A math problem?

[cherdano]

Hand 3 against Meckwell (hand rotated):[hv=d=e&v=n&n=sakq98hkqxdaqjc86&s=sxxh98xdktcakt7xx]133|200|Scoring: IMP

1♣-1♠

2♣-2♦*

2N-6N[/hv]

How do you play on the lead of D7?

 

If it matters, at the other table Nickell-Hemant Lall have these hands.

 

For the record, ♣QJ or QJx onside is 13.6 percent, ♥A onside AND spades running is 19.4 percent.

[ArtK78]

You can combine your chances somewhat.

 

Play for the HA onside. Win the diamond in hand and play a heart towards dummy. If that wins, cross in clubs (hoping that a club honor comes up) and play another heart towards dummy. Assuming that the HA is onside, you can now cash the remaining high club to see if the QJ of clubs comes down doubleton. If that does not happen, try to run the spades.

 

You succeed whenever the HA is onside and EITHER the QJ of clubs falls doubleton or the spades run.

 

By the way, why does the South hand open the bidding 1C? If is it systemic to open this light, then North does not have a 6NT call.

[cherdano]

By the way, why does the South hand open the bidding 1C? If is it systemic to open this light, then North does not have a 6NT call.

Your agreement is you need a nice 11-count with balanced hands to open (but you pass some bad 12 counts), and you open somewhat lighter with balanced hand. This one is very borderline in our style, so I think both the opening and the 6N bid are ok.

[ralph23]

You succeed whenever the HA is onside and EITHER the QJ of clubs falls doubleton or the spades run.

 

If the QJ of ♣ is a doubleton, then you succeed wherever the Ace of ♥ is. You would then have 6♣, 3♦ and 3♠ -- if the Doubleton Theory is true.

 

You will succeed if EITHER

(1) the Doubleton ♣ Theory is true, OR

(2) the ♥ Ace is onside and EITHER

[(i) the ♠ are splitting 3-3 OR

(ii) the JT of ♠ is doubleton].

 

You must lead the ♥ at trick 2, because that's the only way you can try both theories. If you cashed the ♣ first, that would test the Doubleton Theory, but now <_< if that theory is wrong, you have no way back to your hand. You need two entries back to your hand and the top ♣ are all you have.

 

NB -- The QJx of ♣ onside does me no good, as to take advantage of that position, you have to take a first round ♣ finesse with the Ten, and if that loses, you're down once they lead a ♥.

[TimG]

If the QJ of ♣ is a doubleton, then you succeed wherever the Ace of ♥ is. You would then have 6♣, 3♦ and 3♠ -- if the Doubleton Theory is true.

 

You will succeed if EITHER

(1) the Doubleton ♣ Theory is true, OR

(2) the ♥ Ace is onside and EITHER

[(i) the ♠ are splitting 3-3 OR

(ii) the JT of ♠ is doubleton].

 

You must lead the ♥ at trick 2, because that's the only way you can try both theories. If you cashed the ♣ first, that would test the Doubleton Theory, but now :P if that theory is wrong, you have no way back to your hand. You need two entries back to your hand and the top ♣ are all you have.

 

NB -- The QJx of ♣ onside does me no good, as to take advantage of that position, you have to take a first round ♣ finesse with the Ten, and if that loses, you're down once they lead a ♥.

I'm not sure about this. When are you going to test the clubs? If Art's line is followed, he would win in hand, play a heart to the King, play a club to hand and another heart. If the Ace of Hearts of offside, the defenders can likely now cash at least one more heart.

 

If instead, you test the clubs after the first round of hearts, you can't fall back on the heart onside+spade break because there is a danger you will lose a heart and a club when you play the second round of hearts even if the Ace is onside.

[Echognome]

I think this problem is a bit deeper than people are making it out to be. Are you going to be sure that the ♥A is onside just because the K or Q holds? Also, if you lay down a top club honor, lefty may false-card with the Q or J from QJx. I would be more surprised if righty was able to find that play. My personal feeling is that the QJx falsecard is harder on the first round than ducking the ♥A.

[helene_t]

I'll add one detail to Art's analysis: If the ♥ finese loses but spades do split 3-3, you only need three club tricks. So if LHO drops a ♣ honour, restricted choice tells you to finese.

 

But what Matt says is right, I didn't think about that but I don't need either since I rarely face such strong opposition.

[ArtK78]

I never said that winning the first round of hearts implies that the heart finesse is onside. What I said is that I am playing for the HA to be onside.

 

If I lose the second round of hearts to RHO, then I am down. The alternative is to rely solely on the club suit.

[cherdano]

I think there is more to this than what people have said so far.

As the percentages are really close, I think what also matters is:

- If you win ♦A and play a club to the 10, will it be obvious for Meckstroth to shift to a heart (when he has Qxx)? Even if he gets it wrong a very small percentage of the time, it is enough to make it closer.

- If you play on clubs and you are wrong, you typically go down 1 instead of 1-3. 6% of a slam swing is less than (very roughly) 50% of 3-5 IMPs. So if you think the other table is in slam, this should be a consideration.

[Echognome]

I think there is more to this than what people have said so far.

As the percentages are really close, I think what also matters is:

- If you win ♦A and play a club to the 10, will it be obvious for Meckstroth to shift to a heart (when he has Qxx)? Even if he gets it wrong a very small percentage of the time, it is enough to make it closer.

- If you play on clubs and you are wrong, you typically go down 1 instead of 1-3. 6% of a slam swing is less than (very roughly) 50% of 3-5 IMPs. So if you think the other table is in slam, this should be a consideration.

Confidently finessing the club and playing for the mistake is certainly a possibility. The strategy to do this immediately is obviously better than later. However, let's think this through. You have opened and rebid clubs. Thus, West will know that you now have 5 club tricks (that the other honor is now falling or will be finessed). You have 3 spade tricks in dummy and the ♦A. If you also have the ♥A, then you have 12 tricks. Thus, I don't think the strategy of playing for a defensive mistake is really going to work. If it was uncertain whether you could make slam by having say the ♥A, but not the ♦K, then I would think more of the line.

 

As for whether we go one off or several, I'm not too worried about that either. I don't think it'll be too likely that the other table is in slam, and even then, we're talk a few imps vs many if we make it. So I think we should go all out to make.

[Guest Jlall]

Arend, you gave us the answer in the OP.

 

These percentages are not very close in my mind, if your numbers are right there is a huge edge in going for spades+HA. This kind of edge makes casinos and poker experts rich, and the same applies in bridge.

 

I don't buy that the defense won't know what to do if you play a club to the ten. You will get a heart switch 100 % of the time, what else could he ever do? You've shown long clubs and are setting up clubs and have AKQ AKQ in the other suits.

 

I think that giving meckwell credit to always duck the ace of hearts when it's offside is warranted because it is a very easy play. I think a heart to the king will win 100 % of the time.

[ralph23]

I think this problem is a bit deeper than people are making it out to be.

I agree with that, and my first analysis was symptomatic of this.

 

Assume (the "Assumption") that ♣ divide 3-2. Call it wishful thinking or card placement by assumption (CPA) or whatever.

 

What about this for the optimal line:

 

t1. Win this trick in hand with the King of ♦.

 

t2. Low ♥ toward the King. If righty wins this, then I can still try the Doubleon QJ♣ theory, but that's my only hope now. I’m not necessarily down yet. (Is this all true?)

 

t3. Assume the King of ♥ holds. So far, so good. Either defender may hold the Ace of ♥, of course.

 

t4. Return to hand with a top ♣. {NB - I think low to the ten is a sure losing play}. If a ♣ honor doesn't show up from anyone, then the Doubleton ♣ Theory is false, and you must continue with another ♥ toward the Queen, hoping lefty does indeed have the Ace and righty wasn’t just fooling around on you.

--If a ♣ honor shows up from righty, ask yourself if he would have split holding QJx. Or (more brilliant) played high from Hx. If you think "No" then try the Doubleton ♣ Theory out, and cash the other high ♣ and pray for rain.

--If a ♣ honor shows up from lefty, he either has a stiff or has made a clever falsecard from Hx. If you think "No I don’t believe he did that" then you can either apply Res Choice and finesee, or try the Doubleton ♣ Theory, and cash the other high ♣ and pray for rain.

 

 

t5. At this point you’ve either tried the D♣T or not, and it’s either failed or succeeded. If you’ve tried it and it’s failed, then you are going down UNLESS (1) lefty does indeed have the Ace of ♥ as well as (2) a doubleton club. In such a case, you still have a chance to run your ♠ suit as lefty (if he takes the second ♥ round) cannot lead a winning club.

 

I may give a try to computing the odds on this if my head doesn’t explode by then.

 

Can anyone spot a superior line or have a better analysis? [NB - The clubs may indeed be just a red herring, and maybe it is best to just ignore these and try the other theory.

 

Else you lose whenever the Ace of ♥/♠ theory is true, the D♣ theory is discovered to be false, and lefty has more than 2♣. ]

[kenrexford]

No one seems to be saying this, but it seems to me that a decent line is to win the diamond on dummy (with the Ace -- see below) and then play three top spades.

 

If the spades split 3-3, or the spade J10 are doubleton, you then have the option of playing down the spades and saving up for a change of mind in the heart-club situation. The simple line is to cross back to the diamond King, heart toward dummy. If this loses immediately, you may have a club materialize, or even a club-heart (pseudo?) squeeze. If it wins, you can cross back with a club to repeat, cashing the third diamond after the second heart is won.

 

If spades do not cooperate, you have time to try the double-hook in clubs. Sure, you may lose the double hook and establish a spade winner as another option to not fail. However, if you won the diamond in dummy with the Ace, you may induce a diamond return when LHO does not have the problematic spade.

 

Now, you have the hope of clubs splitting.

[cherdano]

I don't buy that the defense won't know what to do if you play a club to the ten. You will get a heart switch 100 % of the time, what else could he ever do? You've shown long clubs and are setting up clubs and have AKQ AKQ in the other suits.

Give partner his ♦K? Okokok, is a little far-fetched....

 

(Btw, I hope my posts don't give the impression that I feel strongly about this hand; I will post later what happened.)

 

Arend

[cherdano]

No one seems to be saying this, but it seems to me that a decent line is to win the diamond on dummy (with the Ace -- see below) and then play three top spades.

[Then go for heart ace onside if spades run or ♣QJx onside if they don't.]

Indeed this seems best, I am somewhat embarrassed that this didn't occur to me neither at the table nor when I posted the problem here.

This is also what Nickell did at the other table playing 6N from the other side on the lead of ♠J.

 

Of course Rodwell ducked smoothly when I took ♦K and played a heart to the king - he had enough time to think about it at trick one of course. I went down 3 as heart ace was off-side, spades didn't split, and ♣QJ9x were offside, Nickell went down 2.

 

Btw, at the other table, this hand passed, but then forced to slam opposite a 2N opening (don't know if 20-21 of 20-22). If I had passed, Han would have opened 2♣ intending to show 22-24 balanced, opposite which I probably would have forced to slam, too.