[Hummer_]

---

In their book "Bridge Odds for Practical Players" Hugh Kelsey and Michael Glauert discuss the above hand after a 1N 3N auction and the ♦2 lead. Declarer plays low and captures east's J with the K. Their analysis follows.
"It is a fair presumption that west has led from a four-card suit, in which case he will have nine vacant places to east's twelve The odds are therefore 4 to 3 that the queen of clubs is with east, and after a club to the king you should finesse on the way back."

In the Granovetter's book "For experts Only" Phil Martin argues in the chapter "The Monty Hall Trap" that we knew all along that west had a four-card suit and that he would most likely lead it with a 1N - 3N auction. Therefore this is not new information and we should not use it. He also suggests that following restricted choice we have a hint that west probably has no other four-card suit or he might have led that. So east's hand might be 5512 or similar. Therefore we should play the ♣A and finesse west for the queen. So which way would you go?

Mike

[TimG]

Hummer_, on Aug 18 2004, 10:52 AM, said:

In the Granovetter's book "For experts Only" Phil Martin argues in the chapter "The Monty Hall Trap" that we knew all along that west had a four-card suit and that he would most likely lead it with a 1N - 3N auction. Therefore this is not new information and we should not use it.

There is new information: we know which four-card suit opening leader has and we know how many cards his partner has in the suit. Martin appears to contradict himself if your recount is accurate: he does use the new information to further construct the opponents' hands.

Tim

[Free]

I'm not an expert on percentages, but it's imo better to play to the K en finesse back. The ♠ suit is quite weak, so I don't want my RHO to play through that suit. Also, when I don't have any idea where the Q is, I always put it behind the K (here East).

[DrTodd13]

I think there is new information. West must have a 4 card suit but you don't know what it is. Once you see the lead you know. Moreover, you know that he is less likely to have clubs. However, I don't totally trust myself on these complicated probability questions so I can write a simulation of this scenario if you are interested.

Free...are you sure you're not a reincarnated Barry Crane? Maybe his rules made some sense with human shuffled cards but we need to abandon those rules for computer shuffled hands.

Todd

[Free]

DrTodd13, on Aug 18 2004, 05:45 PM, said:

Free...are you sure you're not a reincarnated Barry Crane? Maybe his rules made some sense with human shuffled cards but we need to abandon those rules for computer shuffled hands.

Todd

Nope, I'm brand new

With computer shuffled cards, the Q is a lot behind the K, with hand dealt cards, the Q is a lot behind the J Check it out!

[EricK]

I think we can make a couple of assumptions.

1) West would lead a 5 card suit before a 4 card suit
2) West would lead a major before a minor. (some players would go so far as to lead a good 3 card major before a weak 4 card minor, but I shall ignore that possibility)

Now, there are two possibilities to consider

West has exactly a 3-3-4-3 hand, or a (23)-4-4 hand.

In either case, the ♣Q is likely to be with West.

Oh dear! I appear not to have used either vacant spaces or restricted choice.

Eric

[DrTodd13]

EricK is probably right in his analysis. I did the simulation under the assumption that LHO has exactly 4 diamonds but generated the rest of his hand randomly. Under this assumption, the CQ is likely to be with east approximately 58.2569% of the time. I'll modify the simulation to deny west a 4 card major and clubs longer than diamonds and see what happens.

Todd

[DrTodd13]

Hot off the presses. If LHO is constrained to have exactly 4 diamonds but not have 4+ spades, 4+ hearts, or 5+ clubs then RHO has the CQ approximately 33.11% of the time. If LHO has the majority of the outstanding points for defense he may not choose to lead from a 4+ card major in which his holding is subject to giving a trick away if it is led. Of course, leading from Qxxx of diamonds is similarly likely to give away a trick but maybe he has something in every suit and has to underlead something. In any case, I doubt those cases where a major isn't led in favor of diamonds would account for more than 17% so the CQ is more likely to be with LHO assuming he is rational.

Todd

[TimG]

Free, on Aug 18 2004, 11:36 AM, said:

I'm not an expert

But, your BBO profile says you are an expert.

[luke warm]

he said he's not an expert on percentages... if one must be a percentage expert to be a bridge expert, i understand your point... since i'm not an expert either way, i'll leave it to others to say

[Free]

TimG, on Aug 18 2004, 11:45 PM, said:

Free, on Aug 18 2004, 11:36 AM, said:

I'm not an expert

But, your BBO profile says you are an expert.

IF you QUOTE, do it RIGHT, and not with HALF SENTENCES!!! I said "I'm not an expert on percentages", that has NOTHING to do with SKILL LEVEL!

Btw, my BBO profile says my email is "mèhèhèh@sheep.com". Do you really believe that?

[Fluffy]

God damnit!, that´s why you aren´t replying to my mails?.

Where can I send my letters of love then?

[mishovnbg]

Fluffy, on Aug 19 2004, 08:21 PM, said:

God damnit!, that´s why you aren´t replying to my mails?.

Where can I send my letters of love then?

Send it to me ♥ I will make good analysis
Q♣ -> younger player... Can try coca-cola research too to be sure. At BBO ask both about leads and marking and watch answers...
Misho

[paulhar]

ritong, on Aug 22 2004, 04:51 PM, said:

free had an intuition on an important element, imo . the lead goes to east & opps can cash 5!s trix comfortably , assuming west has HJx , resulting in two down
the lead goes to west & they cannot cash more than 3 , assuming west wud have led !s from HJxx, resulting in one down at most. my opinion is this type of element is almost as important than probabilities:)

So you finesse against East, and 67% (see Todd's analysis) of the time you lose to the queen in West who can't set you immediately, but leaves you wanting for an ninth trick so you have to play East for the jack of spades anyway! IMO, better to win the contract 67% of the time on the club finesse, and if it loses, hope to win a spade trick, expecting length in East.

[JRG]

Using "Vacant Spaces" based on the opening lead is fallacious. Perhaps the Monty Hall trap was not explained very well. In their book, "Countdown to Winning Bridge", Tim Bourke and Marc Smith blow the concept of using vacant spaces based on the opening lead out of the water.

At the risk of breaking copyright, here is how you blow it away (this is a quote from pages 75-76 -- for the description of the Monty Hall Trap and other good commentary on the hand in question, you will have to buy or borrow the book!):

Often, you cannot get a complete count of the hand, but you can gather sufficient information to make an 'educated guess' -- an informed decision that will be right most of the time. Such choices are often based on the 'Theory of Vacant Spaces.' The premise for this theory is that if West has, for example, eight unknown cards and East has only four, then West is twice as likely (8 to 4 or 2 to 1) to hold a specific missing card.

This is absolutely true. However, a little learning can be a dangerous thing. Consider the following hand from a team-of-four match:

---

The bidding goes 1♦ by North, 3NT by South and the opening lead is the ♠5

East wins the ♠Q and returns the 9. West overtakes with the ♠10 and you duck again. A third round of spades forces dummy's ace as East discards a heart. If you misguess the diamonds, your contract will fail. How do you tackle the diamonds. West has five spades to East's two, and thus East has eleven non-spades (or vacant spaces) to West's eight. It is therefore obviously the right percentage play to cash the ♦A and then finesse through East for the ♦Q on the second round... Or is it?

Before deciding, take the North seat at the second table in the same match. This time the bidding is:

(I have not repeated the hand, it is exactly as above.) 1NT by North, 3NT by South.

North-South at this table are playing a 12-14 1NT, so you become declarer from the North seat in the same 3NT contract.

East leads the ♥4 and you duck your ace until the third round, discovering in the process that West has only a doubleton heart. How do you tackle the diamonds? Since East has five hearts to West's two, West has eleven non-hearts (or vacant spaces) to East's eight. It is therefore obviously the right percentage play to cash the ♦K and then finesse through West for the ♦Q on the second round...

Ah! We seem to have been here before. One of these two declarers is destined to go down, yet both have apparently taken the correct line of play. How curious! This situation is often called the 'Monty Hall Trap' after...

(Explanation of the Monty Hall Trap omitted.)

This scenario exemplifies a classic probability trap -- treating biased information as random. In the game show context, Monty Hall showed the contents of Door Two because it contained a booby prize. The information itself had a direct bearing on whether you received it, and that must be taken into account when assessing its value. ...

Returning to the hand above, we can see that each declarer is faced with a similar problem, but that the information available apparently suggests opposite lines of play. Clearly, if both declarers base their play on 'vacant spaces theory' using only the information provided by the opening lead, one will go down. The reason for this is that the distribution of the suit that was led is biased information. It is not random at all. What has really happened? Yes, the defender on lead led his longest suit. That is a common enough occurrence, so why should you be surprised because he has more cards in that suit than his partner?

... (There is more -- buy the book, it is very well written.)

[helium]

Free, on Aug 18 2004, 07:25 PM, said:

Btw, my BBO profile says my email is "mèhèhèh@sheep.com". Do you really believe that?

Why cant ur email-adress be real? you can get the mailadress u want now thees days if u pay for it:)))

[Free]

helium, on Aug 23 2004, 09:25 AM, said:

Free, on Aug 18 2004, 07:25 PM, said:

Btw, my BBO profile says my email is "mèhèhèh@sheep.com".  Do you really believe that? 

Why cant ur email-adress be real? you can get the mailadress u want now thees days if u pay for it:)))

cause as far as I know, "è" isn't allowed in email addresses Then again, I could be wrong...

[1eyedjack]

JRG, on Aug 22 2004, 09:53 PM, said:

Using "Vacant Spaces" based on the opening lead is fallacious. Perhaps the Monty Hall trap was not explained very well. In their book, "Countdown to Winning Bridge", Tim Bourke and Marc Smith blow the concept of using vacant spaces based on the opening lead out of the water.

I have not read the book and will clearly have to rectify that, although I already have some understanding, probably only a partial understanding, of vacant spaces theory, the Monty Hall trap and on the perils of relying on volunteered (v. extracted) information. Possibly the book explains it in greater depth but my initial reaction to the example posted here is that the proof is incomplete.

The information imparted by the defence, whether you regard it as volunteered or extracted, is different information in each case cited: When West is on lead the information imparted is the count in the Spade suit. When East is on lead the information imparted is the count in the Heart suit.

If as declarer you had the luxury of the count of both suits you would play for the drop, being the line indicated by a priori odds without taking these suits into account. At the critical juncture (one defender having followed, the other yet to play) the vacant spaces would be in the ratio 6:5 (each having started with 7 major suit cards), so the odds in favour of the drop would be slightly better than the a priori 12:11 odds without accounting for the count in either major, although in both cases the optimal play is the drop.

It is by no means unusual for the odds to differ depending on which information is available to you, but in general such a discrepancy is not necessarily grounds for disregarding the limited information that happens to be available.

To illustrate my concerns about the proof as presented, consider a more extreme example, where the North South hands are unchanged, but West has a void Heart whilst East has a void Spade. West leads Spade King which is allowed to hold, East discarding a Heart (or East leads Heart King which is allowed to hold, West discarding a Spade). Defence continues with a Club at trick 2:

---

The bidding goes 1♦ by North, 3NT by South and the opening lead is the ♠K which wins, followed by Club switch.

As declarer you know that a specific major suit is breaking 7-0 (and which way). You do not know about the other major (OK you could, and perhaps should, burn your boats and cash the other major Ace on the off-chance of it identifying a void, but say you do not ... it should be possible to construct an example where you should not cash it, but I cannot be bothered to think of one). Nothing in the Bourke/Smith theory appears to restrict its application to a 5-2 split in the majors rather than 7-0, and if there is a flaw in that theory it should become more obvious by examining the more extreme example.

The point is I think that a 7-0 split in the other major is a possibility but certainly not a certainty. Indeed it is intrinsically unlikely. Perhaps a bit more likely given the 7-0 split in the exposed major but not I think dramatically more so. That is just gut feel, by the way. But to base your play on that premise would be bizarre, and that is what you are being asked to do if you decide to play for the drop.

The person on lead is likely to lead his longest and strongest suit. With an equal choice he will probably prefer a major over a minor on the auction (perhaps not if swinging from behind in a KO event) but let us keep the model simple as the added complexity is unnecessary to prove the point if it is valid, and just stick with the longest and strongest. The reason that he is choosing that suit is with a view to establishing the suit. It is NOT in order to provide declarer with a count in the suit. It may (but may not) be inevitable that he gives a count in the suit in the furtherance of his objective of establishing it. But given the choice, he would prefer to conceal the count rather than reveal it (unless he regards an accurate count to be of more value to his partner than to declarer, but in that case it is as reliable information, for the purposes of derived conclusions, as if it were extracted rather than volunteered). The player with the shortage, however much he would like to cooperate with the concealment of the count, is constrained from doing so by a forced discard.

So I remain unconvinced that this argument "blows out of the water" the application of vacant spaces in this case, although Bourke and Smith are without a doubt reputable authorities and I have not read their entire text.

[TimG]

JRG, on Aug 22 2004, 09:53 PM, said:

Ah! We seem to have been here before. One of these two declarers is destined to go down, yet both have apparently taken the correct line of play. How curious! This situation is often called the 'Monty Hall Trap' after...

I don't see why the odds can't be different for different declarers depending upon the information they have received. They are odds after all, not absolutes. There is no guarantee that the missing card is in the hand with the greater number of vacant spaces.

Let's take Bourke and Smith's example a step further. West leads a spade and it becomes known that the spades are 5-2. Suppose declarer then cashes the AK of clubs before tackling diamonds and finds that the clubs are 1-7. Can declarer make use of this information? How many significant vacant spaces (significant = those that declarer can take into account) does each defender have at this point?

Tim

[JRG]

I believe the point being made is that the opening leader has to lead something. The fact that he leads his longest suit does not really tell you much (I would agree that if he leads from a 7-card suit, it does tell you something) and that you cannot really apply "vacant spaces theory' in this case.

If, as suggested, you cash some cards in another suit and find out something else about the distribution of the opponents distribution, THEN you can apply vacant spaces.

Their example shows the fallacy of taking too much of an inference from non-random information. The lead is not random (or at least we will assume it is not random). I found their book excellent (partly because I played bridge for too many years before trying to force myself to count out hands) and I recommend it to anyone working on improving their counting.

As an aside, I found their presentation and explanation of the Monty Hall Trap excellent. For anyone who doesn't know the situation, it is:

You are a game show contestant and on stage there are three doors. Behind one is a terrific prize (say $100,000) and behind the other two there are booby prizes. You are asked to pick one of the the three doors, which you do. Monty Hall then fools around a bit, offering you some amount of money, say $20,000, in exchange for your choice. Assuming you don't take his offer (you shouldn't), he says something like, "OK, let's take a look behind door number two" (i.e. one of the two doors you didn't choose), which of course contains a booby prize (Monty Hall KNOWS which door the big prize is behind). Now he ups his offer to $40,000 for your choice.

Do you take his offer?

Suppose he gave you the chance to change your choice of doors to the remaining door, would you switch?

If you understand why you shouldn't take the initial offer of $20,000; why you should take the offer of $40,000 and why, given the chance, you should switch doors, then you will understand why you shouldn't use the Vacant Spaces Theory based on the suit of the opening lead.