[Antrax]

The following was presented as a play problem in my club last night:

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How do you play 6NT on the J♣ lead?

[KamalK]

My 2-bit as an Interm...

Just have to play for ♦ 3-2 with Honours split. Am in trouble tho if West has KQx♦

Is that right?

Kamal

[Trumpace]

KamalK, on 2011-July-03, 23:59, said:

My 2-bit as an Interm...

Just have to play for ♦ 3-2 with Honours split. Am in trouble tho if West has KQx♦

Is that right?

Kamal

You can also cater to some 4-1 splits, and I am guessing that is point of this hand.

[KamalK]

Trumpace, on 2011-July-04, 00:02, said:

You can also cater to some 4-1 splits, and I am guessing that is point of this hand.

Of course, yes. Looking forward to the posts.

Thanks

[jillybean]

(disclaimer I fail hopelessly at these problems)
I have 3 tricks each in ♣,♥,♠ so I must play ♦'s for 1 loser.
I have to hope East has ♦KQ (not likely), they are split or doubleton, if West has KQx I am not making this.
I will play ♦9 and let it run and assuming it loses, play low to 10 next.

[1eyedjack]

Incidentally, you also expect to lose to KQ doubleton offside, not just KQx(x..) as suggested by some.
Leading low to JT (not leading 9) on the first round is preferable, in case East has singleton honour.

[mrdct]

You should cash two tops in each suit outside of ♦ and then run the ♦9 keeping an entry in hand to repeat the ♦ hook just in case RHO is 2272 with ♦KQxxxxx offside. There are a whole bunch of other ♦KQ offside situations you can cater for double-dummy, but these could put a cold contract at risk.

[1eyedjack]

mrdct, on 2011-July-04, 00:32, said:

You should cash two tops in each suit outside of ♦ and then run the ♦9 keeping an entry in hand to repeat the ♦ hook just in case RHO is 2272 with ♦KQxxxxx offside.

DIRECTOR!!!

[mrdct]

1eyedjack, on 2011-July-04, 00:38, said:

DIRECTOR!!!

What - no 17-card ♦ suits where you come from?

[Antrax]

Bummer, I miscopied the hand. The hand given was very similar:

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I hope it doesn't change anything important.
The reason I posted this as "sanity check" is that the proposed solution was to cash the ten non-diamond winners (discarding the 8♦ from dummy), then lead low to the T. The expectation was that either E has both diamond honors, or W is endplayed. What I don't understand is why is W expected to have only diamonds - the lecturer said something about "since our hands are balanced, theirs must be too". I'm not very adept with Bridge probabilities yet, but it seems that playing for no KQ♦ with W is a 75% shot, whereas hoping clubs and diamonds both break 4-3 is already ~40%.
I'm also not sure what happens if E plays high on the diamond lead, it would seem this sticks declarer in dummy. Of course irrelevant if the diamond position in the ending is ♦Kx opposite ♦Qxx, but on that layout just finessing also works quite well, and the line fails if it's ♦Kxx opposite ♦Qx, for instance, where the finesse works.
In short, I couldn't figure out why the finesse isn't always better, and I'm almost certain just cashing winners and hoping the defenders will insist on not baring their diamond honors is not a good line. Is it?

[mrdct]

That changes things a little bit, including making my 17-card ♦ suit layout more plausible. Now I cash 3♠, 2♥ and 2♣ and hook the ♦ which at least gives me a make when RHO has a 3262, but that's the only layout with ♦KQ offside I can safely guard against without risking my contract on cold layouts such as split ♦ honours or KQ onside. At the table you might have a look at your opponent's carding and sniff something else out and some knowledge of how honest their count is might be relevant.

[Trumpace]

Antrax, on 2011-July-04, 00:51, said:

Bummer, I miscopied the hand. The hand given was very similar:

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I hope it doesn't change anything important.
The reason I posted this as "sanity check" is that the proposed solution was to cash the ten non-diamond winners (discarding the 8♦ from dummy), then lead low to the T. The expectation was that either E has both diamond honors, or W is endplayed. What I don't understand is why is W expected to have only diamonds - the lecturer said something about "since our hands are balanced, theirs must be too". I'm not very adept with Bridge probabilities yet, but it seems that playing for no KQ♦ with W is a 75% shot, whereas hoping clubs and diamonds both break 4-3 is already ~40%.
I'm also not sure what happens if E plays high on the diamond lead, it would seem this sticks declarer in dummy. Of course irrelevant if the diamond position in the ending is ♦Kx opposite ♦Qxx, but on that layout just finessing also works quite well, and the line fails if it's ♦Kxx opposite ♦Qx, for instance, where the finesse works.
In short, I couldn't figure out why the finesse isn't always better, and I'm almost certain just cashing winners and hoping the defenders will insist on not baring their diamond honors is not a good line. Is it?

I think it is time to get a new teacher!

[1eyedjack]

I think that the first hand that you posted was the more interesting.

[Antrax]

In retrospect yes, but at my current skill level I also wanted to get confirmation that I'm not crazy in thinking "cashing out then leading diamonds" is an inferior line.

[nige1]

Antrax's 6N on ♣J lead (version 2)

Mrdict's line is clever.
Your main hope is the 75% double diamond finesse but
you retain some end-play chances...
Play ♣Q, ♠KJ, if both follow then ♠QA discarding a ♦.
Then partial strip... ♣A, ♥KQ, finesse ♦
A useful bar conversation-topic when LHO has say...
♠ xxxx ♥ xx ♦ KQxxx ♣ Jx or
♠ xxx ♥ xx ♦ KQxxxx ♣ Jx

Amusingly, a kibitzer can always make 6N by South, against any distribution of opponents' cards

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[semeai]

Antrax, on 2011-July-04, 00:51, said:

What I don't understand is why is W expected to have only diamonds - the lecturer said something about "since our hands are balanced, theirs must be too". I'm not very adept with Bridge probabilities yet, but it seems that playing for no KQ♦ with W is a 75% shot, whereas hoping clubs and diamonds both break 4-3 is already ~40%.

Nigel's line, giving a slight chance of endplay, is very good. Your basic numbers should give the right idea for these lines, but strange things can happen when distributions are so constrained, so let's double check.

Line A: Nigel's line.
Line B: Nigel's line up to the diamond finesse, but cash your last heart and club winners first.

The most favorable case for Line B will be when spades were 4-2, so from now on I'll restrict to this.

A minor addendum to Nigel's line is that if spades are 4-2 and East pitches a club and a heart on the spades, and then both follow to two rounds of hearts and clubs, then you go for Line B is now more interesting which is now 100%. In general, you should watch East's discards on those two spades (and whether they were slow) and think about what distributions he'd make those discards with and/or have a problem with. This gets complex to think about comprehensively, so let's ignore East's discards for our math check.

After spades are 4-2 and both follow to two rounds of hearts & clubs, possible distributions for West are (writing x2 when you get another distribution by swapping hearts & clubs);
4252, 4504 x 2
4333, 4243 x 2
4522 x 2, 4513 x 2, 4432 x 2, 4423 x 2, 4414

The first row you're 100% with line A or line B. The second row you're 100% roughly 75% with line B and on the double hook for line A. The third row you need KQ onside for see below (worse than just KQ onside) for line B and you need the double hook for line A. It should be fairly clear by now line A is going to win out, as roughly 75% of rows 2 and 3 is going to be better than 100% roughly 75% of row 2 and a bit more roughly 25% of row 3, even though the distributions in row 2 are typically more likely than those in row 3. Still, we got this far, so let's keep going.

Start with 4333 for West. Then East is 2434. Ignoring spades, there are (7 choose 3) = 7c3 = 35 ways to distribute the hearts, 7c3 = 35 ways to distribute the clubs, and 6c3 = 20 ways to distribute the diamonds, for a total of 35*35*20. Line B wins on all of these. Line A misses on 4 of the diamond distributions (KQx with West, for 4 choices of x), so gets 35*35*16 of them.

Continuing this analysis for each of the cases (computations omitted), I find (ignoring spades as we already know them) that out of 146216 cases, Line A wins on 123284 of them and Line B wins on 87318 50176 of them. That is, after you find spades 4-2 and at least 2 cards in each opponent's hand in hearts and clubs, Line A is 84% and Line B is 60% 34%.

Added: What I had wasn't right. Line B isn't 25% for KQ onside for 4504 x 2 or row 3. When KQ onside for these you make on all the 4414-2353 hands for West-East because East is certainly stripped now too. On the others, it depends what East discarded, but East can defeat you. Also, the hands row 2 you're not 100% on, because if East has KQ of diamonds and has kept an outside card (always possible on these) you're again set. This makes it roughly 75% for these.

[Antrax]

Oh wow, thanks for the investment
The lines are actually closer than I thought, intuitively it seemed like double finesse (and nigel's line, which improves it) is much better than the proposed line, but I didn't take into account that you can bail out on the proposed line if suits show signs of not breaking properly.

[semeai]

Antrax, on 2011-July-04, 08:41, said:

Oh wow, thanks for the investment
The lines are actually closer than I thought, intuitively it seemed like double finesse (and nigel's line, which improves it) is much better than the proposed line, but I didn't take into account that you can bail out on the proposed line if suits show signs of not breaking properly.

Do look at my edit: I made a bridge error (the math was okay). The strip is foiled when the East hand has KQ of diamonds and isn't itself stripped. This eats away at a huge amount of the line's percentage, actually.

[Antrax]

semeai, on 2011-July-04, 08:53, said:

Do look at my edit: I made a bridge error (the math was okay). The strip is foiled when the East hand has KQ of diamonds and isn't itself stripped. This eats away at a huge amount of the line's percentage, actually.

Ah okay, that's much closer to my "back of the envelope" calculations.

[semeai]

Antrax, on 2011-July-04, 08:58, said:

Ah okay, that's much closer to my "back of the envelope" calculations.

Yes, though if the South hand had AQ10x of diamonds (AQ9x is also interesting) instead of AJ10x of diamonds, my original numbers would be right even though the "back of the envelope" would be what you had above. Really, the "back of the envelope" calculation for the problem hand should include the 75% chance that K,Q are split or with West as part of the endplay line when South has AJ10x, so the 34% I got is somewhat more than you'd expect without taking into account the good breaks.