Best line at 6NT

[shyams]

[hv=d=s&v=n&n=st62hakq982dqtc87&s=saqh75dk84cakqt62]133|200|Scoring: XIMP

6NT by South

Opening lead ♣5 on which East plays ♣J[/hv]After an elaborate and descriptive auction, you reach 6NT declared by South. West finds a passive lead of a low club.

What is your line of play? This is an easy problem (esp. when posed as one); but I wonder if other intermediates (and possibly some 'advanced') would actually find this line at the table.

[Trumpace]

Good hand! I think this is hard for intermediates to find at the table.

 

The line I would take:

 

 

 

 

You have 6 clubs, 3 hearts, 1 spade and 1 diamond. You need one more: most likely either SQ or hearts.

 

Play a heart to K and diamond towards K. If RHO rises with A, you have 12 tricks.

 

If LHO wins, he cannot shift to a spade.

 

Now you can cash your tricks ending in dummy with the following (if hearts don't break):

 

x

9

_

_

 

 

AQ

_

x

_

 

 

You now decide whether to play for drop of SK or finesse (if heart/diamond aren't good) based on the discards and the way opps behave when discarding.

 

The key play is playing diamond from dummy (instead of diamond towards dummy) to prevent East from rising with A and shifting to spade and removing your spade finesse option.

 

 

[vuroth]

If this is easy, then I'm a hopeless declarer.

 

A♣, A♥ in case an honour falls. If it does, assume single.

K♣, ♦ to the Q.

 

If I lose and they return a ♠, A unless someone discarded a ♥ honour, in which case Q♥. If I played the A♠, ♥ to dummy hope they break.

 

If the Q♦ holds, try hearts, and if they don't break, ♠ finesse for my 12th.

 

I can't find anything better than trying to combine my chances in ♥s and ♠s, and if the A♦ is with RHO they can always stop me from doing so.

 

There must be a better line than this.

[vuroth]

The key play is playing diamond from dummy (instead of diamond towards dummy) to prevent East from rising with A and shifting to spade and removing your spade finesse option.

 

Bloody hell! I could even see the danger, and the entry problem, but couldn't see the solution to both.

 

I even mapped out that endgame, but couldn't see how to get there.

 

I should absolutely find that play, but despite spending some time on the problem (more than I would at the table) I didn't see it. :)

[shyams]

I'm ashamed to say that when I was playing the deal yesterday, I played wrongly (

i.e. low D to the Queen

). Fortunately, the deed went unpunished as hearts split normally.

 

While Trumpace mapped out the whole play in detail, his "key play" alone was enough to improve the odds

[andrei]

 

 

The key play is playing diamond from dummy (instead of diamond towards dummy) to prevent East from rising with A and shifting to spade and removing your spade finesse option.

 

 

only remember to cash the clubs first ...

otherwise W might win the diamond and play a heart back so you cannot reach your ending anymore.

 

edit: but if you do that, E might rise with A♦ and play spade back, not good :(

[Trumpace]

 

 

The key play is playing diamond from dummy (instead of diamond towards dummy) to prevent East from rising with A and shifting to spade and removing your spade finesse option.

 

 

only remember to cash the clubs first ...

otherwise W might win the diamond and play a heart back so you cannot reach your ending anymore.

 

Isn't DQ an entry to dummy then?

[PhantomSac]

Note that it would be very strong for LHO to duck a diamond to the king smoothly. You really need the first diamond won or the squeezes are irrelevant.

 

For instance if RHO guards hearts and spades he can just pitch all of his diamonds while LHO comes down to 2 diamonds and 1 spade so there's no showup squeeze in trumpace's endgame nor any endplay, you have to guess who has the SK.

 

If RHO guards hearts and diamonds, he just pitches all of his spades, while LHO guards spades, so there's no squeeze.

 

If RHO guards spades and diamonds he comes down to 2 spades and a diamond while LHO comes down to 1 heart and anything (declarer has to guess), and declarer has to still just guess whether to hook or play for the drop or endplay LHO with a heart.

 

If LHO guards hearts and spades and diamonds he can come down to 1-1-1 while RHO holds 2 spades and 1 diamond and declarer has to guess to play for the drop rather than the endplay or the hook.

 

If LHO guards hearts and spades but not diamonds he can come down to 1-1-1 or 2S and 1H while RHO comes down to 1 diamond and 2 spades, and declarer must guess whether to drop, hook, or endplay again.

 

If LHO guards hearts and diamonds then he can again come down to 1-1-1 and declarer must guess what to do.

 

And if guards spades and diamonds he can come down to 2-1 or 1-2 and declarer has to guess what to do.

 

On paper the trumpace line pretty much doesn't gain anything against optimal defense. In reality since LHO will always win the DA, you can tighten up your position because the count will be rectified, and the opps will often not stiff their king smoothly etc, so it will gain a lot.

[Trumpace]

PhantomSac, yes if DK is ducked, there might be no squeeze, but that does not mean there is no gain.

 

By preventing a spade shift from RHO, you can test hearts before falling back on the spade finesse.

 

If you just play a D to Q, and RHO shifts to a spade, you have to commit then and there. Most likely you will go up with the SA and bank on hearts to break.

 

So this loses to the cases when hearts don't split and RHO has the SK.

 

The squeeze is just another additional chance.

 

Also, if LHO/RHO duck the DA, you have other options which might open up (like an endplay for instance).

[andrei]

 

 

The key play is playing diamond from dummy (instead of diamond towards dummy) to prevent East from rising with A and shifting to spade and removing your spade finesse option.

 

 

only remember to cash the clubs first ...

otherwise W might win the diamond and play a heart back so you cannot reach your ending anymore.

 

Isn't DQ an entry to dummy then?

sure it is, wtf was I thinking? :)

[PhantomSac]

PhantomSac, yes if DK is ducked, there might be no squeeze, but that does not mean there is no gain.

 

By preventing a spade shift from RHO, you can test hearts before falling back on the spade finesse.

 

If you just play a D to Q, and RHO shifts to a spade, you have to commit then and there. Most likely you will go up with the SA and bank on hearts to break.

 

So this loses to the cases when hearts don't split and RHO has the SK.

 

The squeeze is just another additional chance.

 

Also, if LHO/RHO duck the DA, you have other options which might open up (like an endplay for instance).

Sure I meant to say, against perfect defense, there is no extra chance from the squeeze. As you say the main point is to fork RHO, I was just focusing on the squeeze.

[pretzalz]

PhantomSac, yes if DK is ducked, there might be no squeeze, but that does not mean there is no gain.

 

By preventing a spade shift from RHO, you can test hearts before falling back on the spade finesse.

 

If you just play a D to Q, and RHO shifts to a spade, you have to commit then and there. Most likely you will go up with the SA and bank on hearts to break.

 

So this loses to the cases when hearts don't split and RHO has the SK.

 

The squeeze is just another additional chance.

 

Also, if LHO/RHO duck the DA, you have other options which might open up (like an endplay for instance).

Surely the spade finesse is inferior to the squeeze. A diamond to the Q, losing, and a spade comes back. You fly ace and play for the double simple squeeze. Assuming 4-1 hearts for calculation simplicity, SK with long hearts is 9/21, J9 of diamonds[ignoring unlikely Hx in unsqueezed hand] is 9/20*8/19. Combined we get +(9/21)+(12/21)*(9/20)*(8/19) = 53.7%, 5-0 hearts since this is closer than I expected gives +(8/21)+(13/21)*(8/20)*(7/19) = 47.2. Averaging the 2 gives about 52.6% since 4-1 is roughly 5:1 more likely than 5-0. Not much of a difference to an on-average 50% spade finesse, but it is certainly wrong to say leading to the DQ is clearly wrong since they might return a spade. Playing to the DQ also allows the possibility of playing for the strip squeeze in spades/diamonds if West has the short hearts if it looks right instead of finessing spades though it might be hard to judge the diamond count depending on how estute the defenders are.

[Trumpace]

PhantomSac, yes if DK is ducked, there might be no squeeze, but that does not mean there is no gain.

 

By preventing a spade shift from RHO, you can test hearts before falling back on the spade finesse.

 

If you just play a D to Q, and RHO shifts to a spade, you have to commit then and there. Most likely you will go up with the SA and bank on hearts to break.

 

So this loses to the cases when hearts don't split and RHO has the SK.

 

The squeeze is just another additional chance.

 

Also, if LHO/RHO duck the DA, you have other options which might open up (like an endplay for instance).

Surely the spade finesse is inferior to the squeeze. A diamond to the Q, losing, and a spade comes back. You fly ace and play for the double simple squeeze. Assuming 4-1 hearts for calculation simplicity, SK with long hearts is 9/21, J9 of diamonds[ignoring unlikely Hx in unsqueezed hand] is 9/20*8/19. Combined we get +(9/21)+(12/21)*(9/20)*(8/19) = 53.7%, 5-0 hearts since this is closer than I expected gives +(8/21)+(13/21)*(8/20)*(7/19) = 47.2. Averaging the 2 gives about 52.6% since 4-1 is roughly 5:1 more likely than 5-0. Not much of a difference to an on-average 50% spade finesse, but it is certainly wrong to say leading to the DQ is clearly wrong since they might return a spade. Playing to the DQ also allows the possibility of playing for the strip squeeze in spades/diamonds if West has the short hearts if it looks right instead of finessing spades though it might be hard to judge the diamond count depending on how estute the defenders are.

Can you please state a complete line of play so we have some context?

 

Also, you seem to be getting J9 diamonds to be ~19% which seems quite a bit.

 

In any case, if your calculations are correct, I would be surprised, but still would take the line stated earlier. As PhantomSac pointed out it would be quite difficult for LHO to duck the A etc. Also, from the lead, the club length is probably with LHO than with RHO.

[Trumpace]

PhantomSac, yes if DK is ducked, there might be no squeeze, but that does not mean there is no gain.

 

By preventing a spade shift from RHO, you can test hearts before falling back on the spade finesse.

 

If you just play a D to Q, and RHO shifts to a spade, you have to commit then and there. Most likely you will go up with the SA and bank on hearts to break.

 

So this loses to the cases when hearts don't split and RHO has the SK.

 

The squeeze is just another additional chance.

 

Also, if LHO/RHO duck the DA, you have other options which might open up (like an endplay for instance).

Sure I meant to say, against perfect defense, there is no extra chance from the squeeze. As you say the main point is to fork RHO, I was just focusing on the squeeze.

Ok. Sorry, I misunderstood you.

[pretzalz]

PhantomSac, yes if DK is ducked, there might be no squeeze, but that does not mean there is no gain.

 

By preventing a spade shift from RHO, you can test hearts before falling back on the spade finesse.

 

If you just play a D to Q, and RHO shifts to a spade, you have to commit then and there. Most likely you will go up with the SA and bank on hearts to break.

 

So this loses to the cases when hearts don't split and RHO has the SK.

 

The squeeze is just another additional chance.

 

Also, if LHO/RHO duck the DA, you have other options which might open up (like an endplay for instance).

Surely the spade finesse is inferior to the squeeze. A diamond to the Q, losing, and a spade comes back. You fly ace and play for the double simple squeeze. Assuming 4-1 hearts for calculation simplicity, SK with long hearts is 9/21, J9 of diamonds[ignoring unlikely Hx in unsqueezed hand] is 9/20*8/19. Combined we get +(9/21)+(12/21)*(9/20)*(8/19) = 53.7%, 5-0 hearts since this is closer than I expected gives +(8/21)+(13/21)*(8/20)*(7/19) = 47.2. Averaging the 2 gives about 52.6% since 4-1 is roughly 5:1 more likely than 5-0. Not much of a difference to an on-average 50% spade finesse, but it is certainly wrong to say leading to the DQ is clearly wrong since they might return a spade. Playing to the DQ also allows the possibility of playing for the strip squeeze in spades/diamonds if West has the short hearts if it looks right instead of finessing spades though it might be hard to judge the diamond count depending on how estute the defenders are.

Can you please state a complete line of play so we have some context?

 

Also, you seem to be getting J9 diamonds to be ~19% which seems quite a bit.

 

In any case, if your calculations are correct, I would be surprised, but still would take the line stated earlier. As PhantomSac pointed out it would be quite difficult for LHO to duck the A etc. Also, from the lead, the club length is probably with LHO than with RHO.

Cash winners to - AKQx - - opposite Q xx 8 -. If neither the SQ nor D8 are good play on hearts. What did you expect the diamond/heart squeeze to be? I actually thought it would be higher. :P Remember that the long heart hand essentially gets an empty space back by virtue of assuming the spade/heart squeeze didn't work so the SK is in the other hand. Not sure if I should have done anything with the fact that there is no club void in either hand, but normally you don't use incomplete knowledge of suits in calculations.

[Trumpace]

I expected it to be worse than the finesse :P

 

For a squeeze you need SK in the same hand as the one with long suit, which I presume would add up to < 50%, and smaller enough that the minor additional chances (like DJ9 tight, which I think you have an incorrect value) won't make it better than the finesse.

 

Of course, I haven't tried doing all the calculations...

[pretzalz]

I expected it to be worse than the finesse :)

 

For a squeeze you need SK in the same hand as the one with long suit, which I presume would add up to < 50%, and smaller enough that the minor additional chances (like DJ9 tight, which I think you have an incorrect value) won't make it better than the finesse.

 

Of course, I haven't tried doing all the calculations...

It's not J9 tight of diamonds, it's J9(xxxxx) of diamonds...

[Trumpace]

Have you also considered how likely a club lead is from the various hands you give to West?

 

In any case, this is too tough for me to calculate (or cross check your calculations), even away from the table.

 

If someone has any ideas which suggest one line is clearly better than the other, please share.