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Let's first say that the bidding goes 1NT-p-2D-(Dbl)-??

 

Without discussion I would assume that completing the transfer shows 3-card support, passing denies that. Redouble is a suggestion to play 2DXX. You can play superaccepts as usual. There are other more complicated agreements possible but this one is most standard.

 

Now let's say it goes 1NT-p-2D-(2S).

 

To complete the transfer, opener would have to go to the 3-level. Responder could have a 0-count, so opener shouldn't do this on many hands with 3-card support, and certainly never without 3-card support.

 

I play the double as penalty here, and I would assume this without discussion. But you'd better have a lot of tricks in your hand, don't count on partner to help!

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Usually 1NT-Pass-2-Bid-3 should show four-card support. This probably shouldn't show a maximum hand -- it's basically a "law of total tricks" competitive bid on the guaranteed nine-card fit. If you have bids available you can use these as super-accepts (for example 1NT-Pass-2-2-2NT/3/3). In any case it's never right to bid without a fit (except perhaps to make a rare penalty double keeping in mind partner may have nothing). One mistake I see frequently is to bid 2NT "natural" without a fit (1NT-Pass-2-Pass-2NT or 1NT-Pass-2-2-2NT) -- partner could have a zero-count for the transfer and you don't want to play 2NT opposite that!

 

Another useful rule is the meaning of double. If opener passes and responder doubles (1NT-Pass-2-3-Pass-Pass-Double) then this simply shows values and denies freak shape (usually not 5-5 in two suits, not 6+ cards in the suit transferred to). Usually opener will leave this in if holding doubleton in the suit transferred to, or with a strong holding in the overcaller's suit. Otherwise opener can complete the transfer (now at the three or four level) with three-card support.

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