Responder
 1nt       3 <= singleton Hearts        1nt      3 <= singleton Spades
  3 <= relais to search Spades          3  <= relais to search Hearts
 ........     ?                       ..................              ?
 ........    3  <= Ace Spades       ..........         3 <= Ace Hearts
 ........    3  <= King Spades      ..........        3nt <= King or Queen Hearts
 ........   3nt <= Queen Spades    ..........        we lose a response step
 ........    4 <= no honor and 5 cards          4 <= no honor and 5 cards
 ........    4 <= no honor and 5 cards          4 <= no honor and 5 cards

Rule#5: Only after apply the Rule#3 Opener may search for keycards in the minors bidding 4:
Opener
  4 <= asking for keycards in minors with th follow responses:
step1 (4)   => 2 keycards (2A) or (2K) or (1A+1K) and no Queen 
step2 (4nt)  => 2 keycards + 1 Queen
step3 (5)   => 2 keycards + 2 Queens
step4 (5)   => 3 keycards (3A) or (3K) or (1A+2K) or (2A+1K)
step5 (5)   => 3 keycards + 1 Queen    <= maximum 14 hcp
step6 (5)   => 3 keycards + 2 Queens  <= maximum 14 hcp
step7 (5nt)  => 4 keycards (2A+2K)      <= maximum 14 hcp 

Thus these Rules allow search information to give conditions to Opener decide to abort possible game, to bid game and also to bid Slam;

suppose Opener =  Kx Axxx Axx KQxx
 and Responder =
 
Axx x KQ1083 A10xxx
Opener Responder
  1nt      3
   <= singleton Hearts (so hands fits)
   3
   <= relais asking for honors in Spades
  .......... 3
   <= Responder shows Ace of Spades
   4
   <= search for keycards in both minors
  ......... 4nt  <= 2 keycards + 1 Queen
 Thus partnership has all keycards for minors and all controls in the majors.
   7     pass     

REVIEWING
WHAT TO BID AFTER 5431
 
1- Opener bids 3nt when hands does not fits but Opener has good hand with stoppers in the Responder's singleton suit and also in the other major suit like:
example1
Opener Responder
  1nt       3
<= singleton Hearts 5431
  3nt  <=
AJ10 KQ10x Q83 K52
example2
Opener Responder
  1nt       3
<= singleton Spades 5431
  3nt  <=
QJ108 AK107 A8 J102
So without 4 cards in a minor try for Slam
is out of cogitation

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2- Opener jumps to the major Responder's 3 cards when he has 5 cards or good 4 cards in this suit and no good option to play 3nt:
example3
Opener Responder
  1nt      3
<= singleton Hearts
  4  <=
AK1082 Kxx K83 K5
example4
Opener Responder
  1nt       3
<= singleton Spades
  4
  <= J623 AKQ2 K8 K102
Considering that Responder has 3 cards support in Hearts we can play in 4
even with a 4-3 fit. 

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3- When Opener has good stoppers in the Responder's singleton major suit but has poor stopper (Jxx or Q2) in the other majoror it is possible search this major in Responder's hand bidding a relais in the next suit.
example5
Opener Responder
 1nt      3
<= singleton Hearts
 3  <= relais asking for honor in 3 cards major suit (Spades)
            and the responses are:
             ?
            3  <= Ace Spades
            3  <= King Spades
           3nt  <= Queen Spades
            4  <= no third control and 5 cards
            4  <= no third control and 5 cards
  ?
so now Opener can decide:
- to stop in 3nt;
- try Slam bidding 4 for keycards;
- pass in 4/4 if the hand loses 3 tricks in the majors;
- sign-off in 4;
- bid 4nt to show 3-3 in the minors asking for Responder to bid his 5 cards minor;
- bid sign-off in 5 or 5 when have 4 cards minor.

When Responder bids 3 the relais responses lose one step:
Opener Responder
 1nt       3
<= singleton Spades
 3  <= relais asking for honor in Jearts
            and the responses are now:
              ?
             3 <= ace Hearts
            3nt <= King or Queen Jearts
             4  <= no third control and 5 cards
             4  <= no third control and 5 cards
And then Opener may decide if bids 4 to try Slam in case hands fits and Opener is maximum.

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4- When hands fits (Axx - x or Jxx - x) Opener must first search the major 3 cards and then use 4 to search for keycards  both minors (excluding keycards for the major suit 3 card) like in the follows examples:

example6  When hands fits
opener: AJ10 J65 A3 KQ1032  Responder: Q32 5 KJ982 A976
Opener Responder
 1nt       3
<= singleton Hearts 5431
 3
         <= relais asking for honors in Spades
 ........... 3nt <= shows
Qxx
 5
         <= sign-off - Responder will be declarer and lead in Spades no good
 ........... pass

example7
opener: A83
KJ3 K3 AQ865  Responder: 2 A85 AJ972 K1092
Opener Responder
 1nt       3 <= singleton Spades

 3
         <= relais asking for honors in Hearts
 ........... 3 <= shows
Axx
 4
         <= RKB (for 2A 2K 2Q)
 ............ 4
nt <= 2 keycards
 6         pass

example8    when hand fits
opener: Axx AK QJ5 QJ1052  
Opener Responder
  1nt       3
<= singleton Spades 5431
  3        <= relais asking for honors in Hearts
 ............ 4 <= no A or K or Q in Hearts - 5 cards
  4        <= search keycards only for both minors (2A-2K-2Q)

 ...........  ?
 .........if  4  <= 2 keycards then 5 - missing 2 keycards (2A or 1A+1K)
 .........if
 5  <= 3 keycards then 6 - missing 1 keycard (A or K)
 .........if  5  <= 4 keycards then 7


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5- When Opener hands is minimum and hand does not fits Opener try to stop the bidding at a minor in level 4:
example9
Opener Responder
 1nt       3  <= singleton Hearts
  ?
 4 => QJx
KJ543 AQ KJ2 
sign-off but with A and 5 cards support Responder may bid 5  

example10
Opener Responder
1nt        3  <= singleton Spades
  ?
 4 => KQJx
K6xz A7x Qx
sign-off but with A and maximum Responder may bid 5  

example11 for Opener weak hand after 1nt response 3
a)  KQJ
Kxx K7x QJ52 <= with only 1 stopper in Hearts this hand have a great chances in down in 3nt and without aces have 2 losers in the majors, so only if Responder has AQ in Diamonds and AK in Clubs it will be possible have success in 5 or 5. For Opener point of view the hand should stop at 4. Thus opener bids 4 letting Responder decide and with 3 keycards and a Queen Responder may bid game in 5.
 
b)  Kxx
KJxx KJx KJx <= here Opener has a poor stopper in Spades for 3nt and has a  sure loser Hearts without 4 cards fit in a minor. So this hands not fits for his point of view and Opener must bid 4. Of course Responder with maximum, 5 cards support (Responder should be aware that Opener may have only 3 cards in Clubs) and a top honor in the major may try game. 

WHAT TO BID AFTER 5521?
6- 3nt is to play - means that Opener has good stoppers in both majors as we show in some examples;

7- 4
or 4 shows that 3nt is impossible to bid due to the major singleton card, and also shows a minimum hand that does not fits - of course if Responder has a maximum hand with Ace in the 2 cards major assuring that the hand will not lose 3 tricks in both majors he may try game;

Opener Responder

  1nt      3 <= 5521 with singleton in Hearts
             3 <= 5521 with singleton in Spades
   ?
 3nt      <= to play
 4/4 <= minimum - Responder decide pass or game
 4       <= search for keycards in minors (4 keycards + 2 Queens) 
 4
       <= asking for controls in 3 suits
 5/5 <= to play - Responder with maximum can't bid Slam

example12:
Opener Responder
 1nt       3
  <= singleton Hearts 5521
  ?
- suppose Opener with maximum: Kxx
A43 AK QJ952 
Hand fits and the information about Queen it is not so relevant than the information about controls. Total points in the relevants controls are 11 and Opener has 6 points-controls, so controls should be serached:
 4
  <= ask for controls
  ?
 4nt => up to 2 controls then Opener bids 5 missing 1 ace and 1 king

 5  => 3 controls then Openr bid 6 missing 1 ace
 5  => 4 controls missing
one King then Opener bids 6
 5  => 5 controls  all relevants controls - Opener bids 7
  

example13
1nt       3  <= singleton Spades
  ?
 4 => KQx
KJxx AJx Qxx
sign-off but with maximum (x Qx KQxxx AKxxx) Responder may bid 5 but if Opener has no A or K the contract lose 3 tricks in the majors.
In cases like this if Vul bid game if nVul pass. 

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