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What does this 3 heart bid mean to you


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It probably depends on what 2 would have meant over 2.

 

When 2 over 1 is not game forcing, many players play that 2 of a major shows extras and thus forces to game. If opener does not have extras, he may have to bid 2. If that is the case, it is quite possible that 3 over 2 (which, I assume, is forcing to game) is natural.

 

If the partnership has agreed that 2 of a major over 2 is natural and does not show extras, now 3 could be just a probe trying to determine the right contract. Clearly, opener could have bid NT if he had hearts stopped, so 3 doesn't promise a heart stopper.

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I would take it as a NT probe, asking for help in . Responder can't have 4 on this sequence and opener won't bid like this with 5 so I see no reason for this to be natural. The auction after 2 is GF and opener can support either of partner's suits below game, so there is no need for 3 to be an advance cue-bid. Opener can bid NT himself with the well stopped. So there really isn't much left, as far as I can see.
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A 2 reverse after 2 would normally show extras and be GF after a non-GF 2/1. 2 next by responder as here I think now is GF.

 

There seems little point in 3 now being natural, so I think it is a DAB, perhaps looking for something in for 3NT, or undisclosed extra cards in the other suits.

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For me, 3 would be a general force a la 4th suit forcing, initially asking for a stopper. What range of hands it can include would depend on whether 2 was forcing. If you make 3 natural here, even though it is not possible for there to be a heart fit, then you presumably have to use 2NT as some kind of bucket including hands with no fit and no heart stop. The trouble is that that might easily wrong-side our best contract so it seems clear that having 2NT show heart values and 3 ask is better. Responder could still bid 3 over 2NT with 3 hearts to suggest a possible Moysian 4 so it is not like we are losing that option by playing it this way around.
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A minority viewpoint: Opener is describing minimum 6-4 shape, showing values wanting to right side NT against a black suit lead. Also allows for 5-6 if partner is 4=1=3=5 with working values. Since we are already in a game force, 4SF is not "ON" (similar to, say, 1-2-2-2[hearts}= Natural and forward going (slammish)).
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