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Questions regarding a Two-way Multi

Imagine you are playing a 2 opening as either a weak two in a major or a strong balanced hand.

 

(I realize I have turned off most of the audience already, but bear with me).

 

When partner has opened 2 with the strong balanced type, responder most often will hold a non-descript weakish hand. He will therefore most likely respond 2. Some of the time, his non-descript hand will contain a four(+)-card heart suit and he will respond 2. Occasionally, he will hold both majors and bid a pre-emptive 3 or 4. Only very rarely will he be strong enough to bid 2NT. Clearly, the terms "some of the time", "occasionally" and "very rarely" are fuzzy.

Q1. Is there a way to be more precise about the odds of the different responses? 

 

It follows that the standard methods of responding to a 2NT opening, such as Puppet (or Muppet, or Romex) Stayman and transfers, are an inefficient structure if a strong balanced hand is opened with a Multi. It is a little silly to play 2-2-2NT-3 as a transfer to hearts, and the sequence 2-2-2NT-3 to show 5 spades and 4 hearts (or some similar sequence starting with 3) is impossible.

Q2. Does anyone have a better response structure?  Continuations after 2 - 2M - 2NT are ignored by Horton and Van Cleeff in their book 'The Mysterious Multi', despite this particular two-way variant being their preferred option for a 2 opening.

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