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What I've never liked about responses to 2C is that most seem to play 2M as constructive nf. Not saying that this isn't right necessarily, but what does 2M advertise?
Average+ 5 card suit or 6+ that thinks game would be a nice contract, if partner has a maximum hand with fit. Fits are very important here, therefore it is constructive NF. Sometimes you don't want to force game with 5♠ and random 12 count, fearing misfit. But if partner has a fit and fitting hand, you might need very little for game.
IMO constructive NF is by far the best approach here as it is the most flexible.
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Does the response deny club support?
Will we languish in a 5-2 fit when we have a 6-4 club fit available?
Will we languish in a 5-2 fit when we have a 6-4 club fit available?
No, 2 card support is certainly ok, if 3 then it probably depends on your hand.
I would advertise 2♣-3M fit jumps.
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If I can play transfers over interference, then responder can show a constructive hand (I'm thinking 9+ hcps with a 5-cd suit) and then decide after opener accepts the transfer (generally showing 2-cd support) whether to pull to 3C or not. Certainly responder would pass 2M with a minimum hand and a 6-cd suit.
You need 2♠ as NF. Clubs or whatever isn't close to this. If you bid this way, you will lose part score swings and good games frequently.
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I do agree about 2N invitational being a rather narrow target but it seems like an important message to send. I'd have the cue bid (2S for clubs) which then pretty much denies exactly an invitational hand with a stopper but does show some points
Please do not play 2N as nat inv. It is not problem hand at all, you have many options that are usually better than 2N.
1) Show support+inv - 3m will often be safer contract than 2N. And when partners goes for game, 3NT will be rightsided.
2)Pass - typically if you don't have fit or 3m isn't appealing. If we have game partner will reopen. Or you will penalize.
3) Ask partner to bid 3N - rightisiding contract might as well be worth that one trick so if you were up to bidding 2N, you may as well try this.