World-Class Blind Spot?!?!?

[kenrexford]

I kept seeing the same thing on Vugraph. None of the commentators seemed to notice this. Am I missing something???

 

On Board 32 of the 19th round, I saw two declarers in 3NT. Both had eight cashers and needed a ninth. The spade suit was AKQ10x, and that "x" ain't all that important for anything. However, the diamond suit, the other possible (more likely) spot for the ninth trick, was K9xx (opposite AQxx).

 

It seems fairly simple to cash the Ace-Queen of diamonds and then finesse against Hxxx if the other J/10 is stiff behind the K9xx. If you ditch a diamond, however, that play is not available.

 

Both declarers pitched the diamond as the first pitch.

 

Wow.

[fred]

[hv=n=sakq10xhxxdk9xxckx&s=sh10xxxdaqxxcaxxxx]133|200|Scoring: IMP[/hv]

 

I think you missed something.

 

At the table I was semi-watching, South played in 3NT on a low heart lead. East won the first 3 tricks with the A, Q, and J of hearts (not sure about the order, but it doesn't matter). It was clear that West still had the King of hearts left.

 

Declarer did pitch a diamond from dummy on the 3rd heart in order to hold on to the x in spades. At the very least that was a reasonable play in my view.

 

Suppose the defense switches to a club now. Declarer can win the Ace in hand and play 2 diamonds ending in the dummy. If diamonds break then there are 9 tricks. If not then you still have a chance if spades are 4-4 with East having the Jack of spades - you can play 4 rounds of spades to set up your 9th trick in that suit. The x of spades obviously is a valuable card in this scenario :)

 

The above constitutes a fairly serious oversimplification of a fairly complicated hand. There are other lines of play and other contingencies that are at least worth considering. For example you could play the 4th heart yourself to rectify the count for a possible squeeze. There are various 2-loser squeeze possibilities as well. In some cases the card you pitch from dummy matters.

 

But I don't think what you saw was a blindspot. In fact, if you leave all the squeezes out of the equation, I am guessing that the math will favor my "simple" line of play over yours (sorry I am not going to do the computation that would be necessary to verify this assertion).

 

Fred Gitelman

Bridge Base Inc.

www.bridgebase.com

[kenrexford]

When it matters, RHO holds three hearts. When saving spades matters, RHO hold Jxxx in spades. That leaves RHO with six cards in the minors.

 

If diamonds split 4-1 (when it matters), RHO either has 4342 or 4315.

 

If you win the club return and RHO held 4342, your back-up plan can be a diamond throw-in, which will be just as effective. Win the club, test the diamonds, strip the clubs, and endplay RHO (test two spades on route). Granted, that loses to dropping the Jxx of spades, specifically. So, for that layout, the question seems to be whether a Jxx in spades AND diamonds 4-1 behind is more likely that diamonds 4-1 favored but a stiff honor.

 

If RHO held the 4315 pattern, LHO holds 4441 pattern. On the second club, LHO cannot pitch a diamond. If he pitches a heart, you now can endplay him for a spade finesse that otherwise could not be taken.

 

I am curious, now more so, whether the small spade is actually important, but I believe that the spade 10, in its power as a threat card for many purposes, makes the small spade less valuable that the small diamond.

[fred]

I am curious, now more so, whether the small spade is actually important, but I believe that the spade 10, in its power as a threat card for many purposes, makes the small spade less valuable that the small diamond.

The small spade is definitely important if you want to compare your simple line to your blindspot (ie the simple line that I presented) without any consideration of squeezes or endplays.

 

If you feel inclined to make that comparison, you need to answer this question:

 

Given that LHO has 4 hearts, what is more likely:

 

1) That RHO has a singleton J or 10 of diamonds

 

2) That diamonds are 4-1 or 5-0 and RHO has Jxxx of spades

 

Unless you are good at math, have a sound understanding of dependent probabilities, and have some time to burn, I suggest you not get involved in trying to answer this question.

 

If you want to try to put all the squeezes and endplays in this equation, my only advice for you is that you should expect to remain curious :blink:

 

Fred Gitelman

Bridge Base Inc.

www.bridgebase.com

[Mbodell]

If you feel inclined to make that comparison, you need to answer this question:

 

Given that LHO has 4 hearts, what is more likely:

 

1) That RHO has a singleton J or 10 of diamonds

 

2) That diamonds are 4-1 or 5-0 and RHO has Jxxx of spades

 

Unless you are good at math, have a sound understanding of dependent probabilities, and have some time to burn, I suggest you not get involved in trying to answer this question.

 

Or can simulate the situation in question (away from the table).

 

C:\downloads\deal\deal308win\deal308>deal -i my/wcbs.txt 10000000

Out of 10000000 deals RHO has singleton J or T of diamonds 432965 times

Out of 10000000 deals RHO has Jxxx in spades and diamonds are 4-1 or 5-0 either

way 424592 times

 

So case 1 is very slightly favored over case 2 by 4.32965% versus 4.24592%.

 

I'd clearly need to know more about the squeeze lines and add them to the two cases to determine which line is better, but the two above are indeed very close.

[kenrexford]

Or can simulate the situation in question (away from the table).

 

C:\downloads\deal\deal308win\deal308>deal -i my/wcbs.txt 10000000

Out of 10000000 deals RHO has singleton J or T of diamonds 432965 times

Out of 10000000 deals RHO has Jxxx in spades and diamonds are 4-1 or 5-0 either

way 424592 times

 

So case 1 is very slightly favored over case 2 by 4.32965% versus 4.24592%.

 

I'd clearly need to know more about the squeeze lines and add them to the two cases to determine which line is better, but the two above are indeed very close.

If these numbers are accurate, then you also have to take into account a bit more. Of the hands where spades are Jxxx behind and diamonds are 4-1 in front (case two), about 40% of these are the stiff Jack or stiff 10 cases. Thus, the latter case is reduced by about 20% of the ratio of 4-1's to 5-0's.

 

But, then you have to also analyze the number of times where a stiff ten or a stiff Jack of diamonds to the right also accompanies Jxxx in spades.

[Mbodell]

Or can simulate the situation in question (away from the table).

 

C:\downloads\deal\deal308win\deal308>deal -i my/wcbs.txt 10000000

Out of 10000000 deals RHO has singleton J or T of diamonds 432965 times

Out of 10000000 deals RHO has Jxxx in spades and diamonds are 4-1 or 5-0 either

way 424592 times

 

So case 1 is very slightly favored over case 2 by 4.32965% versus 4.24592%.

 

I'd clearly need to know more about the squeeze lines and add them to the two cases to determine which line is better, but the two above are indeed very close.

If these numbers are accurate, then you also have to take into account a bit more. Of the hands where spades are Jxxx behind and diamonds are 4-1 in front (case two), about 40% of these are the stiff Jack or stiff 10 cases. Thus, the latter case is reduced by about 20% of the ratio of 4-1's to 5-0's.

 

But, then you have to also analyze the number of times where a stiff ten or a stiff Jack of diamonds to the right also accompanies Jxxx in spades.

I don't follow what you are saying, why do you care about hands where both are true versus neither true?

 

I just dealt the 10000000 and, separately on each hand, checked if condition 1 were true AND also in addition checked if condition 2 were true. Condition 1 being true didn't cause me to not count condition 2 (nor vice versa). So I don't think anything else needs to be taken into account the way you describe.

 

Other things may need to be taken into account like what are your squeeze or endplay chances that aren't included here or can you discount RHO having 5 or 4 diamonds by the fact that RHO opponent lead hearts from Kxxx and didn't touch diamonds. But the times where both 1 and 2 were true does not effect the numbers I've quoted one iota.

[1eyedjack]

Am sure that I am having a blind spot, but is there anything wrong with discarding a Club on the third Heart?

[Finch]

it stops you playing the 'simple' line.

The simple line is to play for diamonds 3-2 or spades 4-3 (or short jack) with the spade stop in the hand with only 3 hearts i.e.

 

win club return

take two top diamonds

play on spades

 

but if you discard a club on the third heart, you don't have the entries to do this anymore - you need to cash two top diamonds and still leave an entry to both hands

[fred]

Or can simulate the situation in question (away from the table).

 

C:\downloads\deal\deal308win\deal308>deal -i my/wcbs.txt 10000000

Out of 10000000 deals RHO has singleton J or T of diamonds 432965 times

Out of 10000000 deals RHO has Jxxx in spades and diamonds are 4-1 or 5-0 either

way 424592 times

 

So case 1 is very slightly favored over case 2 by 4.32965% versus 4.24592%.

 

I'd clearly need to know more about the squeeze lines and add them to the two cases to determine which line is better, but the two above are indeed very close.

If these numbers are accurate, then you also have to take into account a bit more. Of the hands where spades are Jxxx behind and diamonds are 4-1 in front (case two), about 40% of these are the stiff Jack or stiff 10 cases. Thus, the latter case is reduced by about 20% of the ratio of 4-1's to 5-0's.

 

But, then you have to also analyze the number of times where a stiff ten or a stiff Jack of diamonds to the right also accompanies Jxxx in spades.

I don't follow what you are saying, why do you care about hands where both are true versus neither true?

 

I just dealt the 10000000 and, separately on each hand, checked if condition 1 were true AND also in addition checked if condition 2 were true. Condition 1 being true didn't cause me to not count condition 2 (nor vice versa). So I don't think anything else needs to be taken into account the way you describe.

 

Other things may need to be taken into account like what are your squeeze or endplay chances that aren't included here or can you discount RHO having 5 or 4 diamonds by the fact that RHO opponent lead hearts from Kxxx and didn't touch diamonds. But the times where both 1 and 2 were true does not effect the numbers I've quoted one iota.

I am pretty sure I asked the wrong question (though I am typing this pre-morning-coffee) so maybe I am wrong now about being wrong before :rolleyes:

 

I tried to phrase the question in terms of "if diamonds are not 3-2, when will each of the lines win?". I thought that would be easier than phrasing the question in terms of "when does each of the lines gain over the other line?".

 

But I blew it. For example, both lines also work when diamonds are not 3-2 and when the Jack of spades falls under the AKQ (and I don't think these considerations simply cancel out).

 

Anyways, it is nice to know that apparently there are simulation programs out there that can answer such questions in a relatively easy way. Thanks to you and your computer for the analysis and sorry I asked you to answer the wrong thing :)

 

With or without such a program, the hard part remains asking the right question. I couldn't even get this right for a simple question. Hopefully that will at least help to illustrate the point I was trying to make earlier: that clearly specifying all reasonable lines of play including all contingencies and then accurately enumerating the cases in which each line will succeed (or fail) would be very difficult for a hand this complicated.

 

But it is nice to know that once you have gone that far, there are tools out there that can do the math part for you.

 

Fred Gitelman

Bridge Base Inc.

www.bridgebase.com