I was kibitzing on bbo vugraph when declarer had to play this hand in 6nt:
Dummy: xx KQT9 AKxx AKJ
Declarer: KTx AJx Qxx Q9xx
A heart was led.
The obvious question is, do you (a) play a spade to K without testing diamonds, or (b) test diamonds first? As a straight percentage problem, the easiest thing to calculate, I think, is swing cases. (a) wins a swing when rho has 4 diamonds and SA, about 11%. (b) wins a swing when diamonds 3-3 and sa off, about 18%. Note that when diamonds are 5-1 you can switch to spades, so no swing in that case.
We didn’t take into account that an expert lho may duck the SA (!) when you lead low to the K (if you do it early), hoping you have KQT and misguess later. The likelihood of this is very hard to evaluate.
Of course, it looks attractive to (c) cash your hearts+clubs before committing yourself. The percentages may change. You would come down to:
Dummy: x --- AKxx ---
Declarer: KT --- Qxx ----
and can still choose either option. The drawback to this is that when LHO shows out on the second round of diamonds, you can no longer switch gears (you’re cut off from spades,) so this line looks bad when diamonds are 5-1. You might therefore leave the 4th club uncashed. But cashing all your winners has an advantage: if RHO started with QJxx spades and 4 diamonds, he’ll be squeezed down to a stiff spade honor and you make it if you read the position, which I think you will: who is diabolical enough to pitch a spade honor and keep 2 small, holding such as Jxxxx xx Jxx xxx?
I love how this extremely simple-looking hand has so many wrinkles. Another diabolical falsecard opportunity that might occur is when
My verdict is that I would cash all the winners (this is assuming hearts+clubs aren’t 5-1), then try to get the ending right – if RHO has even two fewer round cards than LHO, my calculations say the percentages shift enough to favor (a).
The real-life story?