[Wackojack]

---

I played this on BBO and the 8♠was led to the2 4 and 10.

My line without too much thinking was to play a heart to the K (hoping that the Ace was onside) It was taken with the ace by west who played the 9♠ and all followed. Next I played a heart to the Q and finessed the J♣ which lost to the Q. Playing this way gave me a 75% chance. At the table after going down I thought that I could have improved on this chance by ruffing my 2 losing clubs the 2nd ruff with the J.

I am going to try working out the odds of this play succeeding in order to get the mathmaticians to correct me if I am wrong.

If trumps break 3-2:
I fail if clubs 5-2 the wrong side = 15.2%
Or if clubs 6-1 and Q not singleton = 0.7%

If trumps break 4-1 I can run out of them before I can get my heart trick if the K♥is with west. Rule out the possibility that the trump lead could have been a singeton so I need to find the odds of east having 4 trumps combined with west having A♥

Trumps 4-1 with east = 14.1% and A♥ with east = 50%. So I fail an additional 7% of the time.

Odd of success = 100- (15.2 + 0.7 + 7) = 77%.

Is this a correct assessment of the odds? Or is there another better line?

[Antrax]

How did you play a second round of hearts? The diagram shows S having a singleton.
Also, what was the contract?

[ArtK78]

Could you please add the 13th card to the South hand?

[Zelandakh]

Antrax, on 2014-July-30, 04:34, said:

How did you play a second round of hearts? The diagram shows S having a singleton.
Also, what was the contract?

I think we can assume that South's 13th card is a small heart and the contract is 6♠.

[Zelandakh]

There is also an obvious error in the description - seems clear the ♥A was taken by East. Presumably the OP has rotated the hand and it was originally played by North.

[ArtK78]

If Z is correct (which seems likely), then one possible line is

EDIT:

Win the opening lead in hand.
♣A, ♣K, club ruff in dummy low.
A and another diamond, winning the ♦K in hand
Club ruff with the J.
You are left with 4 trump in hand, three of which are high. That should be good enough on most distributions.

This works whenever clubs are 4-3 or the club Q falls in the first three rounds. You may also survive if West has a doubleton club but can't ruff effectively in front of dummy.

Using Richard Pavlicek's suit combination analyzer, the successful club combinations amount to 73.22%. But there are also 5.50% of the club combinations where there will be an adverse club ruff in the first two rounds (in some very small percentage of those times, the hand short in clubs will have no trump to ruff with - so the actual odds of suffering an adverse ruff are slightly less than 5.50%). So, without considering the situations where West has a doubleton club but cannot ruff successfully in front of dummy, just playing on clubs is successful 67.72% of the time. I have not tried to figure out how often you can survive if West has a doubleton club without the Q and cannot ruff effectively in front of dummy. This adds something to the chance of success of ruffing out the clubs.

Your line appears to be better, in that the a priori odds are clearly 75%. You also gain a small amount by cashing one round of clubs after playing a heart to the K and losing to the A. The chance that West has a singleton Q of clubs is roughly 0.43%, while the chance that West is void in clubs is roughly 0.19%. This adds 0.24% to your chance of success. It doesn't matter if East has a singleton Q or a void in clubs - you were going to succeed or fail regardless.

If my calculation is off, I am sure someone will point it out and why it is off.

There is also a small chance of a squeeze or that the QJT of diamonds will come down if you play your line and East shows out on the second round of clubs. Again, this adds a very small percentage to the chance of success of your line. Some of these off chances will be available if you start by trying to ruff out clubs but West unexpectedly shows out early.

[rhm]

Zelandakh, on 2014-July-30, 05:57, said:

There is also an obvious error in the description - seems clear the ♥A was taken by East. Presumably the OP has rotated the hand and it was originally played by North.

You can make all sorts of assumptions: Fact is that hardly anything in the description makes much sense.
For example I can not see how declarer could run out of trumps while ruffing club losers if he establishes his heart trick before drawing the remaining trumps.

Rainer Herrmann

[rhm]

ArtK78, on 2014-July-30, 06:17, said:

If Z is correct (which seems likely), then one possible line is

Win the opening lead in hand.
♣A, ♣K, club ruff in dummy low.
Trump to hand.
Club ruff with the J.
Diamond to the K.
Pull trump. Give up a heart and claim.

This works whenever clubs are 4-3 or the club Q falls in the first three rounds. You may also survive if West has a doubleton club but can't ruff effectively in front of dummy.

Using Richard Pavlicek's suit combination analyzer, the successful club combinations amount to 73.22%. But there are also 5.50% of the club combinations where there will be an adverse club ruff in the first two rounds (in some very small percentage of those times, the hand short in clubs will have no trump to ruff with - so the actual odds of suffering an adverse ruff are slightly less than 5.50%). So, without considering the situations where West has a doubleton club but cannot ruff successfully in front of dummy, just playing on clubs is successful 67.72% of the time. I have not tried to figure out how often you can survive if West has a doubleton club without the Q and cannot ruff effectively in front of dummy. This adds something to the chance of success of ruffing out the clubs.

Your line appears to be better, in that the a priori odds are clearly 75%. You also gain a small amount by cashing one round of clubs after playing a heart to the K and losing to the A. The chance that West has a singleton Q of clubs is roughly 0.43%, while the chance that West is void in clubs is roughly 0.19%. This adds 0.24% to your chance of success. It doesn't matter if East has a singleton Q or a void in clubs - you were going to succeed or fail regardless.

If my calculation is off, I am sure someone will point it out and why it is off.

There is also a small chance of a squeeze or that the QJT of diamonds will come down if you play your line and East shows out on the second round of clubs. Again, this adds a very small percentage to the chance of success of your line. Some of these off chances will be available if you start by trying to ruff out clubs but West unexpectedly shows out early.

Why does this work when clubs are 4-3 but the queen does not drop?
Are you not in danger of losing heart ace and club queen?

An improvement:

Win the opening lead in hand.
♣A, ♣K, club ruff in dummy low.
Diamond to the K.
club ruff high in dummy
Heart King

This has a slight risk losing either to a club overruff or when later trying to come to hand to draw the remaining trumps.

If you play a heart at trick 2 and it loses to East heart ace and a trump comes back I would not take the club finesse.
If the club queen is with East you always can make by way of a compound squeeze.
play A, K of clubs and ruff a club high.
Come back to the king of diamonds.

At this point, assuming the club queen has not dropped, the six card end position will be:

---

At this point one trump remains outstanding and if East has the club queen he can not have three cards in each red suit left.

1) If East has at most 2 hearts
Draw the remaining trump and discard a diamond.
play queen of hearts heart ruff.
Now play your last trump to execute a double squeeze with diamonds as the common threat.

If East has at most 2 diamonds left in the above position:

2) Draw the remaining trump and discard a heart.
Play ace of diamonds, diamond ruff.
Now play your last trump to execute a double squeeze with hearts as the common threat.

This wins provided you get the end position right every time when East has the club queen or the club queen drops from West.

Rainer Herrmann

[Zelandakh]

rhm, on 2014-July-30, 06:31, said:

Why does this work when clubs are 4-3 but the queen does not drop?

If clubs are 4-3 but the ♣Q does not drop in 4 rounds we are probably cold.

[rhm]

ArtK78, on 2014-July-30, 06:17, said:

If Z is correct (which seems likely), then one possible line is

Win the opening lead in hand.
♣A, ♣K, club ruff in dummy low.
Trump to hand.
Club ruff with the J.

Zelandakh, on 2014-July-30, 07:17, said:

If clubs are 4-3 but the ♣Q does not drop in 4 rounds we are probably cold.

In the above line there is an error since there is no trump left for the second club ruff after an initial trump lead. .
I guess ARTK78 actually meant my improvement line.

Rainer Herrmann

[Trinidad]

If the contract is not mentioned and one player has only 12 cards, the answer is simple:

No, this assessment is not correct.

Rik

[sfi]

Trinidad, on 2014-July-30, 07:59, said:

If the contract is not mentioned and one player has only 12 cards, the answer is simple:

No, this assessment is not correct.

To be fair, these issues do make it harder to find a better line.

[Wackojack]

Sorry I rushed to get the post off before I went out. Yes I did rotate the hands to get South as the declarer and this caused my description to go wrong. Hopefully, this is clear now.

---

[ArtK78]

rhm, on 2014-July-30, 07:48, said:

In the above line there is an error since there is no trump left for the second club ruff after an initial trump lead. .
I guess ARTK78 actually meant my improvement line.

Rainer Herrmann

Sorry, I never intended to play a trump to hand. I don't know what I was thinking when I wrote my original post.

I edited the line above.

[johnu]

Trinidad, on 2014-July-30, 07:59, said:

If the contract is not mentioned and one player has only 12 cards, the answer is simple:

Those are pretty high standards for this forum I was under the impression that you either needed a final contract or the right number of cards, not both. What next? Giving the entire auction, vulnerability, form of scoring?

[Wackojack]

rhm, on 2014-July-30, 06:31, said:

If you play a heart at trick 2 and it loses to East heart ace and a trump comes back I would not take the club finesse.
If the club queen is with East you always can make by way of a compound squeeze.
play A, K of clubs and ruff a club high.
Come back to the king of diamonds.

At this point, assuming the club queen has not dropped, the six card end position will be:

---

At this point one trump remains outstanding and if East has the club queen he can not have three cards in each red suit left.

1) If East has at most 2 hearts
Draw the remaining trump and discard a diamond.
play queen of hearts heart ruff.
Now play your last trump to execute a double squeeze with diamonds as the common threat.

If East has at most 2 diamonds left in the above position:

2) Draw the remaining trump and discard a heart.
Play ace of diamonds, diamond ruff.
Now play your last trump to execute a double squeeze with hearts as the common threat.

This wins provided you get the end position right every time when East has the club queen or the club queen drops from West.

Rainer Herrmann

Thanks for the insight into the squeeze possibilities. So if you start as I did by playing a heart to King and Ace with a trump back. Then if I have this right:

If the ♣Queen is onside (with east) then this hand can be squeezed, so no need to take the finesse. If the ♣Q is with west there is no squeeze so your only chance is Qx with west. Thus don't try the finesse. The drawback is that you need to know which red suit east is shorter in and to my mind you have no handle on this. If 50% of the time you have selected the wrong threat suit when the finesse works you go down when you could have made. Also to my mind this does not look like a double squeeze. Surely it is a simple squeeze and you have to guess where the red suit cards are in order to decide which hand to squeeze. So I don't see any improvement on 75%.

As for the ♣AK ruff, etc play I thought that a 4-1 break could defeat you but that was wrong as Rainer pointed out.
Quote "For example I can not see how declarer could run out of trumps while ruffing club losers if he establishes his heart trick before drawing the remaining trumps"

So the odds of this play succeeding is around 86% and so the clear winner. Yes? No?

[rhm]

Wackojack, on 2014-July-31, 11:45, said:

Thanks for the insight into the squeeze possibilities. So if you start as I did by playing a heart to King and Ace with a trump back. Then if I have this right:

If the ♣Queen is onside (with east) then this hand can be squeezed, so no need to take the finesse.

This is correct but you have to some extent guess the distribution.
You could go down by mis guessing the red suit East has given up.

Quote

If the ♣Q is with west there is no squeeze so your only chance is Qx with west.

Not quite.
First I said I ruff the third round of clubs in dummy high. So I will make if West has ♣Qxx not only Qx♣ So the queen must always be accompanied by at least three small clubs.
But even if West has ♣Qxxx there are squeeze chances.
If East has the last trump instead of the ♣Q in the above diagram there is now the same squeeze. East can keep parity with dummy only if he has neither the ♣Q nor the last trump.
Only if West has the last trump and the club queen than East can discard after dummy and then there will be no squeeze.

Quote

Thus don't try the finesse. The drawback is that you need to know which red suit east is shorter in and to my mind you have no handle on this. If 50% of the time you have selected the wrong threat suit when the finesse works you go down when you could have made. Also to my mind this does not look like a double squeeze. Surely it is a simple squeeze and you have to guess where the red suit cards are in order to decide which hand to squeeze. So I don't see any improvement on 75%.

Technically this is called a compound squeeze. And compound squeezes always end up in a double squeeze (both defenders are squeezed). I explained this in my previous post.
For example I said

1) If East has at most 2 hearts
Draw the remaining trump and discard a diamond.
play queen of hearts heart ruff.
Now play your last trump to execute a double squeeze with diamonds as the common threat.

On the last trump West is squeezed between the hearts and diamonds and East will be squeezed between ♣Q and diamonds. before the last trump is played both defender control the diamond suit.

The situation is analogous in case only that both defender will now control the heart suit until the last trump is played. If you guess right which suit East has given up the chances of success for this line is above 90%

East must have the ♥A (50%) and West must be longer in trumps than East (50%) and West must have the ♣Q (50%) and he must be longer clubs than East (50%), because otherwise the ♣Q will come down on the third round.
The chance for this is roughly one sixteenth.
However since you will have to get the red suit right which Easts has to give up it is somewhat less.
My guess is chances for success are somewhere between 80 and 90%.

Rainer Herrmann

[Wackojack]

Thanks for all those insights. However, I fail to see this bit below. Perhaps I misunderstand.

rhm, on 2014-August-02, 16:02, said:

Not quite.
First I said I ruff the third round of clubs in dummy high. So I will make if West has ♣Qxx not only Qx♣ So the queen must always be accompanied by at least three small clubs.
But even if West has ♣Qxxx there are squeeze chances.
If East has the last trump instead of the ♣Q in the above diagram there is now the same squeeze. East can keep parity with dummy only if he has neither the ♣Q nor the last trump.
Only if West has the last trump and the club queen than East can discard after dummy and then there will be no squeeze.


Rainer Herrmann

OK Give west ♣Qxxx and east the last trump and you say the squeeze works. So give west 87, J532, 1042, Q985. Then:
1. spade lead to 10
2. heart to Q and ace.
3. 2nd spade to ace
4.5. ♣AK
6. Ruff club with J
7. diamond back to K.

We now get the position analagous to your diagram:

---

When South plays out the spades, West can come down to ♥J5, ♣Q. On the last spade North has to discard infront of east thus giving defence the upper hand.

[rhm]

Wackojack, on 2014-August-03, 06:40, said:

Thanks for all those insights. However, I fail to see this bit below. Perhaps I misunderstand.


OK Give west ♣Qxxx and east the last trump and you say the squeeze works. So give west 87, J532, 1042, Q985. Then:
1. spade lead to 10
2. heart to Q and ace.
3. 2nd spade to ace
4.5. ♣AK
6. Ruff club with J
7. diamond back to K.

We now get the position analagous to your diagram:

---

When South plays out the spades, West can come down to ♥J5, ♣Q. On the last spade North has to discard infront of east thus giving defence the upper hand.

You are right the compound squeeze does not work with a trump instead of the ♣Q
However I still believe the chances overall are better than 75% for this line.

Rainer Herrmann