[the hog]

Hand from the nationals

Best line in 7C on the 7 of C lead?

AQJ32
A52
62
Q56

K4
Q7
AK93
AK832

In case you are wondering why 7C rather than 7NT - we were too high in the relays to find the J of S! We have changed the system now to be able to cope with this . (First pass in spiral scan shows 0 or 3 of the top 4 honors; we used to play 0-3 of the top 3).

[Rado]

Hi all,
Normal play should be:
draw 5 rounds of Trumps pitching 2 He from dummy, A Di, then 3 rounds of Sp and A He, the position is:

Jx
-
x
-

-
Q
Kx

if Sp were 5-1 (otherwise easy 13) now we have:
1. position for double squeeze (W-Sp, E-He, both in Di)
2. various simple squeezez

now J Sp and pitching Q He if K did not appeared from East.

The above is the routine line, maybe upon more careful study a better one might be found.
Regards, Rado

[Codo]

Besides Rados line, you can ruff, win two round of trumps and ruff a third Diamond.
This will loose if diamonds are 5-2 with the 3 trumps together with the shortness.
Or you can just draw one round of club, win two diamonds and ruff the third. This will loose wheenver rho has 0-2 dimonds and or if lho has 0-2 diamonds and two trumps.
I guess that Rados line is the best.

Kind Regards

Roland

[Rado]

Hi Roland,
ruffing Di also deserves some merits, but imagine you tryed the Di ruff and got overruffed while Sp were breking 3-3 or 4-2. How would you go after for checking the results with you teammates? :-)))
Rado

[Codo]

I would explain, that I need a famous bulgarian expert to be around to explain me, that a 5-1 split is less frequent then 5-2...

No, I had choose your line too, but I am in doubt, how much superior it will be?
Maybe in the given hand your line is much superior, because you need the clubs to break and as less freakish one suit breaks, as less freakish will the rest (most times).

Kind Regards

Roland

[Rado]

Well Roland,
First: I'm nor famous, nor expert, but I'm bulgarian, so you had 1/3 correct statement (not too bad % LOL)
Second:
5-1 break is 14.5%
5-2 break is 30.5% (will go a little bit less when playing 1 or 2 rounds of trumps)
Obviously playing on Di ruff is more dangerous than drawing trumps and relying on Sp break.

Meanwhile discussing with Ron (The_Hog) and he convinced me that my line for double squeeze was less effective than simple Sp/He squeeze against any of the opps, so Draw trumps, Cash A of He, AK DI and the last trumps pitching 2 he from dummy seems better %
Regards, Rado

[luis]

AQJ32
A52
62
Q56

K4
Q7
AK93
AK832

My analysis is as follows: I think that ruffing a diammond is inferior to playing on spades + sqz chances, diammonds 5-2 and the hand with 2 diammonds holding 4 trumps should be similar to spades 5-1 (numbers?).

I think that if spades are 5-1 diammonds would be 5-2 and a sqz may fail. So I think against good opponents I'd have played a bluff.

Draw 4 rounds of trumps discarding 1 heart, play hQ and overtake with the hA, then two diammonds and the spades reaching:

J3
5
-
-

-
7
9
2

Now sJ discarding the diammond and then ruff a spade and claim with the h7 :-)

I know I know there're SQZ chances ruined by my stupid line but I have the strong feeling it would have worked well at the table.

[inquiry]

Despite saying it is wise to never disagree with Rado, I think I will make a stab at a third line (fourth if counting luis's... luis, good opponents will give count on the HQ to the heart Ace, so the ploy will not work).

The odds for the location of the heart king changes from 50/50 in either persons hand when you assume that the spade suit splits 5-1 (else no problem). When one player has five spades to 1 in the other persons hand,with no other distributional information. the odds of the Q being in the hand with 1 Spade is nearly 60%. With a 6-0 spade split (not likely since no lead-directing double), the odds are 35% % HK in long spade hand or dropping stiff, and 66.2% it is in the other hand (or dropping stiff).

So of the 5-1 splits

6-0 splits = 1.5%,
5-1 splits = 14.5%

So the Vienna coup is not needed if spades are 4-2 or 3-3, and works. When Spades are 5-1, the heart king will be with the long spade (or dropping singleton in the other hand), 40% of the time. So this is 0.145*.040 = 5.8% and 0.015*0.33==0.5%. For a total odds of 90.3% (this assumes of course a 3-2 club split)

The second line, of playing two rounds of trumps and ruffing one diamond in dummy requires Diamonds 3-4 or the hand with short diamonds to have two clubs. The odds of this combination is only ~77.9%. So the first line is clearly superior. There is another possible line involving a double squeeze. For this squeeze, the heart threat is not your Queen, but rather dummy's x. But you have a huge clue on the bidding.. No one preempted so it is relatively save to assume neither opponent has 8 hearts or even 7 hearts. So hearts have to be at least 6-2 if not 5-3. Also, you assume clubs have to split evenly. So if you start thinking about the conditions in which the spades don't split, the odds of the hand being long in spades also having a doubleton or shorter in diamonds are actually fairly high. Calculating these odds are tough mathematically, so I will ignore this for a moment. Instead for the double squeeze to work you would run clubs, throwing 1D and 1H from dummy, then run spades, throwing away 1H and 1D from your hand. If the last spade is not good, cash DAK and see if the D-QJT have fallen (throw spade on last big diamond), if not, try to cash the heart Ax in dummy. What are the odds of this line?

Once again 4-2 or 3-3 spade split (84%), it is home, like the Vienna coup. If West is the hand with long spades, it is a sure thing (as in the three card ending he has to keep a spade, so at most 1D or 1H…and his partner cant keep four red cards in the three card ending). So right off the bat, it makes 50% of the time spades split. So the odds of the double squeeze (ignoring for the minute the location of any specific red cards) jumps to 16%x0.5=8% plus the original 84% for a total of 92%. This line thus is already fractionally better than the simple Vienna coup.

Now we throw all the spades to EAST's hand, so that on the above line he can discard a spade when dummy does (breaking up the 100% secure double squeeze when West has 5S).. You seem pretty much like you are going down even if EAST has the heart King because you failed to cash your heart ace then run all south winners. However, if EAST has D-QJT(x) or any five diamonds to go along with his 5 spades, he is squeezed. So while QJT or five diamonds with 5S is a bit unexpected, it adds slightly to the chances of the double squeeze line. Such a diamond holding would occur about 5% of the time EAST is 5-x-y-2. So you can add another 16*0.5*0.05 (only have of the 6-0. 5-1 splits will East have five spades, and then only 5% of that will the S-D squeeze work without poor defense by West). This brings the total odds of the double squeeze up to about 92.5% compared to 90% for the Vienna coup. There is also the possibility that if West has Heart King, he will keep two hearts in the four card ending, reducing to two diamonds. Then, you can score three diamonds anytime EAST held originally 2D (chance for defensive error).

Although I calculate the double squeeze as fractionally better percentage wise than the Vienna coup, both lines are very reasonable. I guess most players who end up playing the double squeeze will do so out of lazyness rather than calculating the odds. They simply didn't plan ahead earlier enough to cash the heart ace to set up their heart queen as a threat. Perhaps they will be rewarded with the actual threat ends up being the heart 5 in dummy and West has long spades and east has the heart king.

[luis]

Alternative line: cash 3 clubs and then play spades.
If spades break we are home. If spades are 5-1 then:

QJ3
A52
62
-

-
Q7
AK93
32

If west had 5 spades play for the double squeeze (east should have 5 diammonds) and nobody can guard hearts. Spade (disc a d) spade (disc the hQ), diammond to hand, club (disc a h), dK, club

3
A5
-
-

-
7
9
3

In the 5th club west must keep the 5th spade so we discard the s3 and east is squeezed in diammonds and hearts. Very nice.

Back to base:

QJ3
A52
62
-

-
Q7
AK93
32

If EAST had 5 spades then assuming west has 5 diammonds prospects aren't good. Play the bluff :-) combined with the chance of east having 5 diammonds.

[Rado]

Thanks Ben Inquiry for his detailed study,
As I mentioned earlier double squeeze line I've suggested first was my first opinion and if playing the board I certainly would play that line. After some discussion I thought simple squeeze was more %. Of course when we have enough time and computer to calculate all the chances it's normal to be found better % play (I've mentioned it on my first post). On the other hand when playing live one board has 7.5 minutes for bidding and play - so we may distinguish best practical line and best theory/calculation line:-))))))))
regards, Rado

[inquiry]

Hi Rado,

I certainly need a computer to calculate the odds of the hand with 5S or 6S holding the heart K (it is easily shown this is no longer 50-50, but to calculate what the odds are does require for me a computer). And of course, The_Hog or someone might come up with a different calculation. Math was never one of my strongest subjects, and I have been know to make whooper of mistakes there. I wasn't going to reply cause I thought you had got it right, but when you changed horses, I thought I would investigate for myself (since the lines are close).

Ben

[the hog]

Thx all for replying. S were 5-1 of course. The line which I took and which worked was to cash 2 C, the A of H and run the C. Hand with 5S also had the K of H. I was just wondering whether there was a possible better line. My maths isn't much good either.

[lenze]

This is a very interesting and instructive hand. There are several things to consider. My first instinct was to assume if spades were 5 –1, West would hold them. In that case, 7C can ALWAYS be made. The line of play is this. Win the opening lead and play 3 more rounds of trump. Now, play Spade K and a spade to the Ace If west shows out, you need East to hold something good in diamonds to execute the simple squeeze. If East shows out, he is now the SOLE guard of one of the red suits, Since West only has 4 red cards, he cannot guard both red suits. So, if as declarer, you believe West cannot guard diamonds (likely), the sequence is Spade Q, Spade J, Diamond A, Diamond K, and last club, executing the simultaneous double squeeze. If, however, you believe West can no longer guard hearts., the sequence is Diamond A, last club, Heart A (squeezing West in diamonds and spades), Spade Q, Spade J, (squeezing East in hearts and diamonds), completing the sequential double squeeze. A very cute Compound Squeeze.

The play, however, of cashing the Heart A and running clubs is far superior. It wins whenever the Heart K is with the long spades, or when the long spades have the diamond length. It also has the advantage that if East has the Heart K, the contract can ALWAYS be made, regardless of the remaining distribution. The play would go, win the lead, cash Heart A, run 3 more clubs. After 5 tricks, if East holds the Heart K, he can no longer guard both diamonds and spades. If he has 5 spades plus the Heart K, he can only have 2 diamonds, and if he holds 3 diamonds, he can have at most 4 spades. Admittedly, it is a guess as to his holding, but dummy’s extra spade winners allow us to play the last club, putting pressure on both East and West. Declarer should have a good chance on determining the pointed suit East still holds. If spades, the sequence is Diamond A, Diamond K, executing the simple squeeze. If he believes East to hold diamonds, the sequence is Spade K, Spade A, Spade Q, Spade J, completing the sequential double squeeze (West would have been squeezed on the last club). The advantage of this line of play is that declarer retains more options in the end game. It also preserves the squeeze positions when the Heart K is with the long spades, and also when with the diamond guard. The only time it fails( providing declarer reads the position) is when East has the spades, and West holds the Heart K and a diamond guard

Just my thoughts. I could be wrong

Scotch: Because you don’t solve great bridge problems over white wine.

[inquiry]

Quote

SNIP....
The play, however, of cashing the Heart A and running clubs is far superior. It wins whenever the Heart K is with the long spades, or when the long spades have the diamond length. It also has the advantage that if East has the Heart K, the contract can ALWAYS be made, regardless of the remaining distribution.
SNIP...

Hi Lenze,

Yes this is a good hand. In fact, it is 100% sure to be made double dummy assuming a) no ruff to the first trick (or course with club lead that is out of the question) and a 3-2 club split. That is, there is no distribution of the cards that one squeeze or the other will not work when spades fail to behave, but finding the right line based upon best percentage chance is the question. Thus, while if you knew who held long in spades, and who had the heart king, you could not go wrong.

Having said that, I am not so sure it is as easy as you said. Your line (cash Heart ACE early) fails against perfectly normal hands like West holding,

S-x
H-KJxxx
D-QT8x
C-xxx

Where you could use the ruff the third diamond line, but the squeeze fails, or a similar hand with one more heart and one less club, where the ruff the third diamond is not an option.

Or when West holds five diamonds or more as well as the heart king. In addition, just because EAST has the heart king, doesn't mean you are going to make on your line. When you cash the clubs, you have to try to figure out who has what, as on some lines (east with five spades and the Kx of hearts orginally), you have to cash both diamonds before leading spades.

Having said all of that, I enjoyed reading your analysis.