Fit Jumps Opener has 5422 Hand 5

Board 5 North Deals	♠ 9 5 ♥ A 9 5 2 ♦ A K Q 6 3 ♣ Q 2
♠ Q 8 3 2 ♥ J 10 8 ♦ 9 4 ♣ 8 7 5 3	N W E S	♠ K J 7 6 4 ♥ 6 4 ♦ 7 2 ♣ J 10 6 4
	♠ A 10 ♥ K Q 7 3 ♦ J 10 8 5 ♣ A K 9

West	North	East	South
	1 ♦	Pass	2 ♥
Pass	3 ♥	Pass	3 NT
Pass	4 ♦	Pass	4 NT
Pass	5 ♥	Pass	5 ♠
Pass	7 ♥	All pass

7 ♥ by South

Lead: ♦ 9

Made 7 — NS +1510

Again after the fit-jump north's 3 ♥ shows 12-16 points with no shortage. With 17 points and good points south has slam interest even opposite 12-14 so can cue immediately. Since 3 ♠ would be the frivolous slam try, we use 3 NT to show a spade cue-bid.

Perhaps 4 NT is an overbid. But even if north has ♠ xxx ♥ Axxx ♦ AKxx ♣ xx slam has a play. Although if you swap the black suits lengths there is no play.

Note also having made a serious slam try with 3 NT south can safely bid 4 ♥ and north will move even with only a good 12-14. On this hand north has extras so will definitely move.

Let's say south bid 4 ♥ instead of 4 NT then north has a problem in clubs. Can south not have a club control. The most south can have without the ♣ A or ♣ K is: ♠ AKQ ♥ KQJx ♦ Jxxx ♣ Jx. That hand has almost no slam interest opposite 12-14. It needs the ♥ A and the ♦ AKQ and a club control or the equivalent before thinking about slam and that is outside the minimum range. Therefore from north's perspective south must have a club control. Therefore can safely take control with 4 NT. South would respond with 5 ♦ showing three key-cards. North can ask about the ♥ Q with a bid of 5 ♠ and show would show the ♥ Q and the ♣ K.

Now north has a problem. Opposite the actual hand shown the grand is cold but if we swap the black suit lengths then there is no play.

On balance the actual hand is more likely. Let's see why. We are only concerned with responder being 2=4=4=3 or =3=4=4=2. Any other shape consistent with the bidding we can underwrite the grand (perhaps except 2=4=5=2 - mirror distributions). On the assumption that south has one of those two distributions we know that south has ♠ Ax or ♠ Axx and ♣ AKx or ♣ AK respectively. We can count the number of possible combinations. We know 16 of south's points. If south had 18 with a card like the ♠ Q they probably would not have stopped at 4 ♥. Therefore there are eight possible holdings of ♠ AJ or worse for partner - ten small cards of the jack and below minus the two in north's hand. For ♠ Axx - ♠ AJT or worse - there we have eight cards and need to choose two. This can be done in 28 ways - count them or look up how to mathematically calculate combinations. On the other hand there is obviously only one holding of ♣ AK but there are nine holdings of ♣ AKJ or worse. Putting this together we have 8 holdings of ♠ AJ or worse multiplied by the 9 holdings of ♣ AKJ or worse which is 72 possible hands compared with 28 holdings of ♠ AJT or worse multiplied by just thee one holding of ♣ AK.

It is a happy accident that this adds to 100, but the result is that there is a 72% chance of the favourable holding. The grand is not quite that good as there is the possibility of adverse breaks.

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