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After a troublesome negative double

The auctions

1 (2)

and

1 (2)

present significant difficulties for responder. One important reason is that there are two unbid majors, so negative doubles need to cater for a much larger range of hands that responder might have and be unable to bid any other way.

What hand does responder have when the auction goes

1 (2) X (P)

4 (P) 4?

What agreements do you have to deal with these different hands for responder?

Would your answer be different if opener rebid 3 and responder "corrected" to 3

What about if opener rebid 2 and responder rebid 2?

A hand with a long spade suit where the suit quality was not good enough to make a weak jump shift (perhaps Kxxxxx Kx Kx xxx)
A hand with five spades that has basic support for partner (maybe Kxxxx Kx Kxx xxx)
A hand with four spades and extra (four or more -card) support for diamonds (e.g. Kxxx Kx Kxxx xxx)
None of the above: hearts is trumps
None of the above: 4 confirms hearts as trumps but 5 would be to play
None of the above

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