[aguahombre]

---

Contract: 7S by South
No opposing calls
Opening lead: Club J

Ace was won, then KQ of Spades. RHO Pitched Club on second Spade.
Q of Hearts, Heart to Ace, with all following and no Jack appeared.
Low heart, ruffed, with all following.
Ruffed Club to hand, drew last trump and claimed.

The question -- Was that optimum, were there more chances, or just more risk?

[kenrexford]

Looks like a simple math problem.

If hearts split worse then 4-2, you might be able to survive after pulling trumps if RHO has Jxxxx(x) and the K-Q of diamonds, which is remote but plausible. Thta has sxome quantum of porbability, whatever that is.

If hearts do split 3-3 or 4-2, the first two hearts cause no harm except losing that option, as far as a ruff, but it does force you into playing for the drop or ruffing out the heart. Neither makes any difference, as you can still ruff the heart later after playing the third top heart when it matters, as LHO will still have to follow.

So, the question seems to be whether a finesse outscores playing for the drop OR Jxxx to the left OR Jx to the right, countered by the remote squeeze possibility.

I don't know what the numbers are, but someone else could work that out. I just want to note the perhaps-non-obvious squeeze line possibility.

Actually, I suppose LHO could have ♠Jxx ♥Jxxx ♦KQ ♣KJ1098, minus one of the clubs, which creates another miniscule option if RHO played the missing high club as some sort of unwise carding mistake at trick one or plays it later. You could run down the spades, forcing LHO to save in the end position ♥Jxxx ♦KQ ♣K as his last six cards, meaning that one of these cards must be dropped, likely the diamond. Then, you cross to dummy and play whavere card is now good, squeezing LHO again. A VERY remote, mistake-dependent progressive squeeze that might nonetheless develop and that does not cost you anything except watching pips grow up.

Actually, the progressive squeeze might also develop if RHO makes a mistake of somehow saving down to just the one missing club. Suppose, for example, that RHO started with something like 9xxxx in clubs. For RHO's seven-card ending, RHO could reduce to ♥xx ♦10xxx ♣9, on the theory that a protected diamond 10 might somehow be critical (dumb, but possible). Then, a diamond to the Ace, followed by a club ruff, would establish the club. LHO would have come down in his seven-card ending to ♥Jxxx ♦KQ ♣K.

[gnasher]

I think you played the right line.

The lines I'd consider are:
(1) Draw two trumps before playing hearts
(2) Draw one trump; play hearts; if LHO follows to the third one, ruff low
(3) Draw one trump; play hearts; if LHO follows to the third one, ruff high

(1) and (3) both gain over (2) if LHO is 2-4 in the majors
(2) gains over (3) if LHO is 3-4 or 3-3 in the majors
(2) gains over (1) if LHO is 3-2 in the majors
These all assume that you'd play for the drop in hearts

(3) is obviously better than inferior to (2). (1) and (2) seem fairly close. Using Richard Pavlicek's online calculator (http://www.rpbridge.net/xds1.htm), gave me:
2-4 9.90%
3-4 4.62%
3-3 8.80%
3-2 7.52%

So (1) is better than (2).

Ken said:

So, the question seems to be whether a finesse outscores playing for the drop OR Jxxx to the left OR Jx to the right, countered by the remote squeeze possibility.
I don't know what the numbers are, but someone else could work that out

I'm tempted to tell you to do your own arithmetic, but since Pavlicek has already done the job for me, here they are: the chance of LHO's being 3-1 in the majors is 2.64%; the chance of him being 3-anything in the majors is 24.87%.

Having drawn two trumps, you should definitely play hearts from the top. We could probably have worked that out without any numbers.

[dburn]

The line followed at the table seems reasonable enough, except for ruffing a heart without cashing the king first. That would have cost the contract had West begun with 3=3=6=1 distribution (assuming that, as you should, you attempt to re-enter hand by ruffing a club rather than a diamond).

Admittedly, 8-1 clubs is not very likely, but it is better than a 0% chance, and not cashing ♥K before taking the ruff gains exactly 0% of the time as far as I can see.

[kenrexford]

I think I must be missing something, or others are.

I thought that thequestion concerned what to do about hearts after playing two spades and finding out that spades were 3-1. I'm not sure why I made that assumption, but somehow I did.

But, I think there's more to the mathematics than just analyzing the likely splits for LHO. The possibility of a squeeze has to be relevant, for whatever numbers these generate. Maybe the chance of that is too small to make a difference, but it has to mean something.

If you do go back to various points earlier in the play, then I think the 9 in spades also make a difference. If, when you play the spade King, you see no honor drop (neither the Jack nor the 10), then the possible layouts for spades change. You now have an initial start of Jx-10x, J10x-x, or x-J10x. At that point, the odds change somewhat from ab initio possibilities.

If you see an honor drop, barring falsecards, the possibles change as well. More importantly, perhaps, is when LHO drops an honor. This give Declarer an additional possibility of ruffing a heart high before finessing spades. Thus, Declarer could see the Jack or Ten to his left, play heart-heart, ruff a heart high, and then hook the 9 back to hand. Sure, LHO can counter with a J or T play from J10x as a strangely interesting and sexy falsecard, which works wonders when LHO has Jxx(x) in hearts, but this possible line also needs assessed.

[aguahombre]

kenrexford, on Apr 28 2009, 01:06 PM, said:

Looks like a simple math problem. 

If hearts split worse then 4-2, you might be able to survive after pulling trumps if RHO has Jxxxx(x) and the K-Q of diamonds, which is remote but plausible.  Thta has sxome quantum of porbability, whatever that is.

If hearts do split 3-3 or 4-2, the first two hearts cause no harm except losing that option, as far as a ruff, but it does force you into playing for the drop or ruffing out the heart.  Neither makes any difference, as you can still ruff the heart later after playing the third top heart when it matters, as LHO will still have to follow.

So, the question seems to be whether a finesse outscores playing for the drop OR Jxxx to the left OR Jx to the right, countered by the remote squeeze possibility.

I don't know what the numbers are, but someone else could work that out.  I just want to note the perhaps-non-obvious squeeze line possibility.

Actually, I suppose LHO could have ♠Jxx ♥Jxxx ♦KQ ♣KJ1098, minus one of the clubs, which creates another miniscule option if RHO played the missing high club as some sort of unwise carding mistake at trick one or plays it later.  You could run down the spades, forcing LHO to save in the end position ♥Jxxx ♦KQ ♣K as his last six cards, meaning that one of these cards must be dropped, likely the diamond.  Then, you cross to dummy and play whavere card is now good, squeezing LHO again.  A VERY remote, mistake-dependent progressive squeeze that might nonetheless develop and that does not cost you anything except watching pips grow up.

Actually, the progressive squeeze might also develop if RHO makes a mistake of somehow saving down to just the one missing club.  Suppose, for example, that RHO started with something like 9xxxx in clubs.  For RHO's seven-card ending, RHO could reduce to ♥xx ♦10xxx ♣9, on the theory that a protected diamond 10 might somehow be critical (dumb, but possible).  Then, a diamond to the Ace, followed by a club ruff, would establish the club.  LHO would have come down in his seven-card ending to ♥Jxxx ♦KQ ♣K.

cute layout, but if hearts are 4 times with lho and spades three times with lho, the play at the table works too, and gets the hand over sooner.

[gnasher]

kenrexford, on Apr 29 2009, 12:52 AM, said:

But, I think there's more to the mathematics than just analyzing the likely splits for LHO.  The possibility of a squeeze has to be relevant, for whatever numbers these generate.  Maybe the chance of that is too small to make a difference, but it has to mean something.

As I understand it, you're suggesting drawing two trumps then, when LHO has three, drawing the last turmp and taking a heart finesse.

Finessing gains when LHO has ♥xx, or ♥x and the squeeze works. It loses when LHO has ♥Jx, ♥Jxx or ♥Jxxx. So:

Finesse gains: 7.52 x 2/3 + 2.64 x 5/6 x p(squeeze)
Finesse loses: 7.52 x 1/3 + 8.8 x 1/2 + 4.62 x 2/3 = 9.99

Not even as fine a technician as Ken can make p(squeeze) be greater than 1. It's probably closer than I implied before, but that gives an upper limit for the finesse line suceeding of 6.11, so it's best to play hearts from the top. The probability of a squeeze working following the finesse isn't relevant.

Quote

If you do go back to various points earlier in the play, then I think the 9 in spades also make a difference.  If, when you play the spade King, you see no honor drop (neither the Jack nor the 10), then the possible layouts for spades change.  You now have an initial start of Jx-10x, J10x-x, or x-J10x.  At that point, the odds change somewhat from ab initio possibilities.

If you see an honor drop, barring falsecards, the possibles change as well.  More importantly, perhaps, is when LHO drops an honor.  This give Declarer an additional possibility of ruffing a heart high before finessing spades.  Thus, Declarer could see the Jack or Ten to his left, play heart-heart, ruff a heart high, and then hook the 9 back to hand.  Sure, LHO can counter with a J or T play from J10x as a strangely interesting and sexy falsecard, which works wonders when LHO has Jxx(x) in hearts, but this possible line also needs assessed.

At the top of this page it says "Advanced and Expert-Class Bridge". My advanced or expert opponents are defending a grand slam, so it's reasonable to assume they're trying their hardest. Falsecarding from J10x is a well known tactic. It's likely that my LHO will know from the bidding that I have a heart suit, and will envisage the possibility that I need to ruff one in dummy. I know that most of us don't play compulsory falsecards as often as we should do, but I really don't think you should infer much from the play of the jack or ten here.