[Rossoneri]

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J♣ led. What is your plan to make the contract?

(Apologies if some might find it too easy!)

[Mbodell]

My plan is to win 2 spades, 2 clubs, 1 heart, and 7 or 8 diamonds. I win the ♣A and play a ♥to the K. Later I'll pitch a heart on the ♣K and cash the ♥Q if the K was captured by the A. I'll ruff spades and clubs and hope that it will be a high cross ruff by the time opponents are out of black cards. Presumably on hearts the opponents will win the heart and return a trump to cut down on the cross ruff (I'll win with the QJ hand).

This probably isn't the absolutely best line, but it looks ok to me.

[inquiry]

This is a non-trivial problem. Several lines exist.

One is straight forward spade finesse, planning on 3♠, 1♥, 2♣, 2♣ ruff and 4♦. This is less than 50% (50% for the spade finesse, and no-one can overruff the 2nd club ruff, and spades are not 5-1 and hand with 1 having 3D. Example line (CA, club-ruff, QJ of diamonds, spade hook, club ruff, spade Ace, pull trumps, knock out HAce... something like that). Estimate clubs 5*3 or 4-4 about 80%, so .5 x .8 = 40% (some chance the hand short in clubs, might be short in diamonds too will add a small percentage to this estimate. But the chances of singleton spade has to be factored in too. For simplicity I will ignore both (5-1 spades is 14% or so, with same small chance of hand short in spades is also short in diamonds).

Another line is heart hook (counting on two hearts) and the spade hook (for 3 spades). This plus the AK of clubs and four diamonds means only one club ruff (or 3-3 spades or one spade ruff) is enough. But it requires two successful finesses. Let's call this at best around 25%.

A third line is to go after spades. This line calls for cash two diamonds (lets say AK), then play three round of spades. If diamonds were 3-2, and West follows suit, you ruff. If spades 3-3 you are home. If East shows out, but can't over ruff, you are not out of the woods yet. If you lead a heart, if West has the ACE (he is 7 to 9 underdog to have it), he will win the ace and exit a trump and you are down. I would play for East to have the heart ace, so I would lead a heart now. Assume the king wins, I ruff a spade, and lead another heart (I keep the top club). Now I plan to win 3S, 4D, 2S ruff, 1C, 2H. IF for some reason you think West has the heart ace, you ruff a club, ruff a spade, cash the top club, and lead a heart. This line works if spades are 3-3 (36%) or if the hand short in diamonds is short in spades AND you guess who has the heart ace correctly (9/16;s to guess right). The short diamond hand will be short in spades about 23% of the time (buy Jeff Ruben's book to see where this number comes from). So of the 64% of the time spades are not 3-3, you survive the immediate ruff of the third round 23% of the time. Now you can make it if you guess hearts right (lead heart when hand with heart ACE does not have outstanding trump, ruff a club the other time). Since the hand with the long spade and diamond is less likely to have the heart ace, that is 9/16th you will get the heart right. So you have 36% + (64% * 23% * 9/16) = 34 + 8% = 42%

A fourth line is to play for heart ACE to be onside, planning on 4♦+2♥+2♠+2♣+2 club ruffs. I am not sure you have the entries of this, but lets check. Win club, ruff a club, diamond queen, diamond to Ace, ruff a club, spade ACE, diamond King. However, there is a little trouble with the entries to ruff two clubs and to lead towards teh KQ of hearts twice.

So I guess I will do like my mom, who never sees a finesse she will not take. I win the club, ruff a club, and take the spade hook. IF this wins, I can even survive a 4-1 diamond split. Sigh, not very original.

[Fluffy]

I am not gonna bank all on a finese, assuming that we need to ruff at least 1 spade in dummy, and probably 2.

If RHO has 2 spades we will be in heavy trouble, we cannot make it unless he has exactly 2 diamonds.

So that's the only thing to play for IMO. ♦A, ♦Q, ♠A, ♠K and a spade ruffing low.

But this line has the problem that LHO might win ♥A and play a trump when spades are 2-4.

To avoid this we can win play a heart at trick 2, LHO won't duck this I think, so if ♥K holds assue ♥A is onside and play 2 rounds of trumps, if LHO wins ♥A and retuns a heart, then we have not enough comunication to try for RHO habing doubleon in both spades and diamonds, and we must play him to have 3 or 4 spades.

[Rossoneri]

inquiry, on 2011-February-21, 23:50, said:

This is a non-trivial problem. Several lines exist.

One is straight forward spade finesse, planning on 3♠, 1♥, 2♣, 2♣ ruff and 4♦. This is less than 50% (50% for the spade finesse, and no-one can overruff the 2nd club ruff, and spades are not 5-1 and hand with 1 having 3D. Example line (CA, club-ruff, QJ of diamonds, spade hook, club ruff, spade Ace, pull trumps, knock out HAce... something like that). Estimate clubs 5*3 or 4-4 about 80%, so .5 x .8 = 40% (some chance the hand short in clubs, might be short in diamonds too will add a small percentage to this estimate. But the chances of singleton spade has to be factored in too. For simplicity I will ignore both (5-1 spades is 14% or so, with same small chance of hand short in spades is also short in diamonds).

So, this seems to be the best line if diamonds break 4-1?

[inquiry]

Rossoneri, on 2011-February-22, 19:27, said:

So, this seems to be the best line if diamonds break 4-1?

There are several lines if diamonds split 4-1, for instance, if the heart ace is onside, you can go for six diamond tricks, 2 hearts, 2 spades, 2 clubs but you have to lose a heart. This assumes, that WEST will not duck the heart king. However, this is not clear cut. Imagine that East plays the JACK on first round (marking south with KQ) or plays the Ten (when West has AJ, marking south with KQ), or he give count in hearts and from bidding West can work out three hearts in South and ducks. Now the second round of hearts is only better than the spade hook in the concept that most west would not duck the ace. That reality means the heart ace is greater than 50% to be with East. You can add to that the concept that a lot of people might have lead the heart ace if they had it (I love playing against those players).

The basic idea is heart to king, that wins. Spade to ace, another heart. Now as long as they can't ruff the third round of hearts you have a reasonable chance. Let's assume back a heart. Now, cash one diamond, then try to score a club ruff in dummy.

Similiar idea if the heart king loses to the ACE and a heart comes back. Now you cross to the spade ace, pitch a heart on the last top club. You can play one round of trumps, the try to ruff just on spade in hand and three cards in dummy (two low, one with a top diamond). If you can get 1♥ and 1♣ or 2♣ ruffed in dummy you can survive 4-1 anywhere.

I am not at all sure I know how to play this hand, even after lookiing at it a lot. Maybe someone who can do similations can run some and tell us the right idea. But Fluffy is right. IF, and you can determine accurately who has the heart ace after one round of that suit, playing hearts early might be the best line. I will look at it again as I feel like I am missing something key here but can't put my finger on it. I probably just took the spade finesse because it will never be horrible -- next time I will try to bid a better slam.

[Rossoneri]

Thanks for the replies.

At the table, I tried 2 rounds of diamonds with AK after winning the club lead, EW following both rounds, and played off A and J of spades, winning the second round, and seeing the Q fall from West. After some thought and deciding that it was a true card, I ruffed a spade, ruffed a club, ruffed another spade, cashed K of clubs discarding a heart and now I played a heart off dummy to my K which held. Now I could draw the last trump and concede just a heart at the last trick.

(So the trumps broke 2-3 and spades broke 2-4)

Needless to say, if East had gone up with the A and returned a club I would be in trouble...

I couldn't quite work out what the best line was at the post-mortem as well.

[kgr]

inquiry, on 2011-February-23, 00:08, said:

I am not at all sure I know how to play this hand, even after looking at it a lot. Maybe someone who can do simulations can run some and tell us the right idea.

I entered this deal in Jack and analyzed it at every trick:
- Trick 2: play ♣K and discard a ♥
- Trick 3: play ♥; Trick 4: Suppose RHO took ♥A returns a ♥
- Trick 5: ♠ to A (Expected score A=637.8; J=367.4)
- Trick 6: ♠ to K
- Trick 7: ♠ ruff high if LHO follows ♠
- If RHO didn't follow: play ♦A, ♦Q and ruff another ♠
=> Ruff ♠ without taking the finesse (and without trying to develop an extra ♥ trick)

[inquiry]

kgr, on 2011-February-23, 13:10, said:

I entered this deal in Jack and analyzed it at every trick:
- Trick 2: play ♣K and discard a ♥
- Trick 3: play ♥; Trick 4: Suppose RHO took ♥A returns a ♥
- Trick 5: ♠ to A (Expected score A=637.8; J=367.4)
- Trick 6: ♠ to K
- Trick 7: ♠ ruff high if LHO follows ♠
- If RHO didn't follow: play ♦A, ♦Q and ruff another ♠
=> Ruff ♠ without taking the finesse (and without trying to develop an extra ♥ trick)

I am not familar with Jack's scoring system. I will guess that playing ace (A=637) is nearly twice as good as the Jack (J=367), but what is the scale. If it is 1000, then this line would have a Jack estimate 63.7% chance of success, and the jack not much better than playing for 3-3 spades (35.5%). Of course, at this point, jack as played two rounds of clubs and one round of hearts, which isn't the line one would take if playing the spade hook as it opens up some losing lines (like a potential trump promotion on a third round of clubs, or an unlikely 6-1 or 7-0 ♥ split and they ruff a heart.

If this is 63.7% (which i don't believe can be right), it will give me something to try to calculate and see if that is the odds I guestimate for this line. I will say, ruffing high the first spade before playing even one round of trumps, will mean you are down on a 4-1 or 5-0 diamond split... So I DOUBT that this 637 score means 63.7%.

Obvious reasons are that a it would lose to a 4-1 or 5-0 trump split. 4-1 is around 28%, 5-0 is about 4%, so those two splits alone would reduce the chance for this line to 68%, but then there is 5-1 and 6-0 spade splits that would sink this line too. The 6-0 is not great chance (about 1.5% I think) but the 5-1 has a significant chance, around 15%, lets estimate the total around 16%. These distributions could really overlap the bad diamond splits so this 16% isn't additive to the earlier 32% reduction for the poor trump splits, but it has to be more than teh difference between 68% and 63.6%. It also has potential problems on West win heart ace and leads a third round of clubs when West had a doubleton club.

Anyway, this line does give me a reasonable starting point to try to calculate odds of different lines. No way I could do this at the table

[dellache]

To me this is a MOST difficult hand to analyse : I've no definite conclusion, but finally I'd like to share my thoughts.
1. I don't think the Spade finesse is right : it is definitely LESS than 50% (when it scores, there's still lot of work), when playing on Spades is somewhere between 36% (3-3) and 36+24=60% (24%=2-4 spades, but then we need some guesswork in those cases, see 4. below).

2. I think that playing Heart early is usually right, but not for the reason that Fluffy pointed out (good oppos will duck this most of the time and moreover, playing twice toward KQ is dangerous wherever the Ace may be -- anyway that's part of the difficulty to analyse). We may need to SCORE a Heart trick early before someone can discard Hearts (West).

3. What makes computing odds difficult is also the choice of lead : West rates to have JT9(x+) or even QJT(x+) [deceptive] hence long clubs to justify leading in dummy's suit. That consideration clearly influences the distributions in other suits, and by consequence the choice of the right line.

4. I think that the general line is to ruff a spade LOW at SOME point (obviously making w/ 3-3 spades) and try to survive when West has only two of them (we don't care about East being 2-2 in the pointed suits for the time being : see point3, West has long Clubs). One of the point to analyse is the following : what happens if West is 2x4x ?
Then in order to make we will need some cross-ruff with the good *timing*.

Example : West has the simple xx xxx T9xx JT9x
In that case, we need to cash a Heart early, before playing any spade ([2]K♣ discarding Heart, [3] Heart toward King, East ducks, [4] proceed to ruff spades and guess in which rounded suit(s) West has kept cards).
If we don't cash a Heart quickly, and start with Spades, here's what happens (provided East has the Heart Ace) : West discards a Heart on the 3rd Spade, and when we play a Heart from Dummy, East plays the Ace and fires back the 4th Spade : now West discards his last Heart and the cross-ruff is doomed.

But if West had xx xxxx T9xx JT9 (not probable Club distribution), we must start the same way [123] and exit with a Heart at trick 4 : we must plan to ruff two cards from dummy before West has got any chance to discard on the 3rd Spade.

It seems that there's some guesswork involved (can we read the rounded suit distribution at trick 2 and 3 ?) as well as the interpretation of the lead in order to choose the right timing. If the diamonds are 3-2, we can play on the same line, and we have more leeway for guessing.

Analysis depends on multiple factors difficult to assess :
- the lead ;
- ability to read the parity of the oppos ♥♣ suit early ;
- what will they do when I play a Heart ;
- what will they do after they cash the Heart Ace ?

I think computing a %age is nearly impossible.
Anyway, I'd start like Jack (kgr post) and think about continuation at trick 4 (♠ now probably, Heart maybe, never finesse)

(apologies if this post is to confuse).

[kgr]

inquiry, on 2011-February-23, 20:42, said:

I am not familar with Jack's scoring system. I will guess that playing ace (A=637) is nearly twice as good as the Jack (J=367), but what is the scale.

Ben,
The scoring is the expected average score over 1000 deals that a given card will result to.
So, a score of 637 is to be compared with the slam score (930) to give you the percentage of times that it will make.
I think that the analysis is done for the current trick, assuming that play on the next tricks will be double dummy.
E.g. (Not sure, but I think this is the way it is done):
- card A gives you 80% when you can do a 50% finesse in a later trick always correct
- card B gives you 70% and no guesses to be made later
=> Jack will prefer card A and will give it a score of 80% of your contract score
Koen
Edit: I've done an analysis with Jack when only 2 cards are left: The last D and the last S. It scores 930 for the D and 921 for the S. It is unclear for me why the S scores less at that moment??

[rhm]

kgr, on 2011-February-23, 13:10, said:

I entered this deal in Jack and analyzed it at every trick:
- Trick 2: play ♣K and discard a ♥
- Trick 3: play ♥; Trick 4: Suppose RHO took ♥A returns a ♥
- Trick 5: ♠ to A (Expected score A=637.8; J=367.4)
- Trick 6: ♠ to K
- Trick 7: ♠ ruff high if LHO follows ♠
- If RHO didn't follow: play ♦A, ♦Q and ruff another ♠
=> Ruff ♠ without taking the finesse (and without trying to develop an extra ♥ trick)

This line looks to me reasonable.
This line requires trumps to break all the time and spades to be no worse than 4-2. The third round ♣ ruff must stand up, so LHO needs at least 3 cards in ♣s.
If RHO has 2 ♠ you need him to hold two trumps (about 6% chance)
That RHO has 3 or 4 ♠s is 60% multiplied by a 3-2 trump break this gives you roughly 40% overall chance.
So the total chance for this line looks to me close to 45%

I do not see anything better.

Rainer Herrmann

[robkat]

In my experience, the ♥A will be onside 95% of the time. So I would go for the spade ruff first and then lead a H to the K. This way I can make if spades are 2=4 and diamonds are 4=1.

[rhm]

robkat, on 2011-February-24, 09:02, said:

In my experience, the ♥A will be onside 95% of the time. So I would go for the spade ruff first and then lead a H to the K. This way I can make if spades are 2=4 and diamonds are 4=1.

This unfortunately does not work.
The second ♥ trick is probably useless in most variants. You still need to ruff 2 ♠. RHO ducks the first ♥. Before you can play the second ♥ from dummy you need to cash your ♣ winner. On the second ♥ RHO goes in with his ace and plays a third ♣.
Even if you do not cash your ♣ winner, LHO can discard 2 ♥ on the 2 ♠ you want to ruff. Now RHO ducks again the first ♥. You require LHO to hold 2♠=5♥=4♦=2♣ not to suffer a ♥ ruff. But with this distribution LHO simply discards a ♣ and gets a ♣ ruff instead.

Rainer Herrmann

[Fluffy]

I don't really understand why Jack cash ♣K quickly, it will be very bad if diamonds are 4-1 and south gets tapped after losing to ♥A

[dellache]

robkat, on 2011-February-24, 09:02, said:

In my experience, the ♥A will be onside 95% of the time. So I would go for the spade ruff first and then lead a H to the K. This way I can make if spades are 2=4 and diamonds are 4=1.

Untrue (see my post above).
Say West is 2=3=4=4 : West discards a Heart on the 3rd spade (trick 4).
When you play Heart (trick 5), East takes the Ace and plays the 4th spade (trick 6), allowing West to throw his last Heart :
This leaves :

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... w/ the lead in dummy and you are toast : no way to score ONE(single) Heart AND the trumps separately (an alert East will see that playing the master Spade kills you). Try it.
You don't have THIS problem (but other problems ) if you start with an early Heart.

[rhm]

Fluffy, on 2011-February-24, 14:39, said:

I don't really understand why Jack cash ♣K quickly, it will be very bad if diamonds are 4-1 and south gets tapped after losing to ♥A

Simple.
Jack "realizes" that on his line trumps must always break anyway.
Postponing the ♣ and ♥ play only risks a later ♣ and ♥ discard when the third and fourth round of spade is played with no gain.
Number of undertricks are certainly not important and may not go into Jack's calculations.
However, it makes sense to play ♥ first, than a ♠ to the table and then the second ♣ and continue with the second ♠ to hand, ♠ ruff.
This is slightly safer. However, I can not construct a deal, where this would matter for the success of the contract.

Rainer Herrmann

[inquiry]

rhm, on 2011-February-24, 05:31, said:

This line looks to me reasonable.
This line requires trumps to break all the time and spades to be no worse than 4-2. The third round ♣ ruff must stand up, so LHO needs at least 3 cards in ♣s.
If RHO has 2 ♠ you need him to hold two trumps (about 6% chance)
That RHO has 3 or 4 ♠s is 60% multiplied by a 3-2 trump break this gives you roughly 40% overall chance.
So the total chance for this line looks to me close to 45%

I do not see anything better.

Rainer Herrmann

This isn't totally accurate ("This line requires trumps to break all the time"). You can also survive west being something 2-3-4-4 or 2-4-4-3 thanks to a high cross ruff. A key position would be this... after heart King won and you ruffed the spade with a low diamond instead of a high one because West showed out on third round. Here is an example of theses.

Cash high diamond, ruff a club low, high cross ruff.

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So actually, this raises the chance of success for this line a little bit.

But I am still confused by the JACK analysis. To do the calculations, I figured that 6♦ was only set one trick (there are a few situations where Jack's line could lead to down two). It averaged 636 on a 930 possible score. So solving for "x" where x is the percentage of time Jack's play wins you get

636 = (930)(x) - 50(1-x). This simplifies to
636 = 930x - 50 +50x, or
686 = 980x or
x = 0.7

I just can't imagine how the percentage of this line ever reaches 70%, I can only assume that Jack's random hand dealing program is not so good. Anyone else have ideas on why Jack would rate its hand so high? I am now convinced that this line (although one doesn't have to play it exactly like jack did) is best.

One possibility is it guess right when East has four diamonds and two spades. Yes you can make the hand then, but you need to guess if he is T9xx or only one high diamonds. Maybe Jack always guesses that right, but I still don't think it gets near to 70%.

[rhm]

inquiry, on 2011-February-25, 12:52, said:

This isn't totally accurate ("This line requires trumps to break all the time"). You can also survive west being something 2-3-4-4 or 2-4-4-3 thanks to a high cross ruff. A key position would be this... after heart King won and you ruffed the spade with a low diamond instead of a high one because West showed out on third round.

Is your reasoning totally accurate?
With Jack's line you may survive west being 2♠=3♥=4♦=4♣ via a late crossruff, but not 2♠=4♥=4♦=3♣. West will certainly discard his third ♣ on the third ♠. So you can not ruff the third ♣ low. If West has only 2♠ you probably need to assume West has at least 4 cards in ♣.
However if West is 2♠=3♥=4♦=4♣ his best defense is to ruff the third ♠ to force a high trump from dummy.
Now the cross ruff line succeeds against 2♠=3♥=4♦=4♣ but will loose against west having 2 trumps only, where drawing 2 rounds of trumps before ruffing the fourth trump would work. Which line is better? I do not know, but I assumed jack would go for the trumps to break.
This is what makes the cross ruff anything but clear.It is not specified how Jack would continue if West shows out. Maybe ruffing the ♣ low.
This raises the question why jack cashes the second ♣ before playing ♥. What happens if say LHO takes the ♥ ace and plays a third ♣ prematurely?

The calculations of jack do not look like single dummy probabilities. It seems to me jack does not take into account, that he might later have to take another decision between incompatible lines of play.
He chooses the line which leaves most possibly successful lines open at decision point and adds their probabilities. He samples say 1000 deals and finds out that he can make the contract by finessing in ♠ on 400 deals and if he goes up with the ♠ ace could be successful on 700 deals in theory, if he plays thereafter double dummy. This is of course dubious, but may be the best pragmatic way to come to a reasonable decision in a complex layout like this.

This is in deed a very complex deal.

Rainer Herrmann

[kgr]

inquiry, on 2011-February-25, 12:52, said:

One possibility is it guess right when East has four diamonds and two spades. Yes you can make the hand then, but you need to guess if he is T9xx or only one high diamonds. Maybe Jack always guesses that right, but I still don't think it gets near to 70%.

rhm, on 2011-February-26, 04:07, said:

The calculations of jack do not look like single dummy probabilities. It seems to me jack does not take into account, that he might later have to take another decision between incompatible lines of play.
He chooses the line which leaves most possibly successful lines open at decision point and adds their probabilities. He samples say 1000 deals and finds out that he can make the contract by finessing in ♠ on 400 deals and if he goes up with the ♠ ace could be successful on 700 deals in theory, if he plays thereafter double dummy. This is of course dubious, but may be the best pragmatic way to come to a reasonable decision in a complex layout like this.

kgr, on 2011-February-24, 04:35, said:

I think that the analysis is done for the current trick, assuming that play on the next tricks will be double dummy.
E.g. (Not sure, but I think this is the way it is done):
- card A gives you 80% when you can do a 50% finesse in a later trick always correct
- card B gives you 70% and no guesses to be made later
=> Jack will prefer card A and will give it a score of 80% of your contract score