Author Topic: Line of play with the best odds of making  (Read 3016 times)

wackojack

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Line of play with the best odds of making
« on: April 29, 2020, 01:07:24 PM »
 For working out odds a Ken special?

!S Q109542
 !H J875
 !D Q
 !C 97

 !S A
 !H AKQ962
 !D A762
 !C K2

Bidding: 1 !H - 3 !H - 6 !H
Lead J  !D.


This was played in a TM last night.  Please don't spoil it by looking before you have replied.  Just to say that opps carding may not help you because a reserve stepped in on this hand alone with no discussion.   


kenberg

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Re: Line of play with the best odds of making
« Reply #1 on: April 29, 2020, 05:34:41 PM »
I think it would be tough to convince me not to play Rho for the !C A.  He has it half the time on general principles, plus even if you think Lho  might not have laid down the !c A if he had it, surely he might have done so.
I suppose the !d Q is covered by the K, I take my ace, I ruff a !D on the board and lead a !C.
If I am wrong about the !C A I am now down. If I am right then I guess it depends a little on what happens. If Rho plays low on the !C I take my K after which I probably lead a third !D and pitch the !C spot. The plan is to ruff the last !D with the !H J and to ruff !c 2 low. I might have to think that through  a bit but probably Rho hops up with the !C A if he has it. Then we have to see what he does next.

In these problem hands, finesses never work but I really do think I would play Rho for the !C A. The hand is still not on ice, but pretty decent.   Setting up spades, and then getting to them, seems unlikely. Possible, but unlikely.
Ken

Masse24

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Re: Line of play with the best odds of making
« Reply #2 on: April 29, 2020, 11:14:41 PM »
Seems a bit off to me, Ken.

While I suppose you could gather some inference in LHO's failure to lead the outstanding Ace, it's not enough to base the contract on.

Obviously we need to get rid of the diamond losers. Conveniently, partner has provided a dummy with a stiff diamond and plenty of trump to ruff diamond losers.

What about clubs? Since the !C finesse is only 50% (okay maybe inferentially better due to the lead), I’ll search for better odds.

Whenever I see a five-card suit in dummy, as declarer I think about setting it up. Here, we have a six-card suit in dummy. My goal is to set up the spade suit to jettison clubs--and the final diamond--which does not need to be ruffed.

Transportation to dummy is clearly accomplished by ruffing diamonds. Missing eight diamonds, a 4-4 or 5-3 split is 80%. A 6-2 split is 17% but is slightly less likely due to the lack of a preempt. If RHO has only two diamonds, he could potentially over-ruff my second intended ruff with the trump ten.

Missing six spades, a 3-3 or 4-2 split is 84%. Remember, even if 4-2 you can ruff high in hand.

So barring a bad diamond split (80%) and counting on a decent spade split (84%), I figure around 67%. Maybe even better? I dunno, I'll let the guys who advanced beyond using fingers and toes calculate that one!  ;)

Yes . . . it's rough. There are a couple of funky things that might happen. But it sure seems better than a finesse.
« Last Edit: April 29, 2020, 11:17:29 PM by Masse24 »
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kenberg

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Re: Line of play with the best odds of making
« Reply #3 on: April 30, 2020, 01:54:11 AM »
Maybe I am missing something. Let's suppose that the spades are 4-2. The !S A draws one of them. Now we need to lead spades from the board three more times. and then we need to get back there to cash them. How?  As near as I can see, this means that you cannot draw even one round of trump. If you do, there are three board entries by !D ruffs, and that's not enough
Suppose  we start:

T1: !D JQKA
T2 !S A

Now we can perhaps ruff !D three times and lead !S three times in tricks 3-8. If all goes well the two remaining spades are good, but? We can get there with the !H J but the opponents will still have a trump even if !H are 2-1. A spade play will be ruffed, and that's that.

If !S are 3-3 this line will work, at least if trumps are 2-1, and maybe it will work if, say Rho has !S Kx but I think on most 4-2 !S splits this approach won't work.


My line in more detail:
I assume the !C A is on my right and that Rho has 3+ !D

T1 !D JQKA
T2 !D, ruffed with the !H 5.
T3 !C, I suppose he rises on my right

Suppose Rho now leads a trump. I have ruffed once and this play will draw a trump, but I have two on the board and only two diamonds so I should be good.

If, at T4, Rho leads a black card I am still ok assuming I am not overruffed when I ruff a !D on the board (that's why I need Rho to have three, but even if not I will b ok if he does not have the !H T.  So then back to my hand in a black suit, ruff a !D with the J, lead the last !H from the board and claim.

If I am wrong I am wrong but I just do not see the !S as a reliable source of cashable tricks if they split 4-2.
 
Ken

Masse24

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Re: Line of play with the best odds of making
« Reply #4 on: April 30, 2020, 02:51:59 AM »
Aah, you're right.

I think a 4-2 spade split can work, but only if the !H T is on your left since you would need two more entries to dummy and would need to drop it or finesse it.

That kills my initial calculations.

Back to fingers and toes.
“Kindness is the only service that will stand the storm of life and not wash out. It will wear well and will be remembered long after the prism of politeness or the complexion of courtesy has faded away.” Abraham Lincoln

kenberg

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Re: Line of play with the best odds of making
« Reply #5 on: April 30, 2020, 10:32:51 AM »
And I also woke up with further thoughts. When the spades are 4-2, any give card, the K in this case, will be doubleton one third of  the time. Suppose we take the !D A, then the !S A, ruff a !D and the !S K falls. Now lay down the !H A. If everyone follows we take all 13 tricks! Back to the board with the J drawing their last trump, cash the !S Q, ruff a !S, now the remaining spades are good and we can ruff a !D to get there. Together we have four spade tricks including the A that was played early, six hearts in hand, two ruffs on the board and the !D A. Of course 12 tricks is our goal, but after the !S K falls we will get 12 even if Lho holds all three trump. After the !S K falls we cash the !H A, observe the split, and lead a small trump covering whatever Lho plays. Trump a !S high and lead a trump back to the board. We are still getting four spade tricks etc but now only that one early !D ruff for 12.

So it gets a bit complicated. !S can well be 4-2, but that may go ok. It might really be necessary to get the abacus out to see what the best line is.

We could start with the !S A , the !D ruff, the !S ruff and then, if the K does not fall, we could still ruff a !D and lead a small !C.  I was thinking that if I am going to play for the !C A on my right I might as well do it early before something goes wrong elsewhere. But maybe we can, with not too much danger, try for the !S K drop and still try for the !C finesse.
« Last Edit: April 30, 2020, 11:24:02 AM by kenberg »
Ken

wackojack

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Re: Line of play with the best odds of making
« Reply #6 on: April 30, 2020, 10:58:49 AM »
Yes I think that is correct.  So is not the best line to play for possibly good breaks and as a last resort you go for the K !C being well placed.  Obviously if  !S split 3-3 and  !D split 4-4 you can play on the x ruff and establish spades for the  !C discards.  Here is an example with LHO having 10  !H!D splitting 5-3,  !S 4-2 and A  !C over the King.

                         !S Q109542
                         !H J875
                         !D Q
                         !C 97
  !S KJ63                                !S 87                               
  !H 10                                    !H 43                       
  !D J10943                             !D K85
  !C A64                                  !C QJ10853

                          !S A
                          !H AKQ962
                          !D A762
                          !C K2

   You win with the A !D, unblock the A !S, ruff a  !D, ruff a  !S, ruff a  !D.  So far you would be OK if  !S no worse than 4-2, and  !D no worse than 5-3 and some more if the short  !S are with RHO and more if short  !Ds with LHO.  Next you play another  !S planning to ruff high.  North shows out and you ruff high.

This is the position:    !S Q109
                                 !H J8
                                 !D -
                                !C 97

                               !S -
                               !H KQ96
                               !D 7
                               !C K2
If trumps split 2-1, then you can make the spades winners if the  !H J8 provides 2 entries.  So if the  !H 10 is with LHO then you are there.  So lead the 9  !H and if the 10 is played you win with the Jack, ruff Q  !S and the 8  !H is your final entry.  However, suppose LHO plays small.  Do you play for the 50% chance of 10 being with LHO and finesse.  Or do you overtake and play a  !C to the K for another 50% chance? 

After all this thought it does seem that you can test your cross ruff chances before resorting to the k  !C finesse. 

Ken's post has just come in whilst I have been composing this post and I believe Todd, Ken and I are saying the same things about the chances of making with a x ruff to establish the spades.
 The question remains is how far can you safely go in the Xruff and at the same time preserve your 50% club finesse chance?                                       

Masse24

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Re: Line of play with the best odds of making
« Reply #7 on: April 30, 2020, 11:29:56 AM »

This is the position:    !S Q109
                                 !H J8
                                 !D -
                                !C 97

                               !S -
                               !H KQ96
                               !D 7
                               !C K2
                 

Not quite.
This is the position:    !S Q109
                                 !H J8
                                 !D -
                                 !C 97

                                !S -
                                !H KQ62
                                !D 7
                                !C K2

Because at trick four you would need to be careful to ruff a spade high for safety and so that you could finesse the trumps remaining in dummy while still winning the trick in dummy. You still need to get rid of that pesky !S K if it remains.

This can get a bit complicated and would take a serious effort to come up with accurate guesses.

Just woke up. Need caffeine. I'm guessing Ken has the socks off and will soon bring all toes to bear.
                 
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kenberg

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Re: Line of play with the best odds of making
« Reply #8 on: April 30, 2020, 02:10:37 PM »
We can probably agree it is an interesting hand. Often, looking back on hands, there is a reasonable approach that can be improved upon with more thought. I will try to get back to this one.  Has to wait for a bit though.
Ken

jcreech

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Re: Line of play with the best odds of making
« Reply #9 on: April 30, 2020, 02:19:10 PM »
As the random defender inserted into play on this hand, I stepped back until others had weighed in.

I think the best line is to combine chances.  You cash the SA, and lead a trump to the J (I am not willing to bank on a heart finesse at this point).  If the 10 falls from either hand, then I have both the 3-3 and 4-2 spades as possible lines and the 78% chance plus the 50% chance in clubs.  If the 10 does not appear, then I still have the 3-3 spades plus the club finesse.

As the 10 did not appear, I ruff a spade high, and ruff a diamond to play a third spade.  When the spade break 3-3, then my problems disappear.  I pull the last trump, ruff a diamond and pitch on spades.   If the spades do not break, then I have to cross ruff out the diamonds before trying the club finesse on my last trip over to dummy.  Not sure what the probabilities are at this point, but I feel pretty good about the total.
A stairway to nowhere is better than no stairway at all.  -Kehlog Albran

kenberg

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Re: Line of play with the best odds of making
« Reply #10 on: April 30, 2020, 04:19:49 PM »
After !D A, then !S A, then !H to the J the T falls about 26% of the time, the suit is 3-0 about 22%. When it is 3-0 things get tricky. Even if the !S break 3-3, if you ruff a !S, ruff a !D, ruff a !S establishing !S, you cannot both draw trump and then get to the board.

If you cannot develop spades, then you need the !C finesse. Can you even take it if it is working? It depends. If Rho started with three trump then no. If you lead the !C he goes up with the A and leads a trump so that you can no longer ruff all of your !D.

I have not worked this through completely, the stiff !H T is a bit more likely than the 3-0 split,  and a lot more likely than 3-0 with the 3 on your right, but there seem to be issues.

I remain uncertain about what is best.

As noted, it's an interesting hand.
 
Ken

wackojack

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Re: Line of play with the best odds of making
« Reply #11 on: May 01, 2020, 09:04:18 AM »
I will now reveal that this was the last hand of a team match in which we were -7 imps and this beautiful hand came up.  Bidding 1  !H -3 !H -6  !H-pass. 

At the table with a bit of time pressure, all I saw (incorrectly) was that I needed spades 3-3 and diamonds not to break badly which was against the odds in order to establish the spades.  So I went for the a priori 50% chance of the A  !C being onside.  It was mortifying to see that spades split 3-3 and diamonds 4-4 so incredibly perfectly and my partner politely pointing out that I could have made it. Ironic that hand I been missing both Ace and King clubs in separate hands I would have made with an overtrick. 

From my reading of the Ken's, Todds and now Jim's contributions it is clear that I can do some combining of chances if done carefully.   Play for spades to be 3-3 or 4-2 with LHO having 2 or   !D s to split no worse than 5-3 or LHO having 10 !H singleton giving extra chances.  Anyway, the chance of making is a lot more than 50%.