OK. Here's what Mike has to say about 2NT and 3C (I hope we can agree to dismiss 3H and 3NT as clearly wrong):
2NT I gave you a big hint in the introduction to this hand. You have lots of things you would like to show but no specific thing that you WANT to show. Better to bid 2NT, forcing, and get more news from partner.
3C This is the bid that many would make but it takes up bidding room in an insidious way. See the postmortem for more.
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Carl: I felt that 3C shows shape. Since you do not need FSF, 3C ought to show an honest 4-card suit. This puts the minors at very likely 5-4.
The majors thus can be:
0-4 No, I would have raised hearts on the second round
1-3 Yes, Possible and the only choice as I see it
2-2 No, I would have bid 2NT on the second round
3-1 No, I would have raised spades on the second round
4-0 No, I would have raised spades on the first round
So I feel that this shows 1-3-5-4 with a high degree of confidence, although it does not help nail down strength. Not yet.
2NT does nail down strength, but I feel it misrepresents my shape. I feel like I do have something I WANT to show - my clubs and my shape. I also do not see 3C as taking up bidding space; it is only one more step, for Pete's sake.
So, please comment on my rationale above, so I might learn more, thanks.
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Anyway, here's Part Two:
1S - 2D;
2H - 2N;
3H - ?? quiz choices are 4C and 4H