[jdonn]

This is from memory so you will pardon me if it's a hair off.

Scoring: BAM

---

The auction at the table was

1♥ DBL P 1♠
2♣ 2♠ P P
3♥ P P P

There are certainly many different options with the west hand which might also make the bidding a good problem, but I am focusing on the play after the auction as it actually occured.

North leads a small heart (not the J or 9.) How do you plan to make this? Please elaborate relatively far into the hand after likely defensive counters to whatever you do.

Edited: Originally opener had the heart 8, I changed it to the 6 which I think is closer to the actual layout. I also gave him the 7 of clubs which I'm pretty sure was his highest.

[awm]

The obvious line seems to be to duck the lead to hand (winning as cheaply as possible). Then cash the top two clubs and ruff a club with the ♥Q. Finally lead a diamond up towards the king, planning to play the king if RHO plays low. Ignoring the possibility of clubs 6-1 (which seems very unlikely), this will often get us 9 tricks if hearts break or the diamond ace is on, or 10 tricks if both hearts break and diamond ace is on.

There is some chance that after winning the diamond (in either hand) opponents manage to get RHO on lead to play the 4th club (note that it's probably more likely that the longer clubs are with LHO, but you never know). In this case I'd play RHO for the highest missing heart honor (i.e. LHO to lead from xx, not low from Jx or 9x).

[dburn]

Since South appears to have bid a three-card spade suit, his most likely distribution is 3=4=3=3. Since North raised him, he is likely to be above minimum for his double and therefore to have the aces of diamonds and spades in a classic 4=1=4=4 shape.

In that case, the line suggested by awm will fail whereas this will succeed: win the lead as cheaply as possible and play a spade (you can cash one or two clubs if you like, but on no account must you ruff a club before playing a spade).

North wins and plays a club (he must, to avoid immediate material loss). Cash the top clubs, ruff a club in dummy, ruff a spade and play a club. North wins and exits with a spade (either the queen or a low one to South's queen). Ruff, exit with a diamond, and wait to make three more trump tricks.

Of course, this line will fail if North began with a doubleton heart. But the bidding strongly suggests otherwise.

[jdonn]

David, I think your (very good) analysis made me realize the spots in hearts weren't quite this good. How about if you were missing the 8 as well?

[dburn]

jdonn, on Nov 27 2007, 09:09 PM, said:

David, I think your (very good) analysis made me realize the spots in hearts weren't quite this good. How about if you were missing the 8 as well?

No great matter, except that you need to win the first heart with the queen in dummy, then proceed as I have indicated.

[jdonn]

That was my original analysis too. But it goes down at the table. No matter, except I think another line that would have worked is worthy of strong consideration...

[jdonn]

Well it's not getting interest like I hoped so let me try to generate discussion instead. David's (and my) line would have gone down at the table since south was 3442 with just the jack of diamonds and hearts. However west could have made by simply running 6 rounds of hearts with the help of a finesse. North gets squeezed and thrown in and has to lead into the diamond king. This of course wouldn't work if north was 4144 since south could guard clubs and north could unblock them, although it would be easy to mess up the defense.

However it wasn't until later that what I now think? is the best line came to me. Win the heart queen, play a heart to the ten, and play the spade king. Then presuming north plays a club honor you duck so north has to win. Then win the next club and proceed with the squeeze line. If north plays a low club to south, I would suggest winning it and playing the squeeze anyway hoping that south can't get on lead in clubs later, but it's not clear without knowing what our club spots are. Of course these might not work if south had the spade queen, so nothing is clear.

Anyone got any brilliant ideas about what is right? At least this seems like an alternative to the original line, failing when south was 3424 but gaining against 3442, as well as some other factors involved.

Edit: I suppose it's a technical improvement to win the heart ten then queen, rather than the other way around. However I'm so sure (even before I saw the full hand) that the lead is stiff (and even if I'm wrong it's usually from xx) that I just overlooked it.

[dburn]

As far as I can make out, the line jdonn suggests fails against any 4=1=4=4 North hand unless the clubs are specifically QJ109.

It also fails against 4=2=4=3 - embarrassingly so when North's hearts are Jx, since there are nine top tricks against that distribution simply by ruffing a club in dummy.

It fails against 4=1=5=3 if the intention is to duck the first round of clubs, leaving North on lead (the details are left as an exercise for the reader). It can succeed against that distribution if North's clubs are precisely QJ10, but not the way jdonn intends to play.

It works only against 4=1=3=5, which was of course the actual distribution, but I am not sure that this justifies calling it "the best line".

Certainly, there is no guarantee that North's shape is precisely 4=1=4=4. 4=1=5=3 and 4=1=3=5 are eminently possible; each is individually more likely than 4=1=4=4 and together they are much more likely.

But the Generalised Principle of Restricted Choice applies (see thread on AKQ9xx facing xx): one assumes that South bid 1S because she had to (with 3=4=3=3 shape), not because she chose to (with three spades and a four-card minor). That is why I committed myself to playing as I did. Of course, it didn't work. Life is like that.

[jdonn]

I don't see how I would go down if north had, say, QT9x of clubs, unless when he led a low one his partner put in the 8? I'll hold my cards back next time. Also I don't see how 4243 is relevant, since then both ways were down. Anyway I am not at all sure of the best line, if you say mine isn't then I believe you. But I think it's at least very interesting, and good enough to merit consideration. I just thought it was an interesting hand, that's all. Yours is certainly more natural, since it always works against 4144 which is the obvious assumption.

Not sure why I'm saying "yours", it's how I played too when I was given this problem

[dburn]

jdonn, on Nov 28 2007, 09:29 PM, said:

I don't see how I would go down if north had, say, QT9x of clubs, unless when he led a low one his partner put in the 8? I'll hold my cards back next time.

If North's clubs are (say) Q1098 or any four-card holding other than QJ109, she will not play a club on winning the ace of spades. Instead, she will play either the queen of spades or a low spade to South's queen, and you will be unable to make the contract.

I agree that the hand is an interesting one, and I thank you for bringing it to my attention.

[jdonn]

dburn, on Nov 28 2007, 09:39 PM, said:

jdonn, on Nov 28 2007, 09:29 PM, said:

I don't see how I would go down if north had, say, QT9x of clubs, unless when he led a low one his partner put in the 8? I'll hold my cards back next time.

If North's clubs are (say) Q1098 or any four-card holding other than QJ109, she will not play a club on winning the ace of spades. Instead, she will play either the queen of spades or a low spade to South's queen, and you will be unable to make the contract.

I agree that the hand is an interesting one, and I thank you for bringing it to my attention.

That is true. How about winning the heart ten at trick one and exiting a spade to force the club return? I guess that would at least be the 'correct' version of the line. Alternatively you could win the queen and exit spade, and simply revert to the line you suggested if north plays anything but a high club. But you have shown me the flaw in playing two rounds of hearts first, touche.

Hypothetical question. Would you prefer the squeeze line if south's highest club below the AK were the 8? 9? 10? 10-8?

[dburn]

jdonn, on Nov 28 2007, 09:50 PM, said:

That is true. How about winning the heart ten at trick one and exiting a spade to force the club return? I guess that would at least be the 'correct' version of the line. Alternatively you could win the queen and exit spade, and simply revert to the line you suggested if north plays anything but a high club.

Winning with the queen and playing a spade fails against 4=1=3=5 (North simply exits with the queen of spades, and you cannot reach dummy).

Winning with the ten and playing a spade is a considerable improvement: it works against both 4=1=4=4 and 4=1=3=5 if you duck a high club return from North or win a low club return, provided that South cannot later obtain the lead in clubs. It fails against 4=1=5=3 if you intend to duck a club, win the next club, cross to ♥Q, ruff a spade and run hearts; instead, you must cash the other top club, cross to the queen of hearts and pass the jack of spades to North. If North is 4=1=5=3 without the queen of spades, you cannot make the contract (and the trump lead was the only one to beat you).

[Halo]

Am I misreading or do you need to take away West's spade six as well for 4135 in North to beat declarer?

[dburn]

Halo, on Nov 29 2007, 01:45 PM, said:

Am I misreading or do you need to take away West's spade six as well for 4135 in North to beat declarer?

I should imagine you are misreading, since West does not have the spade six.

[jdonn]

dburn, on Nov 29 2007, 07:36 AM, said:

jdonn, on Nov 28 2007, 09:50 PM, said:

That is true. How about winning the heart ten at trick one and exiting a spade to force the club return? I guess that would at least be the 'correct' version of the line. Alternatively you could win the queen and exit spade, and simply revert to the line you suggested if north plays anything but a high club.

Winning with the queen and playing a spade fails against 4=1=3=5 (North simply exits with the queen of spades, and you cannot reach dummy).

As I said, if he does that you just ruff a club in dummy and revert to the line you originally suggested. In other words that particular suggestion of mine was to follow your line, but consider that when west returns a club at trick 3 you have the option to changes horses midstream and duck if west is retaining the lead.

I can count on you to point out if this is wrong, but it seems that at that point you make either way vs. 4144, ducking is necessary vs 4135, but not ducking is necessary vs 4153. So at best it's a guess perhaps? Even if that's true then you should surely duck just in case west is foolish enough to switch to a diamond at that point (not to mention the trump lead carries at least a slight indication of club length). So my waffling continues, I now think the best line is the one you suggested, except to duck if west returns a high club at trick 3 and go for the squeeze line instead.

(I know west could switch to a spade at trick 4 and you go down vs. 4135, but that seems unlikely when he didn't play one at trick 3, plus you are no worse off for having ducked anyway so it seems irrelevent. Well except for going down more since it's a BAM and all..... ok I give up )

[Halo]

dburn, on Nov 29 2007, 02:12 PM, said:

Halo, on Nov 29 2007, 01:45 PM, said:

Am I misreading or do you need to take away West's spade six as well for 4135 in North to beat declarer?

I should imagine you are misreading, since West does not have the spade six.

Thanks

The six hearts - just good enough to win against 4135?

[dburn]

Halo, on Nov 29 2007, 02:39 PM, said:

dburn, on Nov 29 2007, 02:12 PM, said:

Halo, on Nov 29 2007, 01:45 PM, said:

Am I misreading or do you need to take away West's spade six as well for 4135 in North to beat declarer?

I should imagine you are misreading, since West does not have the spade six.

Thanks

The six hearts - just good enough to win against 4135?

I am not sure what I am being asked here. To reduce the problem to simple terms, we fix the East-West hands as:

Scoring: BAM

---

North has doubled 1♥ for takeout, then raised South's 1♠ response to 2♠. West declares 3♥ on the lead of a trump.

We assume that North has the ace and queen of spades, the ace of diamonds, and a singleton trump in a 4=1=5=3, 4=1=4=4 or 4=1=3=5 shape. We also assume that South has two clubs higher than North's second lowest club.

Given these conditions, West can make 3♥ against any defense, provided that West can guess North's distribution. No line of play, however, caters for every one of the three distributions given above.

In all cases, West can succeed by winning the first heart with dummy's queen. This is the only line that succeeds against 4=1=4=4 under the conditions given. Now:

Against 4=1=5=3, which we will call distribution 1, West has two possible winning lines.

[1A] She can cash two clubs and ruff the third, then play a spade to the king and North's ace. North attempts to exit with ♠Q (any other play is obviously fatal), but West discards her remaining club. Now North must concede a ninth trick either to West's ♦K or East's ♠J (dummy does not need ♠10 in this variation).

[1B] She can play a spade to the king at trick two. North plays a club, overtaken by South, but declarer cashes ♣AK, ruffs a club, and passes ♠J to North who must concede a ninth trick on her return (dummy does need ♠10 in this variation).

One of jdonn's suggested lines, that of winning ♥Q and running hearts with the aid of a second-round finesse to squeeze North, fails if distribution 1 exists (call this line 1J). Another, that of winning the first trick with ♥10 and playing a spade, succeeds provided that he transposes into [1B] above and does not attempt to squeeze North by running hearts.

Against 4=1=4=4, which we will call distribution 2, West has essentially only one winning line:

[2A] She must play a spade to the king and North's ace, then win a club exit, cash a second club, and ruff a third. Then, she ruffs a spade and exits with a club to North. North exits with ♠Q, ruffed by declarer, who exits with a diamond and waits to make three more trump tricks.

Neither of jdonn's suggested lines above succeeds against distribution 2. If, however, South has only one club higher than North's second lowest club, jdonn can succeed by winning the first heart with the ten and playing a spade, then ducking North's attempted club exit unless South overtakes it. Later, the run of the trumps will strip-squeeze North into conceding a trick to ♦K one way or another.

Against 4=1=3=5, which we will call distribution 3, West can succeed after winning ♥Q only by

[3A] at once drawing trumps with the aid of a finesse. This is line [1J] above. After winning trick 1 with ♥10, declarer can succeed by playing a spade at once, or after crossing to ♥Q and following line [1J].

In essence, with no significant spot cards declarer must choose at an early stage which line to follow. If the club spots are such that declarer considers it more likely than not that South cannot overtake both of North's two lowest clubs, then line [1J] is perhaps preferable to line [2A], but it is very close.

Finally, to answer Halo's actual question, the six of hearts is of no relevance whatsoever.