I must say that I don't get this problem at all.
What do you want to achieve by cuebidding, whether serious or non-serious? Do you think that you can tell partner that you have a 5=6=1=1 hand by cuebidding? So, you bid 3NT or 4
♣ and partner bids 4
♦. How is it helping you to know that partner has the ace or king of diamonds?
What you want to know is how many keycards partner has. If he has three, you bid a small slam If he has four, you bid a grand. If he has two, you stop in 5
♠. So, this is a simple hand for Blackwood.
Can it go wrong? Sure! Partner might have
♠Kxxx
♥xx
♦KQJ
♣KQJx
and you will be down in 5
♠ (or 7
♠ ).
But is cuebidding going to work a lot better when partner has a hand like that? I don't see it.
So, go with the odds and assume that partner will have at least 2 keycards. Take the bull by the horns, bid 4NT and place the contract. Buy partner a beer if he has only one keycard.
Rik
I want my opponents to leave my table with a smile on their face and without matchpoints on their score card - in that order.
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