[chasetb]

I was brushing up on how to bid a Strong NT, 4-card Majors system, when this hand came up in a bidding/play problem. Since the book was more suited to Beginners, I can understand why they chose their line.
However, I happen to think there is a superior line, at least by my math. Not sure if I'm right though, and only North-South hands are given. Lead is 3♦ -> Assume 4th best.

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[kuhchung]

win in hand, club up
come back to the top spade, club up
if that holds, too hard

i'd probably just cash a second high spade, cross to dummy's diamond, and lead a spade toward the jack

edit: if my opponents card count religiously then i would pay attention to that!

[mikeh]

The holding of HHxx opposite Hxx, missing the Ace, is a classic and is always, for some reason, presented as QJxx opposite Kxx, when it could be KJxx opposite Qxx or KQxx opposite Jxx.

The point is, assuming the 4 card holding is in dummy, when rho, sitting over HHxx, has Ax, you are never taking more than 2 tricks on normal play. Say you guess to lead towards the Hxx. It holds, and now you lead towards HHx. You are almost always going to play an honour, and now LHO's 109 or equivalent will prevent your remaining Hx taking 2 tricks.

In other words, when RHO has Ax, you can't get it right without peeking or making a bad, and lucky, play.

However, when LHO has Ax, you can lead towards the HHxx, and he has to duck. Now, come back to hand and lead again, and the A beats the air, as they used to say.

This works only when you have lots of communication.

Since this line succeeds on all 3-3 club breaks and whenever LHO holds stiff or doubleton Ace, and (very importantly) doesn't require you to commit too early, it seems to be correct. We only need one top spade to get back to our hand (indeed, we could use a diamond for that, but that might needlessly throw away an overtrick).

We do have a percentage play in spades to gain a trick there: cash the AK and lead towards the J, scoring 3 tricks on all 3-3 breaks, and any doubleton Q and any Qxxx(x) on our right. However, we need club tricks anyway and we have to assume they switch to hearts once they win the lead in either black suit, so it is correct to play on clubs.

If you are playing on clubs, then low towards the HHxx is always the way to go, when you have no big spot cards.

At least, that's my view

[FrancesHinden]

mikeh, on 2014-November-19, 18:18, said:

Since this line succeeds on all 3-3 club breaks and whenever LHO holds stiff or doubleton Ace, and (very importantly) doesn't require you to commit too early, it seems to be correct. We only need one top spade to get back to our hand (indeed, we could use a diamond for that, but that might needlessly throw away an overtrick).

The problem is what to do once two clubs towards the QJ have both won.
Win the diamond in hand, club towards dummy holding.
Spade to hand (say), club towards dummy holding.

Now you have a maths problem. A third round of clubs makes with clubs 3-3 or the spade finesse right. The alternative of cashing the other top spade, crossing in diamonds and playing a spade towards the jack makes with spades 3-3 or the queen onside or the queen doubleton.

Once everyone has followed low to two rounds of clubs, the odds of them being 3-3 become quite high. Is that higher than the added chance of Qx of spades that comes from switching to playing on spades at this point?

[rhm]

FrancesHinden, on 2014-November-30, 05:58, said:

Once everyone has followed low to two rounds of clubs, the odds of them being 3-3 become quite high. Is that higher than the added chance of Qx of spades that comes from switching to playing on spades at this point?

No it is lower.
Spades loses only in one out of 4 cases

LHO could have

1) no spades
2) a lower spade singleton
3) ♠ Q singleton
4) ♠ Qx doubleton

In clubs there are only 2 cases (ace singleton or doubleton, unless RHO is playing a very deep game), one of which is favorable, the other not.
Even if the probabilities of these cases are not exactly the same, the outcome is clear.
Best (at IMPs at least) is probably to cash both spade tops before playing the second club towards dummy.

However, if you do not cash the second spade top, I do not see why you could not use both chances.

If you cash only one spade top you can test clubs first.
If clubs do not break next take the spade finesse.

If we compare these two possible lines:

The last line loses compared to the first line if LHO has the spade queen doubleton (8%) or queen third (18%) and clubs are 4-2 (24%), but it wins when clubs are 3-3 (36%) and LHO has four spades to the queen (16%).

This seems to indicate that it is a tiny bit better to play for the first line and cashing both spade tops without testing clubs if the club ace does not appear.

Rainer Herrmann

[WesleyC]

After the ♣QJ win, switching to spades is definitely the best shot.

The apriori chance of 3 spade tricks after ♠A, ♠K and small to the ♠J is 77%, and only outright fails the 16% of the time that West holds ♠Qxxx.

However, given that West led a diamond, there is almost no chance they hold ♠Qxxxx(x) and also a significantly reduced chance of ♠Qxxx.

I'd estimate that playing on spades was well over 90%.