Inferences from the auction

I am often amazed at the strength of inferences one can draw from the game of bridge.

Inspired by hands that partner and I held at a recent club IMP pairs event, see what inferences you can take from the auction you hear.

Here is the system my partner and I are playing: 12-14 opening 1NT, 15-17 rebid of 1NT, and two forms of checkback for responder after opener has rebid 1NT.  The two forms of checkback are 2♣ invitational checkback and 2♦ game forcing checkback; opener, in reply to checkback, follows a “hearts first” approach, showing three hearts before four spades if responder had responded 1♥, and showing four hearts before three spades if responder had responded 1♠.

Inference #1.  What is opener’s likely distribution when you, as responder, hear this auction: 1♣-1♥-1NT-2♣-2♠?

And, thus, what bids would you consider when holding –, JT963, AQJ3, J964?

Inference #2.  What is responder’s likely distribution when you, as opener, hear this auction: 1♣-1♥-1NT-2♣-2♠-3♦?

And thus, what bids would you consider when holding K653, K, KT86, AK73?  (Side issue: do you agree with opener’s choice to rebid 1NT?)

(My) answers follow.

Inference #1.  Opener is almost assuredly 4=2=3=4.  He might possibly be 4=2=2=5, but would be likely to rebid 1♠ with that hand unless an unduly high amount of his strength were in the doubleton suits.  He might also possibly be 4=1=4=4, but with that hand, he might well have chosen either to open 1♦ or to rebid 1♠.

Responder might choose to rebid either 3♣ or 2NT.  Which of the two bids work out best is likely to be determined by the strength of opener’s four card spade suit: the stronger the spade suit, the better 2NT might work out.  3♣ seems safer, I suspect.

Inference #2.  Responder is likely to have great red suit length in his invitational strength hand.  Five hearts and six diamonds is certainly possible, while 0=5=5=3 is another possibility.

Opener has unexpectedly long diamonds in his hand.  If he had less strength in his spade suit, surely a diamond raise would be in order, even opposite an invitational strength in hand.  On the actual hand, a 4♦ call is still reasonable, as might be a pass of 3♦.

So … what happened at the table?

Responder failed Inference #1 test.  He rebid 3♦ rather than 3♣ or 2NT.

And Opener (whose choice to rebid 1NT seems pretty reasonable to me) failed Inference #2 test.  Rather than settle in diamonds on the auction he heard, he rebid 3NT.

Here are the actual hands.

 

 

You might notice that 3NT is actually makeable, by opener holding off on the first two rounds of spades.  Because the hold off voids RHO of small spades and because all of the defender’s entries are held by RHO, declarer can force out the two high heart honors and limit losses to two tricks in each major suit, while creating slow heart winners to accompany his ♠K, and top minor suit winners.  At the table, opener did not want to chance RHO gaining the lead and leading a spade through the king, and so chose to win the first round of spades and then pray for someone to hold queen-doubleton of clubs.  Prayer not answered and down two was the result.