I am leaving the comment, since I once made it. But see addendum below.
Indulge me a bit/ I am a long time skeptic of using computer programs to analyze such situations. Some thoughts:
For example:
You say: On 45 of them, it DID NOT MATTER which of the 3 thinkable rebids we choose! "2NT", "3H" and 4SGF="2C"
Bidding 2C will put them in game so, if it doesn't matter which bid is made on these 45 hands then I guess opener has enough strength to accept the game inviting bids of 3H and 2NT, else it would matter that 2C was bid. Further, if responder bids the game invitational 3
, I would expect that opener, if he accepts the invitation, will bid 4
rather than 3NT, while if opener has two hearts then, over the game invitational 2NT, he would, if he accepts, bid 3NT rather than 4
. This is matchpoints so even if both 3NT and 4
make, it matters which one we choose.
So the only case I see where it won't matter is if opener has three hearts and the strength to accept an invitation. Then they end in 4
no matter which of the three calls is made. (I am ignoring the possibility that opener could have slam interest). So maybe it is true that on 45 of the hands opener has three hearts and will accept any of the three invitations. Is that it?
Well, I guess I can think of another possibility. If opener has two hearts and will always accept, and if 3NT and 4
both fail by one trick, then it won't matter. If responder bids 3
opener raises to 4
, off 1, and if responder bids 2NT then opener raises to 3NT, off one.
Also, suppose opener has
KJx. Or
Kx. And suppose he has two hearts. Now, if responder bids 2NT he will be playing the NT, while if he bids 2
, opener will be playing the NT. I would be surprised if it never mattered which had was dummy. Although here we also have the possibility that 2NT will be passed. So maybe sometimes, after a 2NT call, the contract is 2NT off 1 because the wrong hand is declarer, but this is matched against the 2
call where opener rebids 2NT but now, since 2
was game forcing, the contract is 3NT down only 1 because opener is declarer.
And I would expect that on may hands there will be options as to declarer play and defense.
Anyway I am trying to understand just why it does not matter on these 45 hands.
Addendum.
Ah yes, while clearly it matters on each hand I guess it could be that while bidding 3
will sometimes be off 1 while 2NT would have made while other times bidding 2NT will lead to +120 while bidding 3H will lead to plus 140, so that no matter which we do we will sometimes wish we had done the other. Still, I am less than convinced. And still not sure just what is being said.
Suppose that the N hand is such that we can be confident that, with the given S hand, the auction will begin 1
- 1
- 1
. Now imagine that 30 pairs are given the NS cards. Ten Souths are instructed to rebid 3
, ten rebid 2NT, ten rebid 2
. Then the auction goes however it goes and the hands are played. I guess a way of thinking of "it doesn't matter" is to say that if you could place a bet on which group of ten will come out best, there is no reason to choose one group over the other. That would indeed be surprising..