Declarer play problem

[fred]

[hv=n=saxhaxxxxxdakxckx&s=skqj10987hkxdcxxxx]133|200|[/hv]

 

You play in 6S. They lead a diamond.

 

Question 1: What do you think is the intuitively best line of play? In other words, don't think about the math and just answer the question!

 

Question 2: Do you think it is close?

 

Question 3: OK you can try the math now if you want. How do you play?

 

Fred Gitelman

Bridge Base Inc.

www.bridgebase.com

[jonottawa]

Seems like the risk of a 4-1 ♥ break is greater than the likelihood that ♥ are 3-2 AND ♠ 2-2.

 

Hope the ♣A is onside.

 

If not, we tell teammates they led a ♣.

[Fluffy]

my first reaction was to go for club finese.

 

gross math says 2/3 for hearts 3-2 and 1/2 for spades 2-2 wich makes it very close (you lose 1/3 to win 1/3).

 

But I believe that non club lead sugests ♣A is onside strongly, so I go for it without risking anything (if it was 50% it would be even, but since I rate it 60% at least, I am losing more than I am winning)

 

I don't think pure math can be applied on this kinds of hands since you cannot calculate how often will LHO lead a club from various holdings, and it plays an important role.

[Winstonm]

My instincts tell me to ruff the first diamond and lead a club at trick 2.

[shevek]

Intuition is to play hearts, because we are taught to set up suits, club up seems crude.

I'll pay out to 4-1 hearts. So ♠K, ♥K-A, ruff, ♠A.

When they are 3-1, club up.

 

Wrong time of year to analyse further.

[Phil]

I find hands like this are easier to think of when you consider what could go wrong, rather than what you need.

 

The club loses when the A is off. But of course it makes when the A is on, so thats basic.

 

Playing for hearts 3-2 goes off when hearts are 4-1 or 5-0. So we are sitting at 67% success; for now. If the hearts live, we can try two spades. If spades are 2-2, we are gin (making 7 actually). So thats 40% of the 67% or 26.8%. When spades are 3-1 (50% of the 67% or 33.5%), we are making 1/2 the time or 16.75% + 26.6 = 43.75% since we can ruff a heart and play a club up.

 

However, we can do even better by trying a high trump first. If spades are 4-0, working on hearts is hopeless and we can abandon that plan. This gets another 5%, so the grand total for the heart play is 48.75%.

 

So the answer is, its close!

 

The club play was my gut reaction, because frankly, I had to look at the hand a minute or two before the heart play even occurred to me LOL.

 

By the way, I think the club play is also better at MPs because the chances of going down playing on hearts (33%) ir greater than what we need for the up (27%).

[rogerclee]

I don't think the 2/3 odds people are using for a 3-2 heart break are accurate, since LHO chose to make what looks like a passive lead rather than a possibly stiff heart. With the ♣A he probably wouldn't try a heart, but without it he certainly might.

 

Also I'm not sure why my opponents are so good that I would credit them to play their heart spots randomly if I play a heart to my king at trick two (though either our heart spots aren't given or we are missing precisely QJT98).

[Winstonm]

I am not a mathematician and will prove it thusly:

 

We need both a 3/2 heart break + 2/2 spades for the heart try to be right, around 40% of the 68% or about 25% I think.

 

If we try the hearts and when it was makable (club ace onside) we go down we have to find hearts 4-1 or 5-0 and the club ace onside, so around 16% I think.

 

So we go down immediately 16% of the time when we could have made by playing clubs; however, we only gain 12.5% of the time (half the 25% when the club is offside). But if we start clubs we go down immediately 50% of the time and lose the 12.5% chance of hearts coming in.

 

So if we combine the chances by starting hearts, is the combined percentage then 84% x 62.5%? Roughly 52%?

[jonottawa]

I thought this thread would get swamped so I got my answer in early.

 

To answer Fred's actual questions:

 

1. My analysis went something like: 3-2 ♥ vs finesse ... oh, entry problem, less than half of 3-2 ♥ vs 4-1♥, finesse.

 

2. I think it's close enough that I have no idea what declarer at the other table will do, so yes. Even though playing on ♥ is just as unilateral as leading ♣, it feels more like you're delaying the decision until later, which bridge players like to think they're doing.

 

3. I think the odds of a ♣ to the King losing and a trump coming back are greater than any of the other mitigating possibilities (opp with 1-1 in the majors and never bid). I also think that I want to give my teammates credit for a ♣ lead if it was beating the hand. Try to win the match on another hand.

 

Maybe if I'm playing a much stronger team or I'm down I play on ♥, but that goes without saying.

 

My math, fwiw, ignoring any and all inferences or correlations between the 2 suits or misdefense or 1-1 M:

 

Playing H wins 13.8%

Playing C wins 16.1%

Down you go regardless 36.2%

You make regardless 33.9%

 

http://spreadsheets.google.com/pub?key=tT4...F7Q&output=html

[pooltuna]

Dealer: ????? Vul: ???? Scoring: Unknown

♠ Ax ♥ Axxxxx ♦ AKx ♣ Kx ♠ KQJ10987 ♥ Kx ♦ [space] ♣ xxxx

 

You play in 6S. They lead a diamond.

 

Question 1: What do you think is the intuitively best line of play? In other words, don't think about the math and just answer the question!

 

Question 2: Do you think it is close?

 

Question 3: OK you can try the math now if you want. How do you play?

 

Fred Gitelman

Bridge Base Inc.

www.bridgebase.com

1) Well gut reaction is to try to ruff the 3rd ♥ and then draw trumps in 2 rounds with leading up to the ♣K as a back up

 

2) Feels close but I'd still try it based on gut reaction

 

3) 32% failure rate on 3-2 breaks means you need the 68% of time that it works to justify doing it. 2-2 split happens 41% and 50% for the ♣A to be onside. So 68%*(41% +59%*50%)=48% so no I just take the straight up ♣ finesse based on the numbers

[Jlall]

Q1: Cash 1 spade and set up hearts

 

Q2: Yes.

 

Q3: Interesting... I feel like if LHO had 4 hearts he would almost always lead that over a diamond, because he has a 4 card sequence (QJT9, QJT8, JT98 are all very strong leads, QT98 is the only bad one). Similarly, with a stiff heart I think he would lead it. With a heart void, RHO would lightner X. That suggests that hearts are very likely to be 3-2 (possibly with LHO having a void).

 

On the other hand, he led a diamond rather than a club, that might well suggest that he has the ace. We know for certain he doesn't have a diamond sequence (he led low), but with any club sequence missing the ace he might prefer that lead. If he has equal club and diamond holdings, he would probably prefer the shorter one. So he might only lead a D over a club when he has the DQ and the CJ or nothing in clubs when he has no CA.

 

However, bad players would often bang down the club ace if they had it, so it depends who LHO is. Also, if it is matchpoints, LHO is even more likely to bang down the CA, even if he's good, so the form of scoring probably matters.

 

Also, if LHO has the CA and a stiff heart, he should definitely not lead his stiff heart. This means that even though LHO is likely not to have a 4 card heart holding, he definitely could have a stiff.

 

However, if LHO has a stiff trump, he also might bang down the CA hoping his partner had a trump trick. This reduces the amount of times that LHO has the CA.

 

Overall, I find this to be very close.

 

If LHO is bad, I am certainly going to play for hearts to split. Bad LHOs will bang down the ace a lot, and bad LHOs are far more likely to lead from a long diamond suit rather than a shorter club suit, almost regardless of the honors (fourth from their longest and strongest). They are also more likely to lead a stiff heart.

 

If it is MP and LHO is good it is a tough decision. I know that I personally bang down my aces a lot in MP, but many good players feel like you will get a bad score if they make a slam anyways, so you should go all out to set it. I would probably play hearts, because I don't think I'm risking down 2 ever (LHO with no club ace and a stiff heart would lead the heart imo).

 

If it is imps and LHO is good, we have a dilemma. LHO is extremely likely to have the CA, but hearts are also extremely likely to be 3-2. I mean we are eliminating half of the 1-4 breaks (LHO having no CA and stiff heart leads a heart), and 3/4ths of the 4-1 breaks (LHO leads a 4 card heart suit except QT98), and we are eliminating half the 5-0 splits (RHO doubles). That is a LOT of combos. Against that, the diamond lead eliminates a lot of club combos that LHO can have, weighting him strongly for the ace.

 

Perhaps the solution against good opps is to cash 1 spade and cash the HK. If RHO drops the jack, play for the club hook. If RHO plays any card other than the jack, play for the club finesse. This is because if RHO doesn't play the jack, we eliminate QT98 of hearts on the left. I'm not really sure tbh.

 

Also, note that our line does give us added equity of someone being 1-1 in the majors, and the CA being onside. Sure it's a slim chance, but it's an added chance nonetheless.

 

Hopefully I have not overthought this one!

[Jlall]

Of course a lot of my analysis depends on the auction. If north bid hearts naturally, it is possible LHO would not lead a heart from a 4 card sequence, figuring it wouldn't be that productive. In that case I would always go for a club hook.

[inquiry]

Question 1: What do you think is the intuitively best line of play? In other words, don't think about the math and just answer the question!

 

Win 2D, throw clubs.

Cash SK

Cash HKA, ruff H

Play spade to A

If spades 2-2 claim, if not play for CK onside

 

 

Question 2: Do you think it is close?

Yes

 

Question 3: OK you can try the math now if you want. How do you play?

3-2 hearts 68%

22 Spades 40.7%

win directly when hearts are 3-2, 27.7%

when hearts 3-2, and spades not 2-2, win when CK onside another 20.1%

Bonus, when hearts are 50 or 41, hand with short heart has 0 or 1 spade (5.4% of time). Make when club Ace is onside for another 2.7%

 

27.7 + 20.1 + 2.7 = 50.5% for "inuitive" play, 50% for leading club up to king immediately.

 

Perhaps I made a mistake, I am sitting here waiting for Santa Claus... and it is late.

[nige1]

I prefer Cascade's line. At MP, it is manifestly superior, giving you the chance of beating pairs in 6N.

[fred]

One day I will figure out how to specify a "pure" declarer play problem (ie where people won't try to draw inferences from the bidding or opening lead).

 

Maybe I should have included a statement like: LHO picks up his hand and, before the bidding starts, drops a diamond face up on the table by mistake. The TD, perhaps mistakenly, says "the opponents are barred for the entire auction and if your LHO ends up on opening lead he has to lead the exposed diamond".

 

Probably some of you guessed that my instincts suggested (fairly strongly) that ruffing out the hearts before trying the club finesse was the way to go. I was therefore somewhat surprised when my attempt to do the math suggested that this is a very close call.

 

As some of you pointed out, it is not very difficult to do a rough estimate of the odds of success of both lines. However, when the numbers are almost the same and you really care which line is "better" (which as a practical matter is not exactly important), you need to be more careful. In particular:

 

1) Rounding (like using 68% for the odds of a 3-2 break or 40% for the odds of a 2-2 break) will sometimes result in you getting the wrong answer.

 

2) Not taking dependent probabilities into account will sometimes result in you getting the wrong answer. For example, ignoring point 1) above, multiplying 68% and 40% does not given you the proper odds of hearts breaking 3-2 and spades breaking 2-2. That is because the way that one suit breaks has an impact on the odds of various possible breaks in the other suit.

 

Note that points 1) and 2) imply that, unless you are Rainman, there is no way you are going to be able to confidently solve this problem in your head (at least not at the table where time constraints matter).

 

I am not confident enough in my math to present it here (at least not yet), but so far my conclusion is that drawing one round of trump and, assuming no 4-0 spade break, playing on hearts is marginally better than relying on the club finesse.

 

As a practical matter, even if at the table you somehow knew the odds of success of the two lines were very close, I would strongly suggest you ignore the math and rely on those inferences I was trying to get you not to think about in order to break the virtual tie. Consider relying on your world famous table presence as well - that rates to be worth more than the small % difference between the two lines.

 

Fred Gitelman

Bridge Base Inc.

www.bridgebsae.com

[Phil]

This is true - the 40.7 (instead of 40) and the 67.83 (instead of 67) make up enough to push this over 50. I had considered the dependent probabilities of 2-2♠ after we get 3-2♥ but didn't know how much of a factor to apply.

 

Furthermore, with 10 diamonds out, its a good bet they aren't splitting 7-3 or worse.

[fred]

This is true - the 40.7 (instead of 40) and the 67.83 (instead of 67) make up enough to push this over 50. I had considered the dependent probabilities of 2-2♠ after we get 3-2♥ but didn't know how much of a factor to apply.

There is a facility in the BBO web-client that tells me that, given 3-2 hearts, the odds of 2-2 spades goes up from 40.70% to 41.35%.

 

Also, given 2-2 spades, the odds of 3-2 hearts goes up from 67.83% to 68.92%.

 

There are two ways you can multiply these numbers out (40.70x68.92 and 41.35x67.83) to get that the odds of both 2-2 spades and 3-2 hearts as 28.05%. Note that you won't get the exactly the same answers both ways (hopefully because of rounding versus a programming or math error by me!).

 

Fred Gitelman

Bridge Base Inc.

www.bridgebase.com

[fred]

There is a facility in the BBO web-client that tells me that, given 3-2 hearts, the odds of 2-2 spades goes up from 40.70% to 41.35%.

Some people have asked me how this facility works...

 

1) Log in to the BBO web-client using the yellow "play bridge now" link on our home page (www.bridgebase.com). If you have never used the web-client before, you do not have to create a new user ID - just use the same ID and password that you normally use. Don't worry about being "forced" to use the web-client once you have tried it - you will still be able to use the traditional BBO Windows client (via your normal desktop icon) if you want.

 

2) Click the blue "My BBO" button near the top of the screen followed by "Hands and results" in the menu that appears.

 

3) A window will appear. Click the "Hand editor" button in the middle-left of this window.

 

4) Enter a suit combination you are interested in by clicking on the cards you want South to hold. Then click "North" label at the top of North's seat and enter the cards you want North to hold. You do not have to enter any cards in other suits. If you enter a wrong card at any point you can click that card again to return it to the collection of unassigned cards.

 

For example, try giving South the KQJ10987 of spades and giving North the A2 of spades.

 

5) Click the "Options" button below the hand diagram. You will see a menu. Click "Analyze suit". You will see another menu. Click "NS spades".

 

6) A window will appear that lists various ways that spades could break along with their odds. At the top of this window you can enter the number of known cards held by each opponent and see how the odds change.

 

7) If you give one opponent 3 known cards and give the other opponent 2 known cards, you can see how I got the odds I quoted of how a 3-2 heart break impacts the odds of a 2-2 spade break.

 

The "Analyze suit" facility is available in various other places for the web-client where it can be used to analyze the suits of hands that have already been played.

 

Fred Gitelman

Bridge Base Inc.

www.bridgebase.com

[eyhung]

Any way to allow keyboard input of cards using the web client? I can type in a hand much more quickly than clicking on 52 different spaces.

[fred]

Any way to allow keyboard input of cards using the web client?  I can type in a hand much more quickly than clicking on 52 different spaces.

You should be able to do it. First specify the suit by typing S, H, D, or C and then specify the cards in that suit (A, K, ..., T, ..., 4, 3, 2). I think you will still have to click to move from hand to hand. The 4th hand should fill in automatically once the other 3 hands have 13 cards.

 

In general, programming issues involving "keyboard focus" in web-applications are nightmarish. If nothing seems to happen as you start to type in cards, trying clicking on the green background of the hand diagram and then try typing again. I suspect you will be able to figure it out, but you may need to experiment a bit.

 

Fred Gtielman

Bridge Base Inc.

www.bridgebase.com

[TimG]

I found it unnatural that the cards in a suit shifted left to fill up the space left by a selected card; it seems natural to me that to enter AQ I would click the Ace and then move two spaces to the right to click the Queen. But, maybe after using it a bit this way will seem natural.

 

Nice feature to have available, I'm glad you mentioned it in this thread or I would not have know it was there.

[dellache]

As some of you pointed out, it is not very difficult to do a rough estimate of the odds of success of both lines. However, when the numbers are almost the same and you really care which line is "better" (which as a practical matter is not exactly important), you need to be more careful. In particular:

 

1) Rounding (like using 68% for the odds of a 3-2 break or 40% for the odds of a 2-2 break) will sometimes result in you getting the wrong answer.

 

2) Not taking dependent probabilities into account will sometimes result in you getting the wrong answer. For example, ignoring point 1) above, multiplying 68% and 40% does not given you the proper odds of hearts breaking 3-2 and spades breaking 2-2. That is because the way that one suit breaks has an impact on the odds of various possible breaks in the other suit.

 

Note that points 1) and 2) imply that, unless you are Rainman, there is no way you are going to be able to confidently solve this problem in your head (at least not at the table where time constraints matter).

 

I am not confident enough in my math to present it here (at least not yet), but so far my conclusion is that drawing one round of trump and, assuming no 4-0 spade break, playing on hearts is marginally better than relying on the club finesse.

 

As a practical matter, even if at the table you somehow knew the odds of success of the two lines were very close, I would strongly suggest you ignore the math and rely on those inferences I was trying to get you not to think about in order to break the virtual tie. Consider relying on your world famous table presence as well - that rates to be worth more than the small % difference between the two lines.

 

Fred Gitelman

Bridge Base Inc.

www.bridgebsae.com

Hi Fred, I definitely agree with your conclusion and I guess Jeff Rubens would too (for those who like these kind of problems, "Expert bridge simplified" is a "Must have").

 

Here's an alternative way for deciding for the best line AT THE TABLE between :

- line A : club finesse ;

- line B : establish hearts, fall back on line A if possible.

- line B': line B but cash High trump first.

 

1. This is a good case for differential computing

- Line A fails, AND line B works : CA East (50%), Sp. 2-2 (40%), He 3-2 (68%) = 13.5%

- line A works, AND line B fails : CA West (50%), HE 4-1 (28%) = 14%

 

So A > B, but by a non significant margin (so A = B practically speaking).

 

2. Computing B' Vs A :

When you cash one High Spade and spades are not 4-0, you don't need to recompute the differences : you just have to perform some kind of "first order" adjustment. When you remove the 10% cases where the Spades don't break 4-0, you just multiply by 1.1 the probability of the 2-2 distribution used in the first difference computed above.

So the 13.5% becomes 13.5 *1.1 = 15%

Now we have B' > A (your conclusion), by a non significant margin.

 

3. Nitpicking.

The dependencies that we could (and didnot) take into account when multiplying Sp2-2 * He3-2 are of *very low order* in general (less than 1% over the overall result) and are of no practical use. Also, using more than 2 significative digits for computing these simple results at the table is of no practical use.

 

4. So your conclusion remains : it's VERY easy to compute the relative merits of A and B' at the table and see that they are PRACTICALLY equal. Then all what remains is to judge the inferences to be taken from the lead (as in Justin very good post).

 

Best regards,

[eyhung]

 

1. This is a good case for differential computing

- Line A fails, AND line B works : CA East (50%), Sp. 2-2 (40%), He 3-2 (68%) = 13.5%

- line A works, AND line B fails : CA West (50%), HE 4-1 (28%) = 14%

 

So A > B, but by a non significant margin (so A = B practically speaking).

I like this method. But isn't hearts 0-5 also a failing case for line B? (We can assume hearts are unlikely to be 5-0 because of the failure to Lightner double). Even if we don't do the first order trick you talked about (eliminating 2% of hands doesn't change things much), that means the failing case for line B is

 

West CA (50%) and HE 1=4, 4=1, 0=5 (30%) = 15%. which means A ~== B'. :)

[dellache]

Yep.

[Cyberyeti]

Isn't there a much more important consideration here as the percentages are very close.

 

If the hearts don't break and a ruff is taken, you're going down.

 

If the club king loses to the ace, you're not down yet if you haven't cashed a high trump first. While I think it is in fact correct to return a club in all conceivable hands for declarer, if you think RHO might return a trump (or a heart) even a pretty small fraction of the time then the play of the club goes well ahead.

 

Stiff ace of clubs offside also allows you to try the hearts if you haven't cashed the top spade honour first.