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After that start:

I was quite close to bid a nonforcing 2 over the double, but no, I xx. If north tries 2 , I would try 3 with the east hand and via 3 3 NT, I will reach the right game.

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I'm not too familiar with 2/1, but isn't it more of a principle than a whole system? Anyway:

 

After the opps double a major, one can play transfers (starting with 1NT). Redouble is then a balanced hand, about 8+ hcp. In this case the bidding would probably go:

 

(P)-1S-(X)-2D*;

(P)-3C-(P)-?;

 

2D was a transfer to hearts and since partner did not accept she probably has singleton or void. The normal bid would be 2S in this case, but partner bid 3C. This should show extras; either 5-5 or extra values. I would probably bid 3NT.

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I still play that 2 over the double is a 1 round force, otherwise pass and back in with 2 on weaker hands. Redouble really wants to punish them and opposite a min opener this hand qualifies for that bid too.

 

Easy to bid game over either, after 2 and anything other than 2 by east, west is good enough to force to game just has to pick which one.

 

After redouble, West is good enough to force to game and likewise plutz along with forcing bids before picking one.

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I play 2 after dbl nf, so i have to start with redouble. East passing of course, if they can not find fit they are dead, if they do we would still probably play 2 doubled. If this is a 4-4 fit we probably get rich. . If they have 5-3 fit they probably score 3+1+1 it still doesnt look good for them.
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It depends what you play after the Dbl, it hasn't much to do with 2/1 imo.

 

The auction at my table would go something like this:

1-(Dbl)-2 (5+ ; transfer )

3-3 (natural with extras ; 4th suit)

3NT-p (stopper nothing else to say ; with Hx partner would've bid 3 so 4 probably isn't great)

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