[gordontd]

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This hand came up against Frances at the weekend, and her partner tells me I took an anti-percentatage line. The hands are rotated and it's done from memory so the spot cards may differ.

The lead was the ♥J which I won in hand, cashed the ♣A, and crossed to the ♦Q, West playing the 10. When I played the ♣K East showed out. How do you play the diamonds?

[Mbodell]

I hook the 9. Good mandatory false card from JTx.

E has 5+ hearts, 1 club. W has 5 clubs and at most 3 hearts.

[Yu18772]

Based on lead I am thinking E is 6 hearts and we saw 1 club. Looking at ♦ in isolate - if west is a good player T means probably 1 of 3 distributions:

• JT8 vs 62
• JT vs 862
• T vs J862

(Tx vs Jxx doesn't count, because it doesn't matter what you do, you will be right). From 1 and 2 W could false card the J as well as the 10 (restricted choice), so combined odds for 1 and 2 are about the same as for 3.
Looking at likely E pattern - 6421 is a bit more likely than 6331, but the 4 can be ♠ as well as ♦.
Overall, I think its close to even, unless you can say that west would false card J always or T always.
So I think I play the K♦ or 9 depending on my feeling, and what would be easier to discuss with partner.
If W is not a good player I would finesse the 9 automatically.

[gnasher]

I think you should have ducked at trick one, because that would have given you a better idea of how the hearts broke.

If hearts are 3=5, the vacant places are 5:7, giving the probabilities:
  H-Hxxx : 2 * 4.42
  HH-xxx: 1 * 4.42
  HHx-xx: 0, because that would make East 5=5=2=1

If hearts are 2=6, the vacant places are 6:6, giving the probabilities:
  H-Hxxx : 2 * 2.27
  HH-xxx: 1 * 3.79
  HHx-xx: 3 * 3.79

The chances of the heart breaks are:
  LHO has J10x: 5 * 0.42 = 2.1
  LHO has Jx or J10: 6 * 0.31 = 1.86

Hence:
  Finesse gains: 2 * 4.42% * 2.1% + 2 * 2.27% * 1.86% = 0.27%
  Finesse loses: 1 * 4.42% * 2.1% + 4 * 3.79% * 1.86% = 0.37%

So against perfect defenders you should play diamonds from the top, unless their carding has told you that hearts are 3=5.

Figures courtesy of Richard Pavlicek

Edit: corrected an arithmetic error, but see my later post with corrected calculation.

This post has been edited by gnasher: 2011-November-28, 07:47

[gnasher]

Of course, even Surrey's finest may forget to make a mandatory falsecard. Perhaps you should have countered by explaining that there's more to bridge than probabilities, and you didn't think he'd falsecard often enough to swing the odds against the finesse.

[phil_20686]

I would say from the top. Even at my level playing the J/T from JTx in this situation is quite routine.

Just by case counting, Jx seems more likely than JTx.

Agree that you should have ducked the heart lead, rho known to have AQ AQ on the bidding.

In order for the false card to show up, rho must be 4-6-2-1 exactly I think. He would likely have found another bid if 5-6 and would definitely have opened a spade if 5-5.

Rho can have 3 or 4 diamonds 3541 4531 3631 2731. and 4-6-2-1 isnt that common to start with. Thus, even if they false card a 100% it just seems unlikely that they would be in a position to do so on this hand, so we can ignore the flase card possibility, and hook the 9.

[phil_20686]

gnasher, on 2011-November-28, 04:27, said:

So against perfect defenders you should play diamonds from the top, unless their carding has told you that hearts are 3=5.

Figures courtesy of Richard Pavlicek

I dont think that this kind of reasoning works after the ten has appeared, as lho would not play the ten from Tx or Txx, only from JTx JT T.

[gnasher]

phil_20686, on 2011-November-28, 05:11, said:

I dont think that this kind of reasoning works after the ten has appeared, as lho would not play the ten from Tx or Txx, only from JTx JT T.

Why does it matter what he'd do from 10x or 10xx? Those holdings are irrelevant, because whatever we do will work.

[gnasher]

My earlier post incorrectly ignored the fact that East is marked with ♠A. The calculations should actually be:

If hearts are 3=5, the vacant places are 5:6, giving the probabilities:
  H-Hxxx : 2 * 3.25
  HH-xxx: 1 * 4.33
  HHx-xx: 0, because that would make East 5=5=2=1

If hearts are 2=6, the vacant places are 6:5, giving the probabilities:
  H-Hxxx : 2 * 1.30
  HH-xxx: 1 * 3.25
  HHx-xx: 3 * 4.33

The chances of the heart breaks are (with vacant spaces 13:12):
  LHO has J10x: 5 * 0.37 = 1.85
  LHO has Jx or J10: 6 * 0.24 = 1.44

Hence:
  Finesse gains: 2 * 3.25% * 1.85% + 2 * 1.30% * 1.44% = 0.16%
  Finesse loses: 1 * 4.33% * 1.85% + (1 * 3.25% + 3 * 4.33%) * 1.44% = 0.31%

[gordontd]

gnasher, on 2011-November-28, 04:27, said:

I think you should have ducked at trick one, because that would have given you a better idea of how the hearts broke.

it might.

[Yu18772]

deleted

[gnasher]

Yu18772, on 2011-November-28, 11:44, said:

Why cant East be 4:6:2:1?

Because the part that you quoted was preceded by the words "If hearts are 3=5"

Later in the same post you will find the words "If hearts are 2=6", followed by a non-zero figure for the chance that diamonds are HHx-xx.

[Yu18772]

gnasher, on 2011-November-28, 12:03, said:

Because the part that you quoted was preceded by the words "If hearts are 3=5"

Later in the same post you will find the words "If hearts are 2=6", followed by a non-zero figure for the chance that diamonds are HHx-xx.

Sorry, didnt read carefully enough