[McBruce]

♠ x
♥ K J 9 x x x
♦ x
♣ x x x x x

Everything is unfavourable:

--you are vulnerable (opponents are too)
--you are the Director, filling in to complete a 5-table Howell
--this is your third time directing a real live game
--your partner is the principal club owner (your boss)
--opponents are one of the city's best married pairs
--after RHO's 1♠ opener, you have taken your life (and perhaps your job!) into your hands by bidding 3♥!

The full auction:

RHO: 1♠
McB: 3♥ (weak, brash and asking for trouble)
LHO: 3♠
Pard: 4♥ (just what I need to hear)
RHO: Pass
McB: Pass
LHO: 4♠ (of course)
Pard: 5♣!

Whatever can this be? I figured it was probably lead-directing should the opponents bid 5♠ over 5♥. So, of course...

RHO: Pass

... when RHO passed, I thought perhaps there is a chance that partner has both red suits here, and against 5♠ when I lead a club to his ace, or perhaps for him to ruff, our best bet is to go A♦, diamond ruff. So, with this possibility in mind, I decided to try...

McB: 5♦!!
LHO: Pass

The result was not quite what I expected:

Pard: 6♦!!!
RHO: Pass
McB: 6♥ (in record time)

I expected a double card from one of the opponents (who had made sure to save as many as they had in case we haggled over which suit to play interminably) but to my amazement it never came, for this was partner's hand:

Scoring: XIMP

A♠ led vs 6♥

---

I ruffed the spade continuation and led the J♥, LHO following low smoothly. I won dummy's A♥, ruffed a third spade in hand, led a club to the ace, and played a small trump from dummy. RHO played low smoothly and I had to guess what to do. I had a choice between Zia's Rule ("if they don't cover, they don't have it") and Barry Crane's Rule ("the queen lies over the jack in the majors, under the jack in the minors").

I decided to follow the Crane rule for no particular reason other than any of the sixteen other players might call the Director at any moment and this would at least get it over quickly.

LHO discarded a diamond. When I finessed the J♣ I lost to the queen...of trumps. Clubs being 4-1, I had no choice but to go down two on a hand Zia's Rule would have made.

The most surprising thing about this hand is that I still have a job!

[paulhar]

I'm going to give you another rule to confuse you even further.

Since I haven't heard or read this rule anywhere, I'm going to claim credit for it even though it's nothing but common sense. I'm ready for 40 or so BBO forum members to tell me who should really get credit for this rule.

Paul's rule (usually for playing for 4 to the queen to drop/finesse) is: Compare the opponent's bidding to the cards they hold. If it appears they have been aggressive, play for 3-1 or worse. If it appears that they have been conservative (which includes auctions where the opponents are silent), play for the drop.

Here your opponents have bid up to 4S with only queens and a jack outside their suit, and only eight spades. Would they be likely to do that when one opponent has ♥Qx and the other has a small doubleton?

I'm not sure how Zia's rule applied here: you led a small card and I think Zia's rule applies to covering honors.

[luke warm]

this brings up something that's bothered me for a long time... fred is quoted as saying he's a big believer in '9 ever', meaning play the A and K, but the odds favor a 3/1 split missing 4 cards so how is it wrong to lead to the A then, if rho follows to the 2nd suit, finessing the J? it seems to me that the very act of following shows something lol

[EricK]

luke warm, on Jul 17 2004, 04:53 PM, said:

this brings up something that's bothered me for a long time... fred is quoted as saying he's a big believer in '9 ever', meaning play the A and K, but the odds favor a 3/1 split missing 4 cards so how is it wrong to lead to the A then, if rho follows to the 2nd suit, finessing the J? it seems to me that the very act of following shows something lol

A 3-1 split is more likely than a 2-2 split but it covers 2 cases - LHO has 3 or RHO has 3.

A particular 3-1 split is less likely than a 2-2 split.

Once one player has followed twice, there are only two options - a 2-2 split, or a particular 3-1 split, so playing for the drop is correct (with the usual proviso that there are always other things to take into account eg the bidding, the known division of other suits, etc etc)

Eric

[1eyedjack]

In a vacuum, the drop is better odds
But only by a tiny margin - about 52:48.
Any factor that disturbs the a priori odds is likely to disturb it by more than this margin of error.

[luke warm]

i'm sorry eric and jack, i don't quite follow this (tho i believe it)... given no other clues, and given the 9 card trump suit shown, isn't it more likely that *someone* has 3 hearts while the other has one? how does the act of playing the ace of hearts change this original assumption? by playing for the drop aren't you doing the same thing, playing for a particular 2/2 split (the one where lho has the Q)? i believe it's usually right to play for the drop, i just don't quite understand why

it's like if you're missing 6 clubs and lead the K from KQ10x then low to the Axxx, then low back... if rho follows to this 3rd round, do you finesse the 10 or play for the jack to drop?

[mpefritz]

"i'm sorry eric and jack, i don't quite follow this (tho i believe it)... given no other clues, and given the 9 card trump suit shown, isn't it more likely that *someone* has 3 hearts while the other has one? "

Yes, but at the point of decision, it is either x-Qxx or Qx-xx. So your question and the real question are different.

"how does the act of playing the ace of hearts change this original assumption?"

Stiff Q has been eliminated AND Qxx-x has been eliminated (RHO has already followed twice). And we are down to a specific Qx-xx versus a specific x-Qxx

" by playing for the drop aren't you doing the same thing, playing for a particular 2/2 split (the one where lho has the Q)? "

Not really. xx-Qx will show itself if that is the case.

"i believe it's usually right to play for the drop, i just don't quite understand why"

The basic (and partially) incomplete solution is at the time of decision is that LHO here has one more card in his hand than RHO. Therefore, the odds are slightly in favor of LHO holding the Q.

(again, as mentioned elsewhere, this is based on the assumption that you have no other knowledge about the shape/HCP)

"it's like if you're missing 6 clubs and lead the K from KQ10x then low to the Axxx, then low back... if rho follows to this 3rd round, do you finesse the 10 or play for the jack to drop? "

You appear to be playing with more than a full deck if the J has not shown up.

fritz.

[EricK]

luke warm, on Jul 17 2004, 07:34 PM, said:

i'm sorry eric and jack, i don't quite follow this (tho i believe it)... given no other clues, and given the 9 card trump suit shown, isn't it more likely that *someone* has 3 hearts while the other has one? how does the act of playing the ace of hearts change this original assumption? by playing for the drop aren't you doing the same thing, playing for a particular 2/2 split (the one where lho has the Q)? i believe it's usually right to play for the drop, i just don't quite understand why

it's like if you're missing 6 clubs and lead the K from KQ10x then low to the Axxx,  then low back... if rho follows to this 3rd round, do you finesse the 10 or play for the jack to drop?

Given 4 cards in opponents' hands here are the ways the suit can be distributed

4-0 1 possibiity @ 4.78% = 4.78%
3-1 4 possibilities @ 6.22% =24.88%
2-2 6 possibilities @ 6.78% = 40.68%
1-3 4 possibilities @ 6.22% =24.88%
0-4 1 possibiity @ 4.78% = 4.78%

When one says that the suit is more likely to break 3-1 than 2-2 it is because 24.88 + 24.88 > 40.68.

However, the probability of a 3-1 break with LHO having 3 is only 24.88%, so a 2-2 break is more likely than a 3-1 break with LHO having 3. And this is the case you are concerned with! If RHO has 3 , then you can't catch the Q anyway.

The other case you quote is similar (but you have written Axxx instead of Axx!). A 3-3 division is less likley than a 4-2 division, but a 3-3 division is more likely than a 4-2 division with LHO having 4.

Does this help?

Eric

[Cascade]

On a macro level:

With nine cards missing the Queen.

Playing for the drop wins when:

The suit is 2-2 - 40.7%
The suit is 3-1 and the Queen is singleton 1/4 of the 3-1s - 12.4%
Half of the time when the suit is 4-0 - 4.8%

This is a total of 57.9%

On the other hand if you play one top honour and then finesse you will win:

Whenever the Queen is onside 50%
When the Queen is offside singleton - 6.2%

This is a total of 56.2%

So playing for the drop is better than playing for a finesse.

The cards do not change places after you start playing this suit so these odds remain.

The odds may change before you play this suit if you discover critical information about the hand. The way these odds change is not always intuitive.

On a micro level:

At the critical moment:

After you have played one round and both players followed and
then led to the second round and one player has followed there are only two specific distributions of interest (assuming the small cards are the 2, 3 and 4:

Q32 4

or

32 Q4

There are 4 possible 3-1 distributions each with a probability of 24.9/4 = 6.2%

There are 6 possible 2-2 distributions each with a probability of 40.7/6 = 6.8%

So it is better to play for the drop.

[luke warm]

now i know why i never really grasped it.. and yeah, i put an extra x in the Axx hand opposite kq10x..

thanks everyone

[MickyB]

I haven't seen anyone mention Empty Spaces yet, I think this is the easiest way to understand it.

Missing Q432, you play off the ace and lead towards dummy's KJ. LHO has shown up with the 2 and the 3, RHO with the 4. Having seen LHO's 3 and 2, there are 11 'empty spaces' in his hand. You have only seen one card in the suit from RHO, so he has 12 empty spaces. Thus RHO is a 12:11 favourite to have any given missing card, including the Q of this suit.

[McBruce]

But on the empty spaces front, there are other suits we know about. Spades have split 3-5, since RHO opened 1♠ and LHO has three. At decision time I have seen two hearts from RHO and one only from LHO. We've also had a club trick that both followed to, leaving RHO with five empty spaces and LHO with eight!

So Empty Spaces and Crane's rule (which is mathematically dubious but you would risk a scene if you ignored it and were wrong with Crane as partner!) both say play for the drop; Zia's Rule (which may not strictly apply here) says finesse.

An old Bridge Encyclopedia lists something called Blackwood's Theory of Distribution: Easley Blackwood's suggestion is to look at the shortest suit held by the declaring side. If declarer and dummy have fewer than four cards, or four cards divided 3-1 or 4-0, finesse; else, play for the drop. Here our shortest suit is diamonds, divided 3-1, so we finesse.

Any more suggestions?

{edit} I think I may have the opening lead wrong since it leaves me with egg on my face if West holds the A♠, leaving few opening bids possible for East without the Q♥...

[Cascade]

This is where you need to be careful.

There is a good article in "For Experts Only" edited by the Granovetters written by Phil Martin and originally published in Bridge Today 1990 entitled the Monty Hall trap and sub-titled "Information that the opponents give you is not the same as information you discover for yourself".

The conclusions from this are sometimes counter-intuitive.

[paulhar]

McBruce, on Jul 17 2004, 08:43 PM, said:

But on the empty spaces front, there are other suits we know about.  Spades have split 3-5, since RHO opened 1♠ and LHO has three.  At decision time I have seen two hearts from RHO and one only from LHO.  We've also had a club trick that both followed to, leaving RHO with five empty spaces and LHO with eight!

You are absolutely right in counting the spades in the empty spaces. I don't think you can count the clubs since all that did was remove the remote possibility of a 5-0 split.

To quote an example, let's say LHO opens 3S, pard doubles, and you bid 4H. You need to find the heart layout. LHO leads out the top three spades while you and partner follow three times (some takeout double, pard!) and RHO discards two diamonds and a club. You can remove LHO's seven spades from the empty spaces but I don't think you can remove those diamonds or that club from RHO's. RHO had to play something. He was dealt 13 non-spade cards, and of course, he's not going to play a heart. So, whatever he plays, it doesn't give you any more information than you already had - he was dealt 13 non-spades. So, I think he still has 13 empty spaces until you find out the distribution of one of the minors for sure.

Any other suggestions? I had one Keep track of your 9 card fits missing queens. I'm challenging some pretty tough company here - Zia, Barry Crane, and Easley Blackwood. I'm up to the challenge - I think the rule I proposed is the only one of the four based on common sense against a good pair. (Against a bad pair, Zia's rule makes sense too. But this stuff about queens lying over jacks )

[paulhar]

Acutally, I wouldn't be using ANY rules on this hand. A hand of bridge has two parts. A great surprise to most of our students, these two parts are interrelated. You're allowed to use information from the bidding in the play! I'm not being facetious here, but this seems to be a point that's been missed during this whole thread. LHO, a player on one of the best pairs in the city, has bid 3S, and then 4S vulnerable with only three trump. Do you think they took a sudden liking to you? There must be some other reason. 4S is a travesty of the Law of Total Tricks, that is, unless LHO thinks your side has about sixteen hearts. Frankly, I'm surprised that LHO had even one heart. RHO made one peep, and then stayed silent. (S)He was happy defending hearts. LHO is doing something rediculous if (s)he has two hearts, and just begging to be doubled for a number.

However, good players know (but aren't telling!) that the Law of Total Tricks understates the total tricks when the shorter trump hand is also the one who is short in the opponents' suit. Indeed, LHO had one heart and only three spades so there are extra tricks avaliable by trumping hearts in his hand. If you lead trump, you give them time to set up diamonds. With only 17 total trump (9 for you, 8 for them), you would expect 17 total tricks, and yet you can make 5♥ while they can make 8 tricks in ♠, a whopping 19 total tricks! LHO knows this because he has the singleton heart. If you creep into his mind and figure out how he could possibly bid 4S, it would be almost impossible to get it wrong.

P.S. You're doing my many potential partners a favor by keeping me busy replying to your posts, thus keeping me off BBO
P.P.S. I like your 3H bid
P.P.P.S how can you make 6H? Don't you have to lose a spade and either a club or a club ruff?

[MickyB]

The queen lying over the jack actually makes a lot of sense, assuming the cards haven't been shuffled too well. Not sure that it is too useful on BBO.

As Cascade mentioned, there is a difference between info you have discovered yourself and info the opps give you. Say you have 9♣, 7♦, 5♥ and 5♠ between your two hands, and bid 1NT-P-3NT-P. The lead is the 2♦, 4th highest. Some would now say 'LHO has 9 empty spaces, RHO has 10, so I should play for the Q♣ to be with RHO'. However, RHO didn't get a chance to lead. The implication of the opening lead is that LHO does not have a 5 card major, and is unlikely to hold 4 card majors, else he would have led from a major suit instead. Therefore it is clear to play LHO for the Q♣.

[Free]

In such situations, I have 2 rules which help me out, and most of they time it works!

1) If I or my partner have a singleton or void, don't play for the drop, cause a singleton/void never comes alone (check it out!). If we both don't have a shortness, play for the drop.

2) If you have to finesse, put the Q behind the K, unless the odds are totally against it.

You can change rule 2 in whatever you want (Q behind J, Q behind A,...) but the principle is that you always play the same way, and you won't lose or win from such situations anymore. In general, with computer-dealt hands, I've noticed the Q is more behind the K than before it, so that's why I play it this way

This helps me in a lot of situations. Here, since I have a stiff, I'll finesse. However, I'll put the Q in my RHO's hand, because our LHO can only have about 2 HCP left (♠A lead, 13HCP divided between the opps, and RHO opened). Finesse in ♥ will be right, BUT, the play in ♣ is another story

[Fluffy]

Wayne already showed the theory of why the drop is better, but notice there is a small edge between them, these means that you may switch your intentions for good reason, common good reasons are preemtives and 2 suiters in certain opponents.

But out of theory here is why every teacher is gonna teach you to play for the drop: because if you fail you retain the control of the deal, and that often means you can still discard those loosers on dummy´s suit, or even crossruff (crossruff also works if you finese and fail).

And the other main reason why teachers teach that way is becasue good players hate matchpoint deals where you have a 50% guess, you could score a top or a bottom but it has nothing to do with your skills, so good players want the crowd to play in a certain way

[1eyedjack]

A few points. Some repetition, sorry.

"Queen over the Jack" rule has some (slight) theoritical basis, but I think only in a "rubber" contract bridge club where the tricks are collated together. In a duplicate environment where hands are kept separate, then even where the cards are inadequately shuffled it will not help, since even if the Queen beat the Jack on the previous deal of the same cards, they were never adjacent in the pack.

McBruce has a valid point re. including the Spades in the vacant spaces. The minor suits should be excluded altogether, even if some minor cards have been played, unless and until a complete count of a minor suit has been elicited from the opponents (and that not voluntarily).

However, if you believe the effect that the Spade length has on the vacant spaces as being the sole deciding factor, you should start with the King from hand and then run the Jack.

But that is not the only deciding factor. The 1S opener not only shows the Spade length, but also makes some disclosure as to total values. Given the general paucity of the opponents' total values, and the fact that the Spade Ace is in opener's partner's hand, there are a lot more hands that qualify as an opening bid in which opener has the Heart Queen than those in which he does not. Don't ask me to put a figure on that, but this would argue strongly in favour of finessing against opener.

[Trpltrbl]

The biggest thing on this hand is that there has been a lot of bidding from opps on 8 card suit and not much else.
Must be because of shortness somewhere.
And it becomes a hard hand to make with singleton ♥ in 1 hand a singl ♣ in other.
Therefore I think it is best to play for singleton ♣ somewhere and it has to be LHO and ♥ 2-2. And now the hand is easy.
But it did help out to know your opps and they seem to be stable well established pdship.

Mike

P.S. Rules are just guidelines. Zia doesn't always play the Ace when J doesn't get covered.