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Alright, since this is unanimous, let me rephrase the question. With 2344 shape, what is the minimum hand that does not bid 3 here?

The given hand is close to the "bubble", IMO.

 

A Leben 2NT opposite a direct double has a range of, say zero to 8. This is too wide, so we make an artificial floor of 3.

 

A Leben 2NT opposite a balancing double of 2M has a range of, say, zero to 10. We make an artificial floor of 6. This seems realistic to us.

 

The given hand is not a great one for trick-taking, and we go low.

 

"We"=us, not necessarily the sane world.

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I don't really play different ranges opposite a direct and balancing double. In part this is because I'm not balancing a lot lighter than I double in direct seat over a weak two bid (this is different from an opening for a number of reasons, including that we are several levels higher and that RHO is more likely to have strength because opener is more limited).

 

The lebensohl bid is normally 0-a bad 8 whereas a direct bid is a good 8-11. While the given hand can easily make game opposite a maximum lebensohl bid, you'll have a lot of trouble opposite a more typical 5-count. So I'd accept the puppet to 3. Rejecting the lebensohl puppet should show more like a 20-count (maybe a really good 19).

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Yuck. 3C. What game are we making if we push that partner won't bid over 3C (i.e. 3NT after partner shows a spade stopper)? The hand you want partner to have is, say, xxx KQxxxx xx xx, maybe KJxxxx. That's a pretty small window to hit.

 

Caveat: I like to keep my actions over weak 2s sounder than most; so this hand really isn't much stronger than minimum. Add to that the fact that there's 2-dead spades (Yeah, Jx turns Qxx into a nice holding, but how is partner going to get that?) and the 4-card suits aren't majors...

 

When would I break? x AJTx AJxx AKJx might be a good start, but I find even that too small. What would I bid?

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