probably a hand with no solution

[rhm]

Again, if the argument were about a risky 2N (which I agree rates to lead to a minus more often than a plus) or a safe 3C, (the only downside of which would be missing the occasional game), I'd opt for 3C. But that is a false comparison, because 3C is not a sure thing. It is definitely much safer than 2N, but that isn't the point. As soon as one allows that 3C can lose by failing as well as by missing a game, the analysis becomes more difficult and less clear-cut.

I dealt out some hands given the South hand on the assumption that East would have 6-7 spades including the ace or headed by the JT with a maximum of 9 HCP.

If North (opener) has less than 4 clubs he must be either 4♠-4♥-3♦-2♣ or 4♠-4♥-2♦-3♣ or 3♠-4♥-3♦-3♣ with 12-14 HCP.

This occurred 13.6% of the time (where 2NT may be superior to 3♣).

If North has more HCP he would either not have opened 1♣ with these distributions or will not pass 3♣.

 

Otherwise North has 4 or more clubs. I assumed at most 19 HCP for North but excluded balanced 15-17 HCP.

Under those conditions North will have four or more clubs 86.4% of the time.

 

Bidding 3♣ does not preclude 3NT (except when North has a weak notrump where 3NT will often fail).

3♣ will often pave the way to a high level club contract when North is unbalanced.

An extreme example in one of my 10 000 deal generations North held ♠A92 ♥- ♦K876 ♣KQJ865 with West holding a 7 card heart suit.

After 3♣ further bidding would be easier for North South than after 2NT.

 

Rainer Herrmann