OldPalooka

Actually the 58% number was based on going all out for the overtrick and risking the contract. [Mea culpa, I did not count tricks when I looked at the problem]. Safely taking the finesse is only about 53%. The difference is a large premium to pay on your matchpoint insurance. This does invalidate your point when the percentages are closer or if you consider 7% a reasonable premium to pay.

Now that Diamonds are known to be 3-2, play one round of clubs before choosing. ~7.5% Clubs are 5-0 on side or Queen drops and we claim. ~1.9 % that Clubs are 5-0 off side and we will pray for squeeze, good luck. Both lines win if JT9 of hearts is tight: ~1.8% So at this point both lines make about 9 percent and fail about 2% and we only care about the remaining 89%. Plan to finesse line wins 50% of remainder plus ~2.5% when East holds 5+ hearts and 3 little clubs. If West errs and throws a heart from 3 the line improves another 6%. Plan to finesse line therefore wins in 9%+ 44.5% +2.5% + a generous 2% for defensive error or roughly 58% overall. Plan to squeeze line wins 27% when CQ is doubleton + 25% when Qxx(x) with long hearts plus 9% where both make less 1% for double counting heart JT9 drop, with very little chance of defensive help, or 60% overall. For what it is worth, squeeze line never goes set more than one, while finesse can lead to -2. If not for the secondary showup squeeze possiblities in the finesse line, it would be decidedly inferior. And I believe this is generally the case.

Why not 3S instead of 2C? Even an off beat fit jump in hearts is more useful than 2C and 3C since it gives the auction some definition rather than just making a purring noise. Still, passing 4D with South's cards after partner has begged you to bid 5 is boggling.

If you play a lot of bridge you can expect a 7 count rule of 20 hand once or twice a decade. I personally would not worry about a potential implicit agreement until the second one is actually opened with a 1-bid in the same partnership in significantly less than a decade. Hopefully by then there will be addenda to the ACBL regs to the effect that freaky seven counts are not actually a king less than average strength since it is difficult for a bridge player, instead of a lawyer or bureaucrat to think so. I assume that NZ regs are more enlightened. It is difficult to imagine less light than ACBL regs about 8-9 point NTs and <8 HCP one-bids.

1 Club because I peeked and it is cold for 6 Clubs unless they lead a heart and a 3-2 favorite if they do. And I expect to get there if LHO passes again after partner's preemptive raise, otherwise we will settle in 5. Seriously I expect to do gain more in slam situations than I lose in game situations by bidding my suits when I hold 8 controls and a good long suit.

I believe the ACBL reg is that you may not _agree_ to open this hand, not that you may not open it. If you pick up a bunch of 76 hands with 7HCP in one session, you could fall afoul of an implicit agreement ruling if the same director gets called to your table a lot. Of course he might also decide the law that allows the ACBL or any other organization to control agreements on hands of a King or more below average strength may not apply in this case. Regardless, I would open 3C and expect to bid again the next round. There will be a next round, right?