Rule of 2 and 3

In bridge points in one board is object of negociation and this rule tell us how many points an preempt bid can lose without great risc if opponents have a game.

A disciplined preempt open need high top honors concentrated in his suit and the valuation of the hand is done by estimating how many loser tricks the hand contain in the worst cenarius where partner's hand is "blank" (no honors to help).

Our vulnerability versus opponents vulnerabilty determine the number of loser tricks that preempt bid is a safety risc in case opponents have a game,  but is also an orientation to our partner to know how many covers we expect in his hand to limit our riscs.

Suppose we open 3 nVul against Vul with 7 cards like:
KQJ10987 xx xx xx or KQJ10987 xxx xx x having 7 losers. This means we need 3 tricks in partner hand to make 9 tricks. Thus, if opponents have a game Vul we will have a good negociation in points because we lose 500 points and opponents have 620 points. Thus, if they
bid a game in 4 partner with one or 2 covers like:
654 x A98xx Jxxx or Axx xx KQxxx xxx
can bid 4 in defense of their 4.
Furthermore the information of the number of losers by the level of the preempt done allows take a decision in bid game (or Slam) if he have a good hand with 4 covers like AK, A and A. 

The basic rules of businees is:

1- we nVul and opponent Vul then if they have a game 600/620 points we can lose 3 downs doubled = 500 points to avoid their game contract.

2- we Vul and opponent also Vul we can lose only 2 downs doubled = 500 points to have advantage against their contract = 600/620 points.

3- we no Vul and opponent also no Vul then we can lose only 2 down doubled = 300 points against game contract = 400/420.

4- Finally if we Vul and opponent no Vul we can lose only 1 down doubled = 200 against their game contract = 400/420 points.

Question: How can we count our losers to make avaliation of the hand?
Answer: In the same way Ely Culbertson did in his 1930 system considering honor tricks where A=1 honor trick, K=0.5 honor trick, Q=0,25 honor trick.
We can assume that the fourth and the fifth card in a suit is not a loser
Ax=1 loser, Axx=2 losers, Axxx=2 losers  Axxxx=2 losers
AKx=1, AKxx=1, AKxxx=1
AKJ=0.5, AKJx=0.5, AKJxx=0.5
AQ=0.5, AQx=1.5, AQxx=1,5
AQJ=0.5, AQJx=0.5, AQJxx=0.5
AJ10=1, AJ9=1.5, AJx=1.75
Kx=1.5   Kxx=2.5  Kxxx=2.5 Kxxxx=2.5
KQ=1, KQx=1.5, KQxx=1.5, KQxxx=1.5
KQJ=1, KQJx=1, KQJxx=1
KQ10=1.5, KQ9=1,75
KJx=2, KJxx=2, KJxxx=2
Qxx=2.75 Qxxx=2.75, Qxxxx=2.75
QJx= 2.5, QJxx=2.5, QJxxx=2.5
Jxxx=3 losers

Examples:
a) AQJxxxx xx Kx xx => sum of losers: ½ +2 +1.5 +2 = 6.
So with 6 losers we can open in 4 if we are nVul against Vul, but if opponent are also nVul then we can only open in 3.
According our open 3 or 4 and the vulnerabilty context our partner know how many losers we have and then he can know how many tricks he must cover with his hand to think if he try a Slam.

b) AKJxxxxx xx x xx  =>sum of losers: 0 +2 +1 +2 = 5.
So with 5 losers we can open in 4 nVul x nVul or Vul x Vul because we will lose only 2 down in the worst cenatirus. Now partner with 4 cover tricks, can trink in Slam, but with only 3 sure tricks he should pass.
But Vul against nVul we should open only 3 and this tell to our partner that we have 8 sure tricks or 5 losers.

c) x KQJ10xxx x J1098 =>sum of losers: 1 + 1 + 1 + 3 = 6.
Thus, with 6 losers, nVul against Vul, the recommended opern is 4, but if we and opponents have same vulnerabillity then we can lose only 2 downs and the recommended open is 3. Finally if we are Vul and opponents are nVul then we are restrict in lose only 1 tricks and so we need openn 2.

d) x Jx Ax KQJxxxxx => sum of losers: 1 + 2 + 1 + 1 = 5.
Thus, nVul against Vul the recommended open is 5.
If we and opponents have same vulnerabillity then we should open in 3, considering that the 4 open is reserved for Namyats open.

Note1: Experience has shows that if we have a hand without a sure entry and not have the ace in the long suit, per example: xxJxJxKQJ9876 it is a very bad an open in 3 if partner is unpassed hand, because if he bid 3nt with good stoppers in the others suit but with only 2 cards in our long suit then opponents will not serve their ace in first round and partner will make only 1 trick in Clubs!

Note2: When we are Vul against nVul and partner is a passed hand the preempt in level 2 is like an open in level 1 but shows six solid cards with good middle like:
AK1098x xx KQx xx or xx x AQJ98x A109x.
But in opposite vulnerability, we nVul, when partner is passed, we can open even with 5 cards to disturb easy auction for opponents and also make a indication of lead:
AK109x xxx xxx xx or xx QJx KQJ9x xx.

Note3: After an open preempt in first or second position is opponents bid a suit the partern's double is penalty, so we must pass.

Note4: Experience has show that we should not preempt having also four cards in a major.

Bluff Situation:
a) Imagine that you have 10xxx xx Jxxx Kxx  and the auction is:
partner opponent1  you
2 pass ? => 4 is a natural bid to disturb possible Slam

b) Imagine that you have 10xxx x Jxxx AKxxx e o Leilão corre:
parceiro oponente1 você
3 pass ? => 5 is a good bid to indication of lead and if you are doubled then you bid 5

c) Imagine that you have Kxx J9xxx xxx Kx  and the auction is:
partner opponent1  you
2 pass ? => 3 is a 100% sign-off to disturb auction   

Special Preempt Open
1- Gambling – The 3nt open shows 7/8 cards in a minor suit with the top 3 top honors and no other A or K.
If opponent pass and partner have 2 aces and stopper in other suit he must pass in a hand like:  J10xx Ax xxx Axxx
but if your hand dont have stopper in 2 suits you should bid 4 and partner will pass if Clubs is his suit or bid 4 if Diamonds is his suit.

But if you have a special hand like: xx Ax Jxx AKJ10xx
and you have an agreement with your partner that 4 is a reserved bid to ask for singleton with the follow answer (4=singleton ; 4=singleton ; 4nt=singleton in the other minor;  and the bid of the minor is sign-off with  7222 no singleton)  you make a try to Slam using this agreement.

Partner  Opponent1  you  Opponent2
3nt         pass 4 passo
4 double ? => you have luck partner is singleton is Spades so
                                                  now you jump to partnes minor bidding 6

Another usual convention is after the gambling open in 3ST the bid of 4nt ask if Opener have 7 or 8 cards. In case of 8 cards Opener bid 6nt and the Responder hand should be like: Axx Axx Jxx AKxx

Nota5: The Gambling open cannot have void. So with void you can open at level 5 with 8 cards or at level 1.

2- NAMYATS – it is a similar open with closed suit having a major with  7º/8º cards like AKQ10xxx or AKQ98732.
So the open of 4 shows AKQ98732 or AKQ9873;
and the open of 4 shows AKQ98732 or AKQ9873

If Responder bid the Opener suit this is sign-off
Opener Responder
   4          4 => sign-off
   pass

Opener Responder
  4           4 => sign-off
 pass

Note6: Asking for a singleton is possible bidding the next suit (relay).

   Opener       Responder
 4 (7+)        4 => ask for singleton
      ?
   4  => 7222 no singleton
   4nt => singleton the other major ()
   5 => singleton in
   5 => singleton in

   Opener       Responder
 4 (7+)        4 => ask for singleton
      ?
   4  => 7222 no singleton
   4nt => singleton the other major ()
   5 => singleton in
   5 => singleton in

After Opener deny singleton Responder can ask for king bidding 4nt after ask for a singleton or bidding 4nt without ask for a singleton.


Note7: This open cannot have void neither another ace, but only one additional king is possible. So if Responder bid 4nt he is asking to Opener if he have any other king or not.
Opener   Responder
   4          4nt => ask for king
     ?
  5 no additional king
  5 one additional king
  5 one king with a Queen in the same suit.

Opener   Responder
   4          4nt => ask for king
     ?
  5 no additional king
  5 one additional king
  5 one king with a Queen in the same suit.


Example:
Opener:       xx AKQ9832 xx Kx
Responder: AKx xxx Axxx Axx
Opener          Responder
    4                 4 => ask for a singleton
    4 = no        4nt => ask for a king
    5 = 1 K       6nt => in MP     

Note8: If Opener have 8 cards in his suit after 4nt he bid 6nt without King.

One advantage of this type of preempt bid with closed suit is that a transfer can be made.
Suppose you have: Kxx xxx Axx AKQJ
and partner open 4 showing 7 with AKQxxxx, you know he cann't have another ace, so he don't have A and you have 5 sure tricks and can if you is the declarer you have control in , so bid 6nt. 

Supose your partner open gambling 3nt and you have:
AKxxx AKxx Jx Jx
What you bid having 2 sure losers in one minor?
You jump to 5 then if Clubs is your partner suit he pass, but if his suit is Diamonds he bid 5, because you know there are 11 tricks.

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