A Grand Slam

[Walddk]

[hv=d=s&v=n&n=sj652haj943dk5cq6&s=sakq104hdaq1042ca72]133|200|Scoring: IMP

S: 7S

Lead: S3[/hv]

 

1♠ - 2NT

7♠!?

 

Perhaps not an auction of beauty, but at least it was short. The deal is from the Danish teams championships last weekend. 2NT was limit or better with support, and South gambled on the grand.

 

We have all been in worse contracts (I have been in much worse). In fact, declarer got lucky. The contract actually has some play. Our only problem now is to make it. RHO follows to trick 1, but when you cash a second round of trumps RHO shows out. You may just as well pull the last trump.

 

Let's take stock. 5 trump tricks, 1 heart and 1 club. The diamond suit must now produce 5 tricks, and that along with a club ruff will see you home. To find a singleton ♣K is not even worth thinking about.

 

So ♦K (all follow small) and a low, RHO following with the 9. What now? Go for the drop or finesse the 10? Do you know your odds?

 

Roland

[cherdano]

[hv=d=s&v=n&n=sj652haj943dk5cq6&s=sakq104hdaq1042ca72]133|200|Scoring: IMP

S: 7S

Lead: S3[/hv]

RHO follows to trick 1, but when you cash a second round of trumps RHO shows out. You may just as well pull the last trump.

I don't understand this. If you draw trump the last trump, you have to play for diamonds to be, aehm, lets say to behave very well to avoid the spoiler. However, if you play 3 rounds of diamonds (discarding a club on the 3rd round from dummy) now, i.e. after 2 rounds of trumps, I think you make whenever they are 3-3 or 4-2 with LHO having 4 plus at least 2 hearts.

If LHO has 4, you ruff a diamond, ♥A discarding a club, ♣ to the A, ruff a club in dummy, ruff a heart in hand, draw last trump and you have a high diamond left.

 

Arend

[ochinko]

I go for the drop. D9 doesn't mean anything so there's no way to apply the principle of restricted choice.

 

There's a very nice rule by Richard Pavlicek that you play for the drop whenever there's a chance to catch all the cards in the suit. It shows why "8 ever, 9 never" is valid, why you finesse the King with 10 but not with 11 cards, and why with 7 cards when you miss the Jack it's better to cash from the top. You win not only when the suit is 3:3 but also when the Jack is doubleton. That is, of course, if there's no additional information.

 

Now I continue with a calculator assuming that West can't have D Jxxx because in that case we're doomed whatever we do. If we don't know how the spades break the chances for the East to have Jxxx are appr. 27%. This percentage climbes up to 31% because East has two more slots available for diamonds. I still play for the drop.

 

--- Edited ---

Oops, I didn't take into account that the finesse works also when East has Jxx so the percentages are actually closer to 38% for the finesse if we don't know about spades, and 42% afterwards. The chances for West to have Jx or Jxx are almost 58%. The drop is still prefered.

[Rebound]

The opening lead suggests that one or both missing kings are with west. Perhaps this means the finesse is the right play. I don't know. I like Cherdano's line. It is dangerous to leave the trump out, but it gives an additional chance for the contract. Essentially, it comes down to: if west has a doubleton diamond you are sunk. Otherwise you're all set. Of course, that theory goes down the toilet if there's some reason to believe west has only 2 diamonds.

[Walddk]

Good point Rebound. If you will go for the drop in diamonds anyway, it is clearly better to stop pulling trumps after 2 rounds and play 3 rounds of diamonds now.

 

Roland

[luis]

I think that declarer has to win the spade lead and play a spade to the Jack, cash the heart ace and ruff a heart then he can choose what to play. Maybe we can get some information from the heart spots they play. There's the chance to drop KQx of hearts tripleton before taking a decision about the diamonds.

So if the Q or K of hearts falls in the 2nd round I play diamond to the K and ruff a heart finish drawing trumps and now I can either win with diamonds 3-3 or if the hearts are stablished entering dummy ruffing a diamond.

If the heart K or Q doesn't appear then depending on the heart spots I may be inclined to take the diamond finesse or play for the drop.

[cherdano]

It seems I was right about the odds, but only very closely so: Here are the exact percentages for the diamond break, given LHO has 3 spades and RHO 1 (LHO=RHO):

a) 3=3 35.38%

:) 2=4 29.85%

c) 4=2 18.58%

(Check yourself at http://www.rpbridge.net/xsb2.htm. This ignores inferences from the lead, of course.)

 

Option A: Play for the drop

Option B: Finesse 2nd round

Option C: Play for LHO to have 3 or 4 diamonds (line in my post above)

 

Option A works for all of a), one third of :) and c), which is 51.38%.

Option B works for half of a), 2/3 of B) and 1/3 of c), i.e. 43.6%.

Option C works for a) and and about 94% of c), i.e. 52.84%.

 

(Of course, luis' line may be best overall.)

[Walddk]

It seems I was right about the odds, but only very closely so: Here are the exact percentages for the diamond break, given LHO has 3 spades and RHO 1 (LHO=RHO):

a) 3=3    35.38%

B) 2=4    29.85%

c) 4=2    18.58%

(Check yourself at http://www.rpbridge.net/xsb2.htm. This ignores inferences from the lead, of course.)

 

Option A: Play for the drop

Option B: Finesse 2nd round

Option C: Play for LHO to have 3 or 4 diamonds (line in my post above)

 

Option A works for all of a), one third of B) and c), which is 51.38%.

Option B works for half of a), 2/3 of B) and 1/3 of c), i.e. 42.7%.

Option C works for a) and and about 94% of c), i.e. 52.84%.

 

(Of course, luis' line may be best overall.)

Excellent job! So declarer opted for the close 2nd best line when he pulled all trumps and went for the drop in diamonds. Impossible to work out at the table. Only plan B would have been successful. RHO had Jxxx in diamonds.

 

For the record, I think your addition in Option B is inaccurate. I make it roughly 43.78%. Not a big deal; the finesse is by far the inferior line. Winning on the actual layout, yes, but not the plan you should select in the long run. Only Deep Finesse (DF) would have made the grand slam.

 

Roland

[ochinko]

It seems I was right about the odds, but only very closely so: Here are the exact percentages for the diamond break, given LHO has 3 spades and RHO 1 (LHO=RHO):

a) 3=3    35.38%

B) 2=4    29.85%

c) 4=2    18.58%

(Check yourself at http://www.rpbridge.net/xsb2.htm. This ignores inferences from the lead, of course.)

 

Option A: Play for the drop

Option B: Finesse 2nd round

Option C: Play for LHO to have 3 or 4 diamonds (line in my post above)

 

Option A works for all of a), one third of B) and c), which is 51.38%.

Option B works for half of a), 2/3 of B) and 1/3 of c), i.e. 42.7%.

Option C works for a) and and about 94% of c), i.e. 52.84%.

 

(Of course, luis' line may be best overall.)

This is the calculator that you should have used instead, and your calculations would've been right :P

 

Luis' line may indeed be best, but if we are to concentrate only on the diamonds we should exclude the possibility of East to have 5 diamonds, or West to have Jxxx. So we put 2 as the minimum length for East and 4 as the maximum, and set the available space to 8 for W and 10 for East.

 

Now we have 6 possibilities:

1. Jxxx xx 10 30 13.33

2. Jxx xxx 10 48 21.33

3. Jx xxxx 5 28 12.44

4. xxxx Jx 5 15 6.67

5. xxx Jxx 10 48 21.33

6. xx Jxxx 10 56 24.89

 

No 4 is impossible and No 1 we assume impossible because no matter how we play we lose. No 5 we exclude because it's irrelevant. This leaves us with #2 and #3 against #6, or 34% against 25%, or if we normalize the result to achieve 100% sum, we have 57.5% for the drop and 42.5% for the finesse.

[cherdano]

This is the calculator that you should have used instead, and your calculations would've been right  :unsure:

Nope. I wanted to compute the odds of each line at the point after the second round of trumps. For this, I have no information about min/max length, so there is no added value in using your link.

 

Other than that, I don't care much about your renormalizations to 100% and throwing out lies where the play does not matter (I think what we want to know is "What is the overall chance that line A succeeds?" Whereas you are computing "Among the lies where our play makes a difference, what is the percentages of the lies in which A succeeds?" For finding out which of 2 lines is better, yours is equivalent, of course, but it gets a mess as soon as you want to compare 3 lines, and other than that, the first method gives an idea along the way how good this slam actually is.)

However...

Luis' line may indeed be best, but if we are to concentrate only on the diamonds we should exclude the possibility of East to have 5 diamonds, or West to have Jxxx. So we put 2 as the minimum length for East and 4 as the maximum, and set the available space to 8 for W and 10 for East.

this is clearly wrong. You need to use 10 and 12.

[ochinko]

This is the calculator that you should have used instead, and your calculations would've been right  :P

Nope. I wanted to compute the odds of each line at the point after the second round of trumps. For this, I have no information about min/max length, so there is no added value in using your link.

 

Other than that, I don't care much about your renormalizations to 100% and throwing out lies where the play does not matter (I think what we want to know is "What is the overall chance that line A succeeds?" Whereas you are computing "Among the lies where our play makes a difference, what is the percentages of the lies in which A succeeds?" For finding out which of 2 lines is better, yours is equivalent, of course, but it gets a mess as soon as you want to compare 3 lines, and other than that, the first method gives an idea along the way how good this slam actually is.)

However...

Luis' line may indeed be best, but if we are to concentrate only on the diamonds we should exclude the possibility of East to have 5 diamonds, or West to have Jxxx. So we put 2 as the minimum length for East and 4 as the maximum, and set the available space to 8 for W and 10 for East.

this is clearly wrong. You need to use 10 and 12.

But you must have realised that you overvaluated the chance for West to have four diamonds by almost a third when East played a second small diamond. That is why you reached the wrong conclusion when accounting only for lengths. The Jack is a significant card, and when East followed twice with a small card the chance for West to have four diamonds is no longer 20% but only 13%.

 

If you don't care about normalizations, we can express the odds as a ratio. Playing for the drop is 1.35 times better than playing for the finesse, and 2.5 times better than playing for West to have Jxxx.

[cherdano]

But you must have realised that you overvaluated the chance for West to have four diamonds by almost a third when East played a second small diamond. That is why you reached the wrong conclusion when accounting only for lengths. The Jack is a significant card, and when East followed twice with a small card the chance for West to have four diamonds is no longer 20% but only 13%.

Nope. I decide at trick 2 which plan I follow, and calculate the a priori-odds of success for each of these lines. Then Jx with East will be included as success for all of these lines, and there is nothing wrong with my calculations.

Your claim that I reached the wrong conclusions makes me wonder whether you read my posts at all. You and me got the same conclusion (drop is better). Just that I think there is a slightly better 3rd line.

I don't know what else to do to convince you, and I am not _that_ interested. Since I am already starting to repeat myself, this will be my last post in this thread unless s.th. new comes up.

[Fluffy]

The odds for the ♦ suit for 5 tricks are to cash AK since you cannot catch 5-1.

However the vacant space theory might have something to say here.