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38 HCP: A Puzzle
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In Monday morning’s Common Game, Board 8, East and West both picked up 19-counts:

West
AK84
AQJ9
K
Q854
East
QJ
K10
AJ9643
AKJ

I don’t ever remember seeing 38 combined hcp; it turns out a given side will hold exactly 38 hcp once in 50,000 deals. It's not the main topic here, but if you like, guess what percentage of the field bid 7nt, with West dealer -- answer next:

West
AK84
AQJ9
K
Q854
East
QJ
K10
AJ9643
AKJ

25% of the field (1400 pairs) bid 7nt, 50% bid 6nt, and the rest were scattered, with 1% managing to go minus. My partner made the deal routine for us when he rebid 2NT with his 4-4-1-4 after 1-1. I started wondering whether, with 38 hcp, some grand slam would always be a good contract. So here’s the puzzle:

What’s the *worst* single-dummy combination of two hands you can construct with 38 hcp, in terms of trick potential in their best strain? I’ll put my best(?) effort so far next, but maybe something better is possible:

West
AK65432
AK
AK
AK
East
J
QJ32
QJ32
QJ32

All grands are 0%(*). At least you're a favorite to make 6 or 6NT, though. Can you find a 38 hcp combination where all small slams are underdogs?

Update: In the first six hours after posting no one has outdone this example, so, showing some faith in the community… maybe it’s not possible?

 

Update, 1/18: See the very nice construction posted by Charles Brenner and later by Gonzalo Goded.

*It’s actually non-trivial to check that no extremely favorable layout lets you get home on a partial crossruff in one of your 4-2s, but I do think it’s truly 0%. It would be a nonzero chance if you had good spots in any suit.

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