Your Line of Play ...

[ralph23]

Ralph, then why do you insist on s.o. else computing odds that are not at all bridge-relevant? The case where RHO can't ruff obviously doesn't matter, as we are down anyway... Is it because you would like to know the odds (I don't see why), or because you think it is useful for s.o. else to compute them (I disagree)...

I think it's useful to learn to compute them & to learn to be alert to all the conditions needed to answer the question posed correctly....instead of just assuming we will lose trick 1 if LHO has led from a six-card suit.

 

Yes we're down if LHO has ♠Kx. But that was not the question posed, was it?

 

Fine with me if you disagree with the pedagogical philosophy or on "bridge relevancy"...each to his own taste.

[jdonn]

Having only skimmed the other answers (sorry too lazy) I think a better line than playing off ace of clubs and keeping the heart entry is playing of three rounds of hearts and keeping the club entry. The general reason is we will see the heart break ahead of time so we will have more sure information about who is being squeezed in what. Plus if they are 3-3 it saves a lot of mental anguish!

 

So, A♥ A♠ QJT♠ Q♥ K♥ and start running spades, which I think keeps all possibilities alive.

I'm assuming you also cashed your Ace of ♦ at some point during the run of the trumps from the South hand, so is your three card ending then:

 

[hv=n=sh6dcaq&s=s2hdtc4]133|200|[/hv]

 

??

 

and now at trick 11, you will play the last trump from the South hand??

I don't know why you assumed that. Make that a 4 card ending including the diamond ace still being in south's hand, and at that point it just matters what everyone has played so far so there is no way to say what I'd do next.

[skjaeran]

Having only skimmed the other answers (sorry too lazy) I think a better line than playing off ace of clubs and keeping the heart entry is playing of three rounds of hearts and keeping the club entry. The general reason is we will see the heart break ahead of time so we will have more sure information about who is being squeezed in what. Plus if they are 3-3 it saves a lot of mental anguish!

 

So, A♥ A♠ QJT♠ Q♥ K♥ and start running spades, which I think keeps all possibilities alive.

I'm assuming you also cashed your Ace of ♦ at some point during the run of the trumps from the South hand, so is your three card ending then:

 

[hv=n=sh6dcaq&s=s2hdtc4]133|200|[/hv]

 

??

 

and now at trick 11, you will play the last trump from the South hand??

I don't know why you assumed that. Make that a 4 card ending including the diamond ace still being in south's hand, and at that point it just matters what everyone has played so far so there is no way to say what I'd do next.

Agree with Josh here. I'd also come down to a 4-card ending with the low diamond in dummy and the ace in hand in addition to the above ending. If LHO holds the ♥'s I'll obviously throw the ♥6 from dummy now.

[ralph23]

I don't know why you assumed that. Make that a 4 card ending including the diamond ace still being in south's hand, and at that point it just matters what everyone has played so far so there is no way to say what I'd do next.

 

Does your method work better than Echo's, I wonder? Or don't they both work in the same circumstance, i.e. West with 4♥ and either minor King, or East with 4♥ and the King of diamonds?

[cherdano]

Ralph doubly dummy you can make, just pitch the ♣Q on the trump and play a club.

[jdonn]

Can you make it from here? NB - Whenever you lead your last trump, West and East will both discard a ♣.

 

Echo's squeeze will work, as Harald correctly noted, whenever EITHER (1) West started with 4♥ and any minor King, OR (2) East started with 4♥ and the King of ♦.

 

a. I don't think your method works when West holds 4♥ and the diamond King, and East holds the club King, as depicted above. Does it?

 

b. And I can't find any compensating advantage to playing it this way, i.e. an instance in which your method works and Echo's fails. Is there one?

 

But I'm ready to be instructed in both a. and b.

a. Easily, discard dummy's club queen on the trump and lead a club to the ace to squeeze west. And though it doesn't actually matter here, I would have thrown QJ of diamonds from dummy on the trumps to unblock, in case it came down to taking the diamond finesse.

 

b. Yes, that you get to see how hearts break before making any decisions. Playing the club ace then running trumps you have to guess about all three suits. Playing hearts first and saving the club ace you get a sure count on the hearts so only have to guess about two suits. Of course when I say "guess", in both cases it will be a very educated guess that you are likely to get right based on the discards and being at the table, but needless to say the more information you get early the more accurate you will be, and the only way to get any real information early is to test the hearts.

 

What in the world does NB mean?

[ralph23]

What in the world does NB mean?

Nota bene, Latin for "note well" ... same school as e.g. and i.e......

 

So Echo's method works whenever EITHER (i) West holds 4♥ and either minor King OR (ii) East holds 4♥ and the diamond King.

 

Will your method work in an additional circumstance (of course, both methods work when ♥ are 3-3)?

[jdonn]

No, double dummy they are equivalent. At the table I am convinced my way will make more often, and needless to say you save a lot of brain cells by finding out hearts are 3-3 sooner.

[ralph23]

No, double dummy they are equivalent. At the table I am convinced my way will make more often, and needless to say you save a lot of brain cells by finding out hearts are 3-3 sooner.

Is there a method that is better than either of the squeeze methods? And that saves brain cells, too?

 

Here's where that gross math part comes back in and rears its ugly head... B)

[cherdano]

b. Yes, that you get to see how hearts break before making any decisions. Playing the club ace then running trumps you have to guess about all three suits. Playing hearts first and saving the club ace you get a sure count on the hearts so only have to guess about two suits. Of course when I say "guess", in both cases it will be a very educated guess that you are likely to get right based on the discards and being at the table, but needless to say the more information you get early the more accurate you will be, and the only way to get any real information early is to test the hearts.

What you say about the straightforward squeeze line is just not true, it is a completely automatic show-up squeeze, the only thing you need to notice is if someone discards a king, there is no guessing.

 

Maybe your line works better if you guess very well at the end but I am too lazy to look at that right now.

[jtfanclub]

and now at trick 11, you will play the last trump from the South hand??

That would depend upon who has the four hearts, yes?

 

If West started with 4 hearts, you should play the last trump for the obvious squeeze.

Case 1. Suppose West started with 4♥ and one of the two missing honors (call those "H").

 

You are in the stated three-card ending, and you now play the final trump from the South hand. West at this point remains with three cards also, namely:

 

♥Ten

H

small ♣

 

West discards his small ♣ on your final trump. He was not squeezed.

 

East of course remains with H and two worthless clubs. He will just toss a worthless card. He will not be squeezed.

 

You, meanwhile, must discard one of your threat cards: either the Queen of ♣ or your long ♥.

 

(1) If you discard your long ♥ at trick 11, then you are reduced to taking the ♣ finesse at trick 12.

There is no club finesse.

 

There are only four cards left- a small club, a heart, a diamond, and a high club.

 

I know one of West's cards is a heart. Therefore, when I lead a club, if he plays a small club, I know East's cards are a diamond and the king of club, and I drop the king.

 

If West's other card is the king of clubs...well, that one should be obvious.

 

So when West has the heart guard, this works whenever West either has neither honor, both honors, or just the club honor. It fails only when he has just the diamond honor.

 

Not sure which method is better when East has the heart guard. If I play the last trump and sluff a heart, East has an easy heart sluff. If I play the last stup and sluff a club, East has an easy club sluff. So I don't see how playing the last trump helps there.

[ralph23]

No, double dummy they are equivalent. At the table I am convinced my way will make more often, and needless to say you save a lot of brain cells by finding out hearts are 3-3 sooner.

Is there a method that is better than either of the squeeze methods? And that saves brain cells, too?

 

Here's where that gross math part comes back in and rears its ugly head... :)

Is the squeeze line optimal ? (Choose your favorite squeeze...).

 

Or another way of saying that: is there another line, other than the squeeze line, and how do its chances compare to your favorite squeeze-line chances?

 

http://www.rpbridge.net/xsb2.htm

Edited August 12, 2007 by ralph23

[ralph23]

There is no club finesse.

 

There are only four cards left- a small club, a heart, a diamond, and a high club.

I'm afraid I lost you ... sorry. Try again. I don't know what the "only four cards left" is referring to..... I think it's referring to the defender's holding after trick 11 is played, but what happened in trick 11?

 

We were in a 3-card ending, as you recall. Here was the 3-card ending.

 

[hv=n=sh6dcaq&s=s2hdtc4]133|200|[/hv]

 

And the question raised (my post of Aug 11 at 11.11 AM) was (with the lead in South), "What do you lead at trick 11?"

 

And you said in reply, in the next post, something like "It depends. If West started with the four ♥, then I'll lead the last trump (at trick 11) for the obvious squeeze."

 

So you do that -- lead the last trump -- at trick 11.

 

Then West played the Jack of clubs on your trump.

 

Now it is your play from dummy at trick 11..... What do you play?

 

PS -- The EW cards combined, before you led this final trump at trick 11, were six (6) in all: the ten of ♥ (which you "know" {ex hyphothesi} that West has), the two minor Kings, and three clubs (say the 9TJ).

 

PPS - Yea, it would be cool if East threw away the King of ♦ on trick 11, but it ain't gonna happen ... he's gonna play the 9 or T of ♣. And he may not even have the King of diamonds anyhow !!

 

Sorry if this got so long, I may have just been confused and missed a step in what you were saying. Or I just missed what happened at trick 11, one or the other....or brain cells disconnected ... or whatever...

Edited August 12, 2007 by ralph23

[ralph23]

>>>Not sure which method is better when East has the heart guard. If I play the last trump and sluff a heart, East has an easy heart sluff. If I play the last stup and sluff a club, East has an easy club sluff. So I don't see how playing the last trump helps there.

 

When East started with the long ♥, the "squeeze" plan only works if he also started with both minor Kings. If that's the case, then at trick 11, he is down to ♥8, ♣K, ♦K. Your only chance is that he has already been squeezed, and to lead your club to the ♣Ace, dropping his ♣King, cash your Queen of ♣ and trump the final trick.

 

So your overall success rate is:

 

If West has 4♥: You win in any combination of minor honors EXCEPT West holding only the ♦King.

 

If East has 4♥: You only win if East holds both minor Kings.

 

True??

 

Or aren't you better off in the East-long-♥ case, just taking the ♣ finesse at trick 11?

[jtfanclub]

So your overall success rate is:

 

If West has 4♥: You win in any combination of minor honors EXCEPT West holding only the ♦King.

 

If East has 4♥: You only win if East holds both minor Kings.

 

True??

 

Or aren't you better off in the East-long-♥ case, just taking the ♣ finesse at trick 11?

OK, yes, obviously you saw the final play on West being long (you sluff a heart on trick 11).

 

That looks true to me. Obviously, if hearts are 3-3, you're cool too.

[ochinko]

This is my 4 cards ending, and we are in dummy:[hv=n=sh2d3caq&s=s2hda10c4]133|200|[/hv]

 

First case: West has longer hearts. We play a diamond to the Ace and draw the last trump.

If West has the ♣K as well, he is squeezed. With two cards left he has bared his King if he didn't drop the heart.

If West doesn't have the ♣K we make if East has both Kings. East is squeezed when we draw the last trump. When neither the last heart, nor ♦K has appeared all we have to do is to cash ♣A (Two combined 50% chances give us 75% total).

 

Second case: East has longer hearts. Now if one of the defenders has both Kings he is squeezed, and when we ruff our last heart all we need to do is to cash both Aces. (50% total)

 

And, of course, 36% when hearts are 3:3.

 

All in all approximately 48% chance for making 7♠ or 92% after the spades hurdle is cleared. I play for ♠1:1 (52%).

[ralph23]

This is my 4 cards ending, and we are in dummy.....

 

All in all approximately 48% chance for making 7♠ or 92% after the spades hurdle is cleared. I play for ♠1:1 (52%).

 

I'm sorry, I think I misunderstood. (BTW congrats for being the only one so far who's ventured into trying to caculate the odds on this mother!)

 

Are you saying that, once we get to trick 3 (having won the opening ♥ lead and cashed the Ace of ♠ at trick 2, and {whew!} finding the defender's ♠ did in fact split 1-1), that we now have a 92% chance of making this?

 

Yes, assuming that we survive until trick 3, we will prevail 36% (approx) of the time that we get to trick 3 (which happens about 52% of the time, on a 1-1 trump split) on the heart-splitting theory.

 

What about the other 64% of the time, when the hearts do not split 3-3? For us to come out to 92 overall (provided we make it to trick 3), we have to prevail in (56/64 = 7/8 = 87.5%) of these non-♥-splitting situations.

 

{nb because 56+ 36 = 92)

 

Do you really think that it's as high as 87.5%, just thinking about it impressionistically and not analytically?

Edited August 13, 2007 by ralph23

[ochinko]

Hm, it seems like I got carried away.

 

(75% * 1/2 * 64%) + (50% * 1/2 * 64%) + 36% = 76%, not 92% :(

 

So the total is 76% * 0.52 = 39.5%.

 

I hope I did it right this time.

[bid_em_up]

deleted

[ralph23]

Hm, it seems like I got carried away.

 

(75% * 1/2 * 64%) + (50% * 1/2 * 64%) + 36% = 76%, not 92% :(

 

So the total is 76% * 0.52 = 39.5%.

 

I hope I did it right this time.

Well, just a little carried away :( .

 

I'm not sure I follow all the reasoning, but before I try, let me ask a question.

 

Q. We are assuming (for the sake of analysis A) that West has been dealt four ♥.

 

Thus, East was dealt two ♥.

 

With this assumption in place: Is it equally probable that West and East have the King of clubs? Or is one more likely to hold His Majesty than the other?

Edited August 13, 2007 by ralph23

[Finch]

Second case: East has longer hearts. Now if one of the defenders has both Kings he is squeezed, and when we ruff our last heart all we need to do is to cash both Aces. (50% total)

If East has 4+ hearts, then the chance of West having the CK is 57%, once trumps are 1-1.

 

So after winning the lead, drawing trumps, and finding that East has long hearts, surely it is better just to take the club finesse?

[ralph23]

Lets consider the minor suit honor possible distribution in Wests (or Easts) hand:

 

♣K 25% of the time

♦K 25% of the time

♦K♣K 25% of the time

Neither 25% of the time

 

The same goes for East's hand.

Well, that is the a priori probability, assuming you know nothing about their cards.

 

But you know each one held precisely one spade. (Or we were down right away).

 

You also know that (for purposes of the analysis anyhow) one of them holds more ♥ than the other. If each holds 3 ♥, it doesn't matter who has what in the minors....

 

Are you with me so far?

[bid_em_up]

deleted

[ralph23]

Second case: East has longer hearts. Now if one of the defenders has both Kings he is squeezed, and when we ruff our last heart all we need to do is to cash both Aces. (50% total)

 

If East has 4+ hearts, then the chance of West having the CK is 57%, once trumps are 1-1.

If East was dealt precisely 4♥, and the probability of West having the King of ♣ is X% in that case (where X > 50), then is the probability of West having the King of ♣ even higher when East was dealt precisely 5♥?

 

Same reasoning of course for a 6-0 split, except those get special treatment because West led a ♥.....

[ralph23]

You are looking at it the wrong way.

 

Are you with me so far?

 

.......

So in the end, I think it all equals out in trying to figure out what to play for, and playing for the drop of the club K rates to be the winner.

1. No, I'm not with you at all. Sorry, you will have to be more explicit. I don't see how I am "looking at it wrong" -- please let me know...

 

2. In the end, you say that it "all equals out"??? hmmm..... not sure how that works mathematically.... or really what it means....

 

But let me ask you this, if you haven't already made up your mind for sure, and closed your mind to other possibilities ... would you consider that perhaps Line A of play might be superior if the ♥ split 4-2, and Line B might be superior if the ♥ split 5-1?

 

I'm not saying that's true, or not. I'm asking whether or not you would consider that to be plausible.