A lucky or reasonable 7♦?

♠♥♦♣  

Matchpoints Pairs
Board 5, NS Vulnerability
You sit West:

♠	KT5
♥	32
♦	KQJ7
♣	JT96

 

W	N	E	S		Explanations:
	－	2♣	－		2♣: 22+ any or 9+ tricks.
2♥!	－	3♦!	－		2♥: 5+RP (A=3 K=2 Q=1) any.
4♦	－	4♥	－		3♦: 5♥+ 4+♦ or 4+♥ 5+♦.
4♠	－	4N	－		(Usually bid 2N instead of 3♦ if suitable)
5♣	－	5♥	－		4♦: 4+♦. (3♥ here shows 3+♥ and ask if 5♥)
5♠	－	5N	－		4♥: Cue-bid with at least 2 of ♥AKQ.
??					4♠: Control of ♠.
					4N: RKCB to ♦.
					5♣: 1 or 4 keycard(s).
					5♥: Ask for ♦Q.
					5♠: ♦Q & ♠K.
					5N: Ask for side K and interest in grand slam.

What would you bid?
Have you ever shown all of your hand?
How do you imagine partner’s hand?

♠	A?
♥	A??x(x)
♦	Axxx(x)
♣	A?

East must have 22+ and all of the keycards with 1543/1453/2542/2452/1552/ 2551/1651/1561. Also, he should bid 7♦ with solid ♥. That is to say, we must lack of one or more side K/Q.

1651/1561:

(a)			(b)			(c)			(d)
♠	A		♠	A		♠	A		♠	A
♥	AKxxxx		♥	AKxxx		♥	AQxxxx		♥	AQxxx
♦	Axxxx		♦	Axxxxx		♦	Axxxx		♦	Axxxxx
♣	A		♣	A		♣	A		♣	A

With (a) & (b), East should bid 7♦ by himself or ask for ♥Q by bidding 6♥. It would better to play 7♥ instead of 7♦ if possible when playing matchpoints. Of course, it is not necessary if no one bid a grand slam.

With (c) & (d), East should open 1♥/1♦ instead in our agreements.

2542/2452:

(e)			(f)			(g)			(h)
♠	AQ		♠	Ax		♠	Ax		♠	AQ
♥	AKxx(x)		♥	AKQx(x)		♥	AQxx(x)		♥	AQxx(x)
♦	Axxx(x)		♦	Axxx(x)		♦	Axxx(x)		♦	Axxx(x)
♣	Ax		♣	Ax		♣	AQ		♣	AQ

All of above would open 2N or 2♣ then bid 2N because of too many points in short suits and bad quality of ♦.

1543/1453/3451/3541:

(i)			(j)			(k)			(l)
♠	A		♠	A		♠	AQJ		♠	AQx
♥	AKJx(x)		♥	AKQx(x)		♥	AQxx(x)		♥	AQJx(x)
♦	Axxx(x)		♦	Axxx(x)		♦	Axxx(x)		♦	Axxx(x)
♣	AQx		♣	Axx		♣	A		♣	A

With (k) & (l), East would open 1♥ or 2N. Also, with (i), (k), (l), there is over 50% to make 7♦. (j) would be a problem.

But why East cue-bid 4♥ before 4N RKCB? East need to know ♦KQ but a ♠ control. East will create a big problem for himself if west cue-bid 5♣. 5N after 5♣ will be RKCB. East can ask for trump K but no way to know trump Q. Thus, (j) is not likely to be East’s holding.

1552/2551:

(m)			(n)			(o)			(p)
♠	A		♠	AQ		♠	A		♠	AQ
♥	AKxxx		♥	AKxxx		♥	AQJxx		♥	AQJxx
♦	Axxxx		♦	Axxxx		♦	Axxxx		♦	Axxxx
♣	AQ		♣	A		♣	AK		♣	A

East is most likely to be 5521. There is almost 50% to make 7♦ with (o) & (p), and far over 50% with (m) & (n). For the same reason mentioned above, (n) & (p) is the most likely to be East’s hand.

All in all, West decided to bid it and got the top.

On the other hand, could East directly ask for ♥Q by bidding 6♥ after 5♠?

The first question is the meaning of 6♥. Would it be to play with solid ♥ and bad ♦? 
No, East should then bid a grand slam. 6♥ could be to play only if lacking of trump Q.

Next, is East enough to bid 6♥? Can it afford to play 6N without ♥Q?
No, he can count for 3♠+2♥+5♦+1♣, only 11 tricks.

Can East just bid 7♦ when he knows ♠K+♦KQxx?
No, though West can bid 3♥ to show 3 cards ♥ and ask for if 5 cards ♥, he can be 3 small ♥ & 4+♦. Then, 7♦ will be only 25% with ♥QJ onside.

Hence, the best East can do after 5♠ is to bid 5N.

Isn’t there any way to distinguish the hand (n) & (p)?

Yes, if EW have much more detailed agreements for RKCB. East can bid 5♦ instead of 5♥ to ask for trump Q. It is almost impossible to ask for 2 keycards to reach a slam for a 2♣ opener. However, it is difficult to define and easy to cause misunderstanding.

In my opinion, this is a reasonable and lucky 7♦. :p