Let's talk capabilities first. In general, Grand Slam should not be bid unless one can identify all 13 tricks expected to be made.
If North is making the final 6/7 decision in Spades after a Blackwood auction then only 12 tricks can be counted unless the Diamond J is somehow located: 5 Spades; 3 high Diamonds; fifth diamond after one ruff; and A,A,K in Clubs and Hearts.
If South is making the final decision small slam is likewise the maximum. It is hard to conceive any auction enabling South to count tricks instead of relying on controls and an overall strength assessment of 32-43 combined points.
Now for a possible auction playing Two-Over-One-Game-Force, (assuming no interference from the weak and unshapely E-W hands):
- N: 1 Diamond
- S: 1 Spade:
6+ points, 4+ Spades.
- N: 3 Spades:
Game invitational in Spades showing 18-19 points, and either 4 Spades or 3 to a top honour (ie A/K/Q) with a side singleton.
- S: 4 Hearts*:
Slam invitational showing a (either first or second) high card control in Hearts and denying such in both minors.
- N: 4 Spades:
- S: 4NT:
Roman Keycard Blackwood (1430) as South can see the 8/9 card fit in Spades and 32-34 points in the two hands.
- N: 5 Spades:
Two plus the Spade Q.
- S: 6 Spades:
As discussed above, there's no way for South on this auction to identify the tricks needed for Grand.
* This cuebid sytle is one well worth discussing with partner:
First cuebid by each partner must be a high-card control, either A or K, and denies such in any suit skipped over.
Subsequent cuebids by each partner can be either a high-card or a distributional control, but again denying such in every suit skipped over.
First and second round controls are treated equally.
The goal is to more quickly identify, or eliminate possibility of, any suit with two fast losers. This expedites small slam investigation at the possible expense of grand slam investigation. Many partnerships find this trade-off worthwhile.
Also, some partnerships reverse the meaning of North's 3 NT (to convey "just joking partner - I've lost interest." In that case North would call 4 Clubs instead to show continued interest, and the auction would continue as before.
Here's an auction that finds 7 Spades without being ridiculously aggressive:
- N: 1 Diamond
- S: 1 Spade
- N: 3 Diamonds:**
Game invitational showing 16-19 with five or more good Diamonds.
- S: 3 Hearts:
Game forcing as showing 10+ vs 16+.
- N: 3 Spades
- S: 4 Diamonds:***
I have a face card for you, but no A/K in Clubs.
- N: 4 NT:
RKC-1430 with Spades agreed.
- S: 5 Diamonds:
Zero or three.
- N: 5 Hearts:
Do you have the Spade Q also?.
- S: 5 NT:
Yes I do.
- N: & Spades:
I can count 13 tricks: 5 Spades, 5 Diamonds, and A/A/K in the round suits.
** It is unclear to me that the North hand here is quite the right holding for a rebid of 3 Diamonds instead of 2 Clubs, most particularly because it both hides the Spade fit and should promise a good six card suit; but it certainly would work on this hand (with the right partnership agreements).
*** One must have good understanding with Partner when making a call such as this to ensure Partner doesn't mis-read it - in particular:
- when it shows a control;
- when it shows a high honor (ie A/K/Q); and
- when it shows a face card (ie A/K/Q/J).
One possible agreement is to use them when Partner has, respectively:
- opened or simply bid;
- opened and rebid; or
- opened and jump rebid
The South hand evaluates as about 14 points at the deal, and possibly upgrades to about 15 if North rebids Diamonds strongly:
- A/K/A in the majors for 11;
- J/J in the short minors for 1; and
- Both doubletons (Goren style) or one doubleton and Spade length (more modern) for 2;
The North hand evaluates to about 18-19 points as follows:
- Spade Q, Diamond AKQ, CLub A for 15;
- Heart K for 2; and
- Heart Singleton and Diamond length for 2-3
Call it either a good 18 or a weak 19.
With a total combined strength of 32 at the deal, rising to 33-34 on the bidding and both an easily identified fit in Spades and a strong side suit in Diamonds, finding small slam at least should not be difficult.
In a strong club game or better I would expect at least half the field to find a small slam in either Spades or Notrump. With two good five card suits in 8 and 7 card fits respectively, plus all the aces and keycards in both suits and no interference, there seems no excuse to miss the slam unless one has poor partnership understandings. Even a dedicated Goren partnership with just 1430 RKC should find at least small slam in Spades or Notrump on either the same auction as (1) above or:
1D 1S; 3D 3H*; 3S 4D; 4NT 5D; 5H 5NT; 6S/NT Pass
where [*] creates a game force.
Evan an egregious first rebid by North of 2 Clubs should still find a small slam after a 2 Heart (Fourth-Suit-Forcing (and artificial) rebid by South.
The auctions described above and in the answer by ruds all hinge on the first rebid by North, and its correct interpretation by South. There are three possibilities:
- 2 Clubs:
Non-forcing, non-invitational, and hides the spade fit: a problem. Partner can pass 2 Clubs with better Clubs than Diamonds and a bare minimum of points, say 5-7. A hand such as KJTxx xx xx Jxxx will find it difficult to avoid passing 2 Clubs despite being almost cold for a 4 Spade contract.
- 3 Diamonds:
Non-forcing and invitational, but still hides the Spade fit. It works on this deal because South has extras, and in particular the Diamond J. However again partner can pass with a preference and a bare minimum, say on KJTxx xxx xxxx x.
Yes, this will be taken as showing 4 Spades; but three to a high honour, a working singleton, and full values elsewhere is quite acceptable. With a balanced hand and a bit extra Partner can (and should) accept the invitation with 3NT rather than 4NT when holding a 4-card Spade suit.
All choices for East are a lie in some regard: but which call involves the smallest or least error-prone lie? To not make this call puts a lot of pressure on Partner to rebid a five card Spade suit - which is a bad habit to be avoided not encouraged. Hence this is my choice of call for the hand.