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With my usual partner, 6C=0, 6D=Q, 6H=A or K, higher=2 of top 3.

 

But "whatever shows 1" has to be the right answer. We don't know why partner asked, just that he had 21 other calls between 1H and 5NT available if he had wanted to find out something else.

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Whatever my agreement is. For me, 6C shows the A or K, 6D the Q and 6H none (6NT 2), so I will bid 6D. The same answer as Siegmund, but from the opposite direction. Partner must be 0580 or similar.
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6C or whatever shows 1, partner may well be v KTxxx AKQJxxxx v or something. Partner can bid 6D to ask whether it is the queen or A/K.

You were pretty close to the hand:

 

void

K 10 8 x x x

A K Q J x x x

void

 

I just took a stab at 6H ( over partner's 1H rebid ) since I had no GSF "enhanced system" .

 

But I should have played Culbertson's "plain vanilla" GSF just in case partner had BOTH A and Q to end in 7H .

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

So far, I think Frances' "opposite direction" system is best ...

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Playing Jeff Rubens' original responses for Kickback GSF, 5 is GSF for hearts

 

1 Step - i.e. 5NT                     ace or king, but not ace with 3 or more trump than expected
2 Steps - i.e 6[clubs]                queen and/or 2 more trump than expected, or 3 or more trump than expected
3 Steps - i.e 6[diamonds]             No trump honor but 1 more trump than expected
6 of trump suit - i.e. 6[hearts]      No trump honor and expected length
higher (6NT or other to try for 7NT)  2 of the top 3 or ace with 3 or more trump than expected

 

Your response would be 6. Since you showed 4 or more hearts in the bidding, this could be queen, or 6+ trumps which is almost impossible on this auction.

 

These methods give you a chance to safely bid a grand with 12 trumps missing the king, or 10 or 11 trumps missing the queen.

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Whatever my agreement is. For me, 6C shows the A or K, 6D the Q and 6H none (6NT 2), so I will bid 6D. The same answer as Siegmund, but from the opposite direction. Partner must be 0580 or similar.

Same for me.(expect with 2 we bid 6NT; or 6S/7C/7D with an extra honor in the suit bid)

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Whatever my agreement is. For me, 6C shows the A or K, 6D the Q and 6H none (6NT 2), so I will bid 6D. The same answer as Siegmund, but from the opposite direction. Partner must be 0580 or similar.

 

While having a hughmongous jump like 5s to show GSF for hearts is ideal; even using

5n for all suits can be bid well if you use the above method to save space when you

have a better holding. There is zero practical benefit to showing the Q with your

bid (6c) if you use 6c to show the A or K partner will (on rare occasion) be able

to bid 6d asking you to bid 6h with the K and anything else with the A. 6n to

show 2 is ok if it promises two outside aces while a bid of another suit shows that

ace (and 2 of the top 3) and denies any other ace and a bid of 7h shows 2 of top 3

and no outside aces:)

 

The 5N as GSF pops up rarely but using a refined agreement like the one proposed by

franceshinden is an upgrade that should be a part of every improving players bidding.

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Frances' scheme looks good to me for the hearts + 5NT case. If we instead use 5 as the GSF then one option is bumping these responses down one step (which is effectively what Rubens is doing) while another (posted a couple of years ago) is simply to use a reverse step method:

 

1st step = 5NT = ace (then 6 asks for extra length)

2nd step = 6 = king (then 6 asks for extra length)

3rd step = 6 = queen

4th step = 6 = none

5th step = 6 = KQ

6th step = 6NT = AQ

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