Play this

[wackojack]

The play of this hand, I believe, revolves around getting the best chance given the probabilities of various card combinations.  I would be interested in opinions on the best line.  I went down.

Also you can comment on the bidding if you like.  I clicked on opening 1 too quickly and believe that 1N was the best opening.  Having opened it 1 , there was no way I was going to rebid either 2 or 3  , so I stretched to 2NT.  Had I opened 1N I still think we would have finished in 3N.     

976
  K872
  106
  KQ96

  AJ3
  Q4
  AJ9842
  A3

The bidding goes 1 - 1  - 2NT- 3NT.  Lead 2  6, 10 J.

Plan the play

[kenberg]

Seems as if I need some diamond tricks (more than 1).  It would be nice if I could run the T and then alter lead small from the board but there are entry problems. Still, I think that after winning the first trick with the J  I lead a small to the board and run the T.  If W has both honors we will bring in five tricks (unless w shows out, unlikely). If E has Hx we also bring in the suit since even if he ducks, and he probably won't, his honor drops. If E holds Hxx then he certainly can make life tough for me by ducking the T. I can at least try to get back to the board with a small , playing W for the A.  Of course if W  started with a stiff honor this won't go so well, but nothing is perfect.

An alternate line is, at T2, to lead a small from hand. If I can trust that W would often hop up when he shouldn't, this might be best.

I probably would have opened this hand 1NT, assuming that shows 15-17.

[jcreech]

I don't like the lack of transportation of this hand, so I am feel like I will need to play this one all out.  I will start out leading toward the 10, if LHO wins, I will cash some clubs and finesse RHO for the other honor; otherwise I will lay down the Ace at my next opportunity and see what happens. I am hoping to get 4 or 5 diamonds, depending on defensive decisions, 3 clubs and 2 spades.  I am also hoping that LHO has doubleton honor in diamonds and either pops when I lead toward the 10, or crashes under my ace.

[wackojack]

Still, I think that after winning the first trick with the J  I lead a small to the board and run the T.  If W has both honors we will bring in five tricks (unless w shows out, unlikely). If E has Hx we also bring in the suit since even if he ducks, and he probably won't, his honor drops. If E holds Hxx then he certainly can make life tough for me by ducking the T. I can at least try to get back to the board with a small , playing W for the A.  Of course if W  started with a stiff honor this won't go so well, but nothing is perfect.

An alternate line is, at T2, to lead a small from hand. If I can trust that W would often hop up when he shouldn't, this might be best.

I will start out leading toward the 10, if LHO wins, I will cash some clubs and finesse RHO for the other honor; otherwise I will lay down the Ace at my next opportunity and see what happens.

It appears that Ken favours running the 10 and then finessing again hoping to find LHO with the A  although he hedges his bets with the alternate line.  Jim favours leading towards the but does not specify what he would do next. 

My thoughts:
http://www.automaton.gr/tt/en/OddsTbl.htm

Chance of success of let us call it Ken's way:  The only possible entry to take the 2nd diamond finesse is the K  .  This depends on West having the ace. (50% chance)  Odds of split hons or K and Q with East = 76%.  Chance of success = 38%.

Jim's way:  The chance of this line succeeding depends somewhat on guessing what West will do with Hx and Hxx. Say you play for west to have Hx regardless of he plays, then your chance of success = 26% according to the odds table.   This chance may increase a little if West decides to play H from Hxx. 

At the table I tried Ken's way.  East had the A  so I went down.  One my distinguished opponents suggested that my chances would have been better with Jim's line.  I did think at the table that playing for West to have doubleton or singleton honour might be close to 38%, but the odds table tell me that this is not so.     

[kenberg]

I think more is needed to calculate the chance of success. At T2 I led the to the K and led the T, and let's say it loses to H on my left. Presumably a comes back, I take the A and lead a toward the board. Say it loses to the A and they cash two . I am not down yet. If E started with Hx there is no need to get to the board to finesse, I just play the A  and drop his honor. This was part of my thinking although I did not work through all of the probabilities.

 Also, while I expect that the 76% figure is right when we look at the combined chances of the honors splitting (a little more than 50%) or both being on my right (a bit less than 25%) we can't lump  those two together. If the honors are split, I need to get back to the board, and  so I need the A to be right. If both honors are on my right then I don't care where the A is.   So a first approximation is that I get the entire 25% chance when the honors are on my right, and half of the 50% chance when the honors are split, for about 50%. That's not quite right either, because when the honors are split the honor on my left could be a stiff. I lose to the stiff and I still cant bring in the suit  even if I can get to the board to repeat the finesse.

I haven't gone through ll of the possibilities, but my guess is that while my line might be  less than 50%, maybe around 45%, I think it is  closer to 50% than it is to 38%.

[jcreech]

To add to my plan,

If LHO pops with an H, then I win the third , run three or four clubs, depending on whether JT drops, then hook the diamond and hope the other H is doubleton or tripleton onside.

If RHO wins the T, then I win the third spade, play the A, and continue the suit if an H doesn't drop on my left, and hope that RHO has both the A and H.  Then when in again, run my diamonds and clubs

If the is ducked, play the A, and hope they are 3-2 or everything left is with RHO except the spades (when spades are led, again I duck to the third round).

If I block the clubs, I have to count on the ace being onside, but that is also becomes an entry to the spades.  But I cannot lead the diamonds twice or risk blocking the clubs unless I can assume that, but if I risk the heart and it loses, a lead through my K now is a possible/probable entry to the remaining spades.

[Masse24]

Diamonds!  It’s all about the diamonds, which is obvious based on everyone’s plan.
IMPs, yes? I don’t much care about the clubs, except as an entry to the board. The entry problem is, well . . . a problem.

My approach is similar to Ken’s.
Trick 2: A – x- x-x
Trick 3: to the board.
Trick 4: T, intending to run it. Will obviously cover if an honor appears. If it wins, great. If it loses to an honor, when in again I play the Ace.
This should handle all cases where East has a stiff honor, doubleton honor, HHx, HHxx, as well as West having a doubleton honor.

I’ve no idea if this is probabilistically best.

[kenberg]

Jim's line creates some interesting situations for the defense. He wins the J and leads a small toward the T. let us suppose W holds Qx. If he hops up then later Jim goes to the board in and hooks the D, making. Suppose instead W plays low. E wins with the K (not good for them both to duck!) and presumably plays a . Now declarer can make the hand by laying down the A, dropping the Q, but presumably he goes to the board and takes the finesse, losing two , two and a .

Aha, I see Jim in fact plans to play the D A if the T loses to H on his right. Maybe so, but if the A doesn't drop the other honor there is a fair chance the opponents are going to take five tricks. But it does mean that Jim will make this with Hx on his left. But with Hxx on his left doesn't this give the opponents two tricks (assuming the long is with W) and two and a ?

Should it be clear to W to duck (and duck in tempo)?

It's true that my line might also depend on the defense. If E holds Hxx and covers the K I will be very grateful, especially if E holds the A. I think ducking there is perhaps easier for E than it is for W in  the Jim situation. Part of my thinking for leading a small at T2, rather than A and then small, is to give as little info as possible. W would presumably play a small at T2 if he held the A, so let E worry about whether that is the case.

[kenberg]

I thought a little more about the percentages. I think my line works about 58% of the time.

Outline of the argument:

The split 3-2 about 68% of the time, I will argue that when are 3-2 my line works 65% of the time. Multiplying these percentages gives about 44%.

The split 4-1  about  28% of the time. I will argue that when are 4-1 then my line works 50% of the time.  Multiplying these percentages gives 14%.

Adding the two cases gives 58%.

I think it is all correct.

Details:

 in those cases where the are split 3-2, it appears that my line works 65% of the time. Here is the reasoning:


I will assume that E never covers when he holds Hx or Hxx, if he does cover, that helps me. So assume he doesn't.I also assume that are 4-3. And I call the spots x, y and z, their exact value does not affect my play.



There are twenty ways, all equally likely, for the suit to split 3-2. The plan is to go to the board in and lead the T. If it loses, I try to get back to the board with a .  If I can get back to the board, I again finesse in . If the is taken by the A, I will, when next in, cash the A and hope. 

Here are ten ways that I succeed no matter where the A lies. I will give the E holding:

KQ
KQx
KQy
KQz
Kx
Ky
Kz
Qx
Qy
Qz

In the first four of these I don't care whether E covers or not. If he does I take the A and then play the J, if he ducks the T wins, I repeat the finesse, winning and then I play the J.

in the remaining six cases the T loses. Either I get back to take the finesse or if that fails I just lay down the A dropping East's remaining honor. So in these ten cases I make it, regardless of where the A is.

Now there are six cases where I will bring in  the contract if the A is with W:
Kxy
Kyz
Kzx
Qxy
Qyz
Qzx

In these six cases I will make it providing I can get to the board with the A. The T will lose to a doubleton honor. I get back in and lead a toward the board. If the K holds I repeat the finesse and pick up the suit.

The first ten are ten out of 20 for 50%, the next six are six out of twenty which would be 30% but it only works when the A is onside so I cut that in half to get 15%.

I add 50% and 15% to get 65%.

Note. I have listed 16 possible holdings for E. The other four are xy, yz, zx, xyz. That's the twenty possible holdings that I was referring to. For these four, my line fails.


Ok, this is 65% of the 3-2 cases and I guess the are 3-2 only 68 % of the time. That's about 44%. But we still have to look at the 4-1 splits. We get 4-1 spits 28% of the time. There are ten ways to split the cards 4-1. Here are ways for that to work out, again I give the E holding. Note that it's good that we have the 8 in our hand. If the T is covered we win and play the J establishing the 9 and 8, if the T is not covered we lead again toward the hand etc.

K
Q
KQxy
KQyz
KQzx

That's five. So when the cards are 4-1 I think half the time we make it. Again we don't care where the A is.

So that's another 14%.

So I get:


I think this makes about 44% plus 14% for 58%.

Added: I mentioned that when E holds xyz, so W holds KQ tight, I will go down. But I might not. The T will lose to an honor and then, if I can get back to the board, i will repeat the finesse and it will lose. Think about it. This means that when E is holding xyz and also the A, he should not take the K with his A. If he does, he leaves me with no option but to lay down the A and I am delighted to see the fall of the other honor. He must duck the K and then, after I take the second finesse, losing, then W cashes his and leads a to his partner's A. Since I doubt this duck would occur to most E players, this slightly, very slightly, ups the chances for success.

[Masse24]

I like yours better, Ken.

I worked my line out to be around 52%.

[kenberg]

Thanks. Perhaps, going into lecture mode, I could say a bit about probabilities and adjustments to a priori calculations. I'm a retired prof, sometimes I can't help myself.


For example, the probability that are 3-2 is, a priori, 68%, the probability of 4-1 is 28%

On this hand the lead (not a good choice) apparently was from KQ82.  E would have put up the K/Q at T1 if he had it, so W has both. Surely he did not lead the 2 from KQ2 alone, and unless he is getting cute, or they are playing something other than fourth best, W has exactly four spades.  Now if W had five clubs, he probably would have led a club instead of a spade and, although it is less certain (since N had bid 1 ), he,at least might have led a if he had five  of those. If we take the lead of the 2 to strongly suggest that W has no five card suit then the only way W can have a stiff is for him to have been dealt exactly a 4=4=1=4 distribution. A void in for W is even less likely since then he would surely have had a five card suit.  This substantially lessens the likelihood of E holding four or five  and thus increases the likelihood of fewer . So, here, we could adjust the a priori calculation although by how much is uncertain.

This can be contrasted with the calculations involving which cards are where, once we assume the suit is split 3-2. As mentioned, there are twenty ways to distribute five cards in a 3-2 manner. There is a formula for that, but we also can just list all 20. I noted that each of the twenty possibilities was equally likely. This is true a priori, but it remains true after the opening lead.   It's hard to imagine that any two or three card holding coming from K, Q, and three spots would have any influence on his choice to lead a small .  If he would lead a small spade from KQ82 when he held Kxy in I suppose he would also have led a small spade from KQ82 when he held the Qz of diamonds. So all twenty possibilities were equally likely before the lead, and there is no reason to revise that after the lead.

Both in bridge and in life, I advise people to be very cautious in using statistics. I guess Mark Twain and Benjamin Disraeli agreed with this (Lies, damn lies and statistics). Of course probability and  statistics can be useful, in fact very useful. But care is needed.

[wackojack]

Yes thanks Ken.  My corrected analysis with the help of the odds tables give me 58.2%, the same as you.  This was the line I took at the table which was not successful. I appreciate these are a priori odds and that post priori odds of success increase in the light of the fact that the lead was from 4 spades and so west will be balanced or semi balanced.   

West's hand was  KQ82,  J9,  Q7,  108742.  So my line failed.  Instead playing west for Qx or Kx 26% chance succeeds. (2  towards dummy's 10) .  At least I am now satisfied that I took the right line

I have tried to post the hand from the files but failed

[kenberg]

Whew! 58.2! Even though I went through it all I was happy, and maybe a little surprised, to see such good agreement .

Of course we cannot stop at the table for this sort of extended calculation. The best we can hope for is "Well, it will work of E has both honors, it we=ill work if he has Kx or Qx, and it will work if he has Kxx or Qxx if I can get back there with a , that must be pretty decent, I'll go with that.

I didn't have you or specifically anyone in mind with what I said about odds, but I often see, again both in bridge and in life, people going beyond what is really there when probability and statistics get into the act.  A text from long ago, I forget the author, had several pages devoted to real life examples of statistics being very seriously mis-used. Sometimes intentionally, often just by not being careful.

[jcreech]

Although I have an applied statistics background, I tend to keep probabilities to rough estimates and make adjustments from either the practicalities of the hand or gut instincts.

On this hand, my gut feel was that I was likely to go down, but what can I do to improve on that feeling.  I did not want to lead a small club from the Ax because I was afraid to strand a good club so soon in the hand.  I did not want to lead a heart to the K, because that would leave me with stiff Q, they were attacking spades, so that left diamonds.  I don't really think I have much of a chance if diamonds break 4-1, so I assumed 3-2.  Often when you lead a small card toward a 10, if the first hand has Hx or Qxx they fly, though the better the player, the more likely they are to duck smoothly.  In IAC, if someone does duck smoothly, I will pay off and compliment them publicly; if less smoothly, I will still pay off and compliment them privately (reminding them of the importance of playing in tempo).

With unlimited entries to dummy, of course I would take the double hook.  With even one more entry that was less dangerous, I would have taken a line more consistent with Ken or Jack, but I didn't.

I love the analysis that Ken did, but I was trying to be faithful to how I would approach this hand at the table.  What I outlined in the 2nd paragraph, is my working out the rationale that underpinned my gut plan.  I don't always slow down my thought process like that, but it is fun to do so every so often.

[wackojack]

Quick footnote:  The odds table program does have the facility to allow for vacant spaces.  Thus if I put in that there a 4 vacant spaces in the West hand and 3 in the East hand as deduced from the lead, then the chance of success increases from 58.2% to 58.9%.  Again I appreciate that this does not go far enough in getting the true odds with the inference that west has a balanced hand.  However, I doubt that it will be significant.   
 http://www.automaton.gr/tt/en/OddsTbl.htm;