Posted 2021-October-04, 14:38
I'm having a bit of trouble placing the hearts and the HCP around the table. How strong was the fit jump? The 2/3 or 3/5 comment places a lower bound, but I'd like to know in more detail.
I've assumed IMP scoring, at matchpoints it's an entirely different problem.
My initial guess: 3♣ shows an invitational raise probing 3NT and 5m, so a good 9 HCP minimum. Incidentally, very few players would bypass hearts to show a minor suit fitbid, so West is very unlikely to have four of them. East jumped to 6 over that and is looking at some monster hand with long diamonds and clubs, at least 5=5 but more likely 6=5 (and, again, not many hearts in either case) and basically all the honours in the minor suits that West doesn't have. It is not that uncommon for fit-jumps to show only four cards in the suit bid, but some pairs insist on at least 5. This would leave partner with approximately 5=5=0=3 or 5=4=0=4 and something like 7 points max (king of spades, ace of hearts) but more likely 5 or fewer (queen instead of ace of hearts).
With a presumed double fit and very few minor suit losers this might be a double slam swing. Picture East with, say, ♠-, ♥Ax, ♦AKJTxx, ♣KJTxx and partner with ♠Kxxxx, ♥QJxxx, ♦-, ♣xxx. But there is a lot of uncertainty - perhaps 6♠ might be off on a heart ruff, or perhaps 6♣ is down if partner has the ace of hearts and two rounds cash, or perhaps partner has a minor suit trick.
Now let's look for a horror scenario if we bid on. If neither opponent has psyched (if they did, my hat's off to them) partner is marked with diamond shortage and doesn't have long clubs either, so I don't think we are ever conceding more than one diamond trick (give East 5=5 minors and West 4=5 for the fitbid and we might lose the one diamond. Oh well). As both East and West have at most three hearts and East is strong, I think it is probable we don't concede more than two heart tricks. We might lose a spade as well, for 3 off in a slam at the worst. So bidding on is 'always' right if their slam makes, and might even have chances of making as noted above.
The last question: what is the chance that 6♣ makes? You said East is a solid opponent, which limits the motivation for 6♣ to two options. Either East expects to make, or East expects us to always bid 5M over 5♣, and is taking an advance sacrifice - something like ♠x, ♥Ax, ♦KTxxx, ♣KJxxx. But in this case, where are the points? We don't have them, partner doesn't have them, so that means West has a killer of a hand and 6♣ might again be a favourite to make.
I'm bidding 6♠, fully expecting to go down one or two against 6♣ making. On a bad day 6♣ is down and I might get a misguided lecture on expected value and cost-benefit analysis with pointed reminders of the vulnerability. On a good day 6♠ makes.