[uday]

---

This is a hand from the Spingold, in NYC.

Contract: 6NT, with silent opps

Opening lead : low club.

Any opinions as to the correct line? I might have messed up a pip or two but the hands are substantially the same as in "real life"

At the table, the declarer won the club in dummy and played a diamond to the T.

[inquiry]

Yes, I know Ax in front of KQ.. but I think right play is to hook twice in ♦, if [dii] jack is onside... that is the road to 12 tricks. I think this is better than small to King and then hook on the second round...

Ben

[xx1943]

inquiry, on Jul 18 2004, 06:14 AM, said:

Yes, I know Ax in front of KQ..

and J, Jx, Jxx behind KQ too. That is something for the mathematicians. But sure it is right first to cash as many black winners, as possible, watching discards and try to to count the hand. Perhaps u'll get a clou.

Bidding may be important, in case you could persuade opp to take the first !D trick. Setting up squeeze positions.

There are many other possibilities.

Imo it is definitely wrong to take the ♦ finesse in the second round.


Al

[Cascade]

This might be the best line for the diamonds in isolation but there are extra chances in clubs and hearts if you can get only two diamond tricks.

Not sure of the exact odds but my very small simulation is coming out with more hands with small to the King working than small to Jack.

[paulhar]

xx1943, on Jul 18 2004, 03:25 AM, said:

Bidding may be important, in case you could persuade opp to take the first !D trick. Setting up squeeze positions.

I need to be educated on these squeeze possibilities that are better than a 50% finesse that gain three tricks. You have 3 spade tricks, 2 hearts, 1 diamond (by promotion), and 3 clubs. You need three more tricks. Chances are pretty good that you're going to have to finesse the D10 later anyway.

Even if you win the King and Queen of diamonds early, you only have 10 tricks, and need a large slice of luck to make 12. You have to guess right away whether to play for diamonds 3-3 or a miracle in clubs and hearts. And, of course, the heart finesse is going right into the player with the ace of diamonds if your K&Q win.

IMO the player who finessed the D10 didn't do anything wrong.

[Fluffy]

xx1943, on Jul 18 2004, 08:25 AM, said:

inquiry, on Jul 18 2004, 06:14 AM, said:

Yes, I know Ax in front of KQ..

and J, Jx, Jxx behind KQ too. That is something for the mathematicians. But sure it is right first to cash as many black winners, as possible, watching discards and try to to count the hand. Perhaps u'll get a clou.

It is not for mathematicians since it depends on how often would LHO duck a ♦ with ♦Ax or ♦Axx, and that is imposible to calculate I am afraid.

With poor opponents it may be better to try ♦K before ♦10, and then combien the chances on rest of the suits if it loses to the ♦A, Alas!, not the case, and that is dangerous, don´t think you can achieve better than 50%** against perfect defence.


**:♦10 is not 50% because of teh 5-1, but on usch hand knowing a 5-1 will most of the time lead to a trick somewhere else via squeeze.

[the hog]

I would have played a D to the K and crossed back with a black card and pull another D. If rho ducks, I play the T.
Don't know if this is with the odds.

[whereagles]

Best line seems to me twice towards 10 and 9. Catches up to Jxxx in RHO. Any dictionary of suit combinations online?

[Free]

My instinct tells me to play to the K first, and play later on to the 10. However I don't know if this is the best line.

[flytoox]

even h finesse is on, u still have only 3s,3h,3c, so u still need 3d. The best line is to play toward hand twice finessing d jack I think.

[luis]

This is a VERY common combination so the answer is plain straightworward theory.
Low to the ten is the correct play for 4 tricks in the suit. (wins against AJxx, Jxxx, AJx, AJ, Jx, Jx, Jxx)
So declarer played correctly.

Luis

[PriorKnowledge]

Agree with Luis. You have 8 tricks, so need 4 from diam. Wrong to play for 3d plus 2nd finesse when you could play for 4d with only 1 finesse.

Small to KD and then small to 10D works better only when stiff J is offside or Ax is on-side (7.7%). Small to 10D works better when AJxx, Jxxxx, Jxxx is onside (17.4%)

Wrong to cash side winners first as AD can then cash 2nd trick to set you.

[EarlPurple]

let's work it out then.

Low to ten wins on all the 4-2 and 3-3 breaks where the J is onside. That is 42% of the hands. Also either player with singleton J though that is only 2 of 12 possible 5-1 breaks (including positions) and is an extra 2.5%. Total percentage is 44.5.

There are 30 possible 4-2 breaks, each one is 1.6%
Consider the line of low to a top honour. If it wins low to the other top honour (unless Ace appears on right). We will be successful whenever East has a doubleton honour. This is 9 of the 4-2 combinations so 14.4% total. In half of the 3-3 combinations East will hold the ace. That's another 18% so 32.4% total so far.

Some of the time our LHO will duck when he has the DA. We know we will succeed when our RHO has Ax, Jx or Ax(J)x but that is only 1/6 of the 4-2 breaks + 1/2 of the 3-3 breaks which is 24% total. Given that when the queen or king wins and East plays low on the next round I will put up the other top honour, I will lose when West has Axx and East has Jxx. Perhaps then my policy will be to play the other top honour next time as West will take his ace when he has AJ alone. If we allow this to be the case we can add another 4-2 break where West has both honours but this is only one of 30 possible 4-2 breaks so it's only 1.6% on top. Total is only 34% now. Note that if West has Ax in diamonds there is no way to make 4 tricks from the suit regardless of whether or not he wins it first round nor what we guess to do second round. We will pick up singleton J by East (1.25% as before). Whole total is 35.25%

Low to the ten is the right play on the suit alone though, by a reasonably big margin.

I think the margin is big enough to remove other considerations. i.e.
If low to the queen loses to the ace, and next round we don't drop the J, we can fall back on some other lines.

We can work out the odds if we have a weak left-hand opponent whom we know will not hold up the ace. Now we will succeed on any 3-3 split except AJx with West. There are 20 3-3 combinations and we fail on 4 of them. (West has A, J and any of the 4 small ones), thus gain now on 16 of them (instead of 10). Each combination is 1.8% total so 16 of them are 28.8%. Add that to the 9 winning 4-2 combinations (14.4%) (we now lose when West has AJ alone) and the two successful 5-1 breaks (2.5%) and our total is 45.7%, better than before.

So against a weak opponent who never holds up, this is the best line.

[Free]

My little program tells me to play small to the 10, with a succesrate of 43.1988%.

[inquiry]

There is a similar problem in one of Fred's MAster Solver packages you can buy. In that hand, the position is not complicated by other lines of play, it is just how best to play a suit KQT987 opposite small doubleton to lose only one trick (at nt) where you need to bring the suit home.

If it is any consequences, I think maybe Fred got that one wrong. The reason being the silly program says I played it wrong. LOL...

Anyway, the line there is easy, you are missing 5 cards to AJxxx, one can take out a computer and calculate the odds for the three lines...

• A - small to king then hook next time
  
• B - small to the king then small to the queen next time
  
• C - hook the very first time

Some holdings win in all three cases (like Jx in front of dummy or AJ in front), some win in two of the cases, like Ax infront for the dummy. And some lose in all (like AJX or longer behind the KQT9xxx). When one starts doing the math, on the one on master solvers, the odds seem to favor the play the declearer made in this even.. small to the TEN. I calculate them to be (for the mastersolver hand)...43% for lines A and B, but 48% for line C.

Now to this problem, as I pointed out long time ago, small to the ten is the right technical play. I still believe it. When i calculate it, i get 44.4% splitting the differnence between Earl and Free, but essential we all agree, and the vast consensus of the replies here (mine, the original person playing it, free, earl, luis, priorknowledge, flytoox, whereagles, and paulher.

On side of something else.. .Thehog, cascade, xx1947 (and free originally). I am not quite sure where fluffy stands, sounds like against poor opponents small to teh king first, but these where definietly not poor opponents, so I couldn't tell if something else would be done against world class.

I guess Fred might come down on small to the King then small and hook... (you have to buy his level 4 master solver to find out why)... They really are EXCELLENT tools and cheap too...

Ben

[cherdano]

Ben, are you sure about the master-solver hand? I get (only comparing lines A and C):
C wins when you have AJxx or Jxxx in front. Line A wins when you have Axxx or Ax in front. Since Ax is slightly more likely than AJxx (and Axxx and Jxxx are obviously equal), Line A is a tad better.

[inquiry]

cherdano, on Jul 27 2004, 10:09 AM, said:

Ben, are you sure about the master-solver hand? I get (only comparing lines A and C):
C wins when you have AJxx or Jxxx in front. Line A wins when you have Axxx or Ax in front. Since Ax is slightly more likely than AJxx (and Axxx and Jxxx are obviously equal), Line A is a tad better.

Well of course I am not sure. After all, for me to right, Fred has to be wrong.. and what are the chances of that? Not very good I think...

If West has Jxxx and East has xx only first hook wins. If West has Axxx only going up with K the up with Q works (line , and if West has AJxx only hook twice works. The four two's favor hook clearly.

Here is a table
W    E    Total
-    AJxxxx    0.745 no line
x    AJxxx    4.845 no line
xx    AJxx    9.689 no line
xxx    AJx    7.106 no line
xxxx    AJ    1.615 B only
J    Axxxx    1.211 All
Jx    Axxx    6.46 All
Jxx    Axx    10.658 A and C
Jxxx    Ax    6.46 A and C
Jxxxx    A    1.211 no line
A    Jxxxx    1.211 no line
Ax    Jxxx    6.46 A and B
Axx    Jxx    10.658 B only
Axxx    Jx    6.46 B only
Axxxx    J    1.211 A and B
AJ    xxxx    1.615 All
AJx    xxx    7.106 All
AJxx    xx    9.689 C only
AJxxx    x    4.845 no line
AJxxxx    -    0.745 no line


If my math is correct, and I used spreadsheet, this is the odds for the line...

• Line A, low to king, then low hook Ten... ~41.2%
  
• Line B, Low to king then low to Queen ~42.8%
  
• Line C, hook Ten, then hook 9, ~43.2%

The odds here are different than odds in the slam in this problem because of the number of cards in the suit (they have 5 in this problem, 6 in the bridge master problem), but the principle seems to still stand up... it seems to me.

Ben

[cherdano]

And I thought it was the other way round, they have 6 cards in uday's hand and 5 cards in Fred's problem -- and I still think like that if I reread the posts.

I still think finessing the J twice is right in uday's problem and low to the king and the hook in second round is best in Fred's problem. The big win in Fred's problem is Ax in front of the
KQT987 hand.

[inquiry]

Thank you cherdano,

You not only are correct, that it is the other way around, I got confused when I did the math and I did it the same for both. The way I showed it above.

If you do the math on the correct, 5 missing cards you get a different result altogether. The first being if the simple blind man number, and the second taking (appropriately) defenders play into account. Turns out (what a huge surprise), Fred was right after all... But now with your help, I have satisfied my itch to know why I didn't get it.....

The seven in the suit comes out to be 43% as I stated earlier. Missing only six in the suit (fred problem in Master Solvers), the math actually swings the other way with the initial hook being the worse option. Here are the odds.

If my math is correct, and I used spreadsheet, this is the odds for the line...

• Line A, low to king, then low hook Ten... ~49.7%
  
• Line B, Low to king then low to Queen ~53.13%
  
• Line C, hook Ten, then hook 9, ~48.0%

W     E     Total    
-     AJxxx     1.957     None
x     AJxx     8.478     None
xx     AJx     10.174     None
xxx     AJ     3.391     B only
J     Axxx     2.826     All
Jx     Axx     10.174     All
Jxx     Ax     10.174     A or C
Jxxx     A     2.826     C only
A     Jxxx     2.826     None
Ax     Jxx     10.174     B only
Axx     Jx     10.174     B only
Axxx     J     2.826     A or B
AJ     xxx     3.391     All
AJx     xx     10.174     All
AJxx     x     8.478     C only
AJxxx     - 1.957     none

So, on the surface it looks like the best line is low to the K the low to the Q. But that doesn't take into account that with AJ EAST must win the first trick with the ACE, else the hand is over. So this becomes a restricted choice situation. The small difference in percentage between lines A and B disappears when you take into account the effect of this restricted choce, thus favoring the small to the king, then if that wins, small to the Ten.

Ben

[Trpltrbl]

I play ♦ to the K.
I have other chances too, to make this hand. I don't have to live of the ♦, I have squeeze possibilities, ♣ might be 3-3 or J drop doubleton, ♥ finesse.
I don't like going down 1 at trick 2, if I wanted to do that I might as well duck the ♣ lead.

Mike