What should the responder do in the sequence 1m   1M    2M? Should he pass or made a game try with 12 DH? The following study contradict what is usually admitted. Always pass whatever vulnerability.

Why this error? Of course when you play the game, the opener being maximum, you are potentially winner because the prime game(particularly vulnerable) outweighs the discount of defeat. However, when you stop to  the 3 level, the opener being minimum, you are inevitably loser when you are defeated. Now you play more often at 3 level than at 4  level and calculate the average  show that you are winner to always pass. Let us engage in the calculations.

 

Declaring game green or red ?

Should you continue with 12 DH *, 11 HCP with a doubleton for example.

The opener is in the zone 12-15 DH. So you have in the line 24-27 DH.

12 * DH: not too small parasites honors ( queen, jack doubleton for example)

 

3 possible actions we will compare:

1st action "pessimistic": you always pass.

2nd action "very optimistic": you always announce game.

3rd action "STANDARD": Game try and you play 3M  if opener is  12-13 DH.

                                                                        and play 4M (or 3NT) if opener is 14-15 DH.

Note first that a lot of high competition players open today all hands of 11 HCP.

I remember a very simple principle : starting from 10 HCP, the hand frequency diminishes with its strenght.  We can then estimate the hands of 12-13 DH represent 60% of cases and the hands of 14-15 DH account for 40% of cases (estimates validated by Bridge Calculator). In taking the action "STANDARD"  you play a part-score at the 3 level in 60% of cases with 24-25 DH and the game in 40% of cases with  26-27 DH.

 

Let us look then the odds of gains and losses by the STANDARD compared to the action of one who decided to always pass .

First make calculations not vulnerable :

With 26-27 DH you win the game in 47% of cases, a gain of 6 IMP.

1 down in 35% of cases, a loss of 5 IMP.

2 down in 15% of cases, a loss of 5 IMP.

3 down in 3% of cases, a loss of 3 IMP.

With 24-25 DH you win your part-score in 61% of cases, no gain.

1 down in 28% of cases, a loss of 4 IMP.

2 down in 9% of cases, a loss of 2 IMP.

Calculate the expected mean value of your STANDARD action :

0.4 * (0.47 * 6 + 0.35 * (- 5) 0.15 * (- 5) 0.03 * (- 3)) + 0.6 * (0.28 * (- 4) 0.09 * (- 2)) = -0.688.

Not vulnerable your action will take you to an average loss of 0.7 IMP.

I also calculated that non-vul, Action No. 2 was  worst. It brings an even greater loss of 1.2 IMP. This is not surprising since you play the game with 24-27 DH more often with 24-25 DH than 26-27 DH.

When you play the MAJEURE SECURISEE and after opening 1 ♣ with balanced hands, you never play 3, the opener having had time to tell you he was 12-13 DH. And when you play 4, not vulnerable you earn 0.1 IMP compared to the one who always passes.

 

Vulnerable , identical calculations lead to :

0.40 * (0.47 * 10 + 0.35 * (- 6) 0.15 * (- 7) 0.03 * (- 5)) + 0.6 * (0.28 * (- 5) 0.09 * (- 3)) = -0.44.

Vulnerable your action will take you to an average loss of 0.4 IMP.

I also calculated that  vul, Action No. 2 was worst. It brings an even greater loss of 0.9 IMP. This is not surprising since you play the game with 24-27 DH more often with 24-25 DH than 26-27 DH.

When you play the MAJEURE SECURISEE you never play 3. When playing 4 vulnerable you earn 1.2 IMP compared to the one who always passes.

We see that to make efforts to declare a game which will be at best 50% is not a good bet, whatever the vulnerability.

Only the MAJEURE SECURISEE is a winner (especially vulnerable) because it plays 2 or 4 but not 3.

But you tell me that it contradicts the commonly accepted rule and (badly) demonstrated that it is enough to have 38% chance vulnerable and 45%  non-vul to play the game. In fact why 38% vulnerable ? Because this flawed study says you win 10 match points 38 times out of 100 and thus you lose 6 match points 62 times out of 100.  Expectation is then 10 * 0,38-6 * 0.62 = + 0,008 IMP.

But this rule is not valid because it does not say what was your action before declaring the game. Have you made a clumsy attempt which led to the 3 level without playing the game? Did you declare the game directly? The study that I make take into account all these risks.

 

And with 13 DH *, what are you doing? You have  25-28 DH,   not vul the 3 actions are equivalent: it's like you feel it, but you must declare the vul game directly.

 

And now in pairs tournament ? To mark more than 50%, the game you bid must be more than 50%. Vulnerability is not a matter so adopt the tip before : pass with 12 DH, make efforts with 13 DH.

Remark : you have the same problem whith 9 DH and a 4-4 major fit on the opening of 1NT(15-17 HCP).

You are in the 24-27 DH range and for the same reasons you have to pass after discovering the 4-4 fit.

* Different statistics are from: Bridge- STATISTICAL EVALUATION OF HANDS

Bernard CHARLES & Jerome GIGAULT