[pclayton]

Dealer: ????? Vul: ???? Scoring: Unknown

♠ Ax ♥ Kx ♦ AQT9876 ♣ Ax ♠ QTxxx ♥ Jxxx ♦ J2 ♣ xx

AT MP's, the opponents reach 6N by South. In a very illuminating strong club auction you learn that South has exactly 4 controls and specifically xxx of diamonds.

Say you lead a small spade.

Assume that your RHO thinks that you are at the expert / world class level. Is there an optimum % of time that you should play the ♦J? How about if your RHO thinks you are merely 'advanced'?

Thanks for your comments and reasoning.

[flytoox]

I would simply play 2. Playing DJ is tricky if RHO is a good player, coz he know u may play DJ from j2. On the otherhand, if u have k2, then u r forced to play 2.

bad false card is worse than no false card. Just my two cents.


Hongjun

[paulhar]

I play 2 50% of the time, and J 50% of the time. Declarer will presumably play restricted choice and finesse in either event. (Not to mention that either of these could be from KJ2, so your play shouldn't matter.)

[pclayton]

Yes, I'm thinking about the same lines as Paul.

In ascending order:

1. An INT or below player will not consider the play of the J♦ from J2. Accordingly, hook against this player when he plays the Jack, because he will 'never' play the J from J2.

2. An ADV / EXP - will have recently figured this out, and will play the Jack always (or at least, more than he should). When the Jack pops up, flip a coin, as restricted choice doesn't apply, since the J and 2 aren't really random cards.

3. EXP + and higher - assumably this player takes both the J-2 and shuffles them (well, maybe not literally ) and plays one. Randomness has been reintroduced and restricted choice comes back into play.

I'm still thinking about the 2nd level of this reasoning what declarer thinks of your ability. But a stab:

I think if Declarer thinks you are a hack, you can get away with the Jack more than you should.

I still have to think it about if Declarer thinks you are adv / exp / better

[paulhar]

I think declarer should always finesse regardless of how you play. Let's say you always play the 2 from J2. If you play the J, clearly the drop can't work. If you play the 2, you could have held J2, KJ2, or K2 (or just 2, where it doesn't matter.) The finesse picks up K2 and saves a trick against KJ2.

[hrothgar]

pclayton, on Aug 5 2004, 11:18 PM, said:

Dealer: ????? Vul: ???? Scoring: Unknown

♠ Ax ♥ Kx ♦ AQT9876 ♣ Ax ♠ QTxxx ♥ Jxxx ♦ J2 ♣ xx

AT MP's, the opponents reach 6N by South. In a very illuminating strong club auction you learn that South has exactly 4 controls and specifically xxx of diamonds.

Say you lead a small spade.

Assume that your RHO thinks that you are at the expert / world class level. Is there an optimum % of time that you should play the ♦J? How about if your RHO thinks you are merely 'advanced'?

Thanks for your comments and reasoning.

I'm confused by the example

If North holds AQT9876 AND
South holds xxx AND
I hold Jx

Then partner holds the stiff King of Diamonds.

When South leads towards the 7 card Diamond suit, partner is forced to insert the King...

The oppos have 13 tricks off the top. My card on the first round of Diamonds seems immaterial...

[TimG]

hrothgar, on Aug 7 2004, 10:49 AM, said:

pclayton, on Aug 5 2004, 11:18 PM, said:

Dealer: ????? Vul: ???? Scoring: Unknown

♠ Ax ♥ Kx ♦ AQT9876 ♣ Ax ♠ QTxxx ♥ Jxxx ♦ J2 ♣ xx

AT MP's, the opponents reach 6N by South. In a very illuminating strong club auction you learn that South has exactly 4 controls and specifically xxx of diamonds.

Say you lead a small spade.

Assume that your RHO thinks that you are at the expert / world class level. Is there an optimum % of time that you should play the ♦J? How about if your RHO thinks you are merely 'advanced'?

Thanks for your comments and reasoning.

I'm confused by the example

If North holds AQT9876 AND
South holds xxx AND
I hold Jx

Then partner holds the stiff King of Diamonds.

When South leads towards the 7 card Diamond suit, partner is forced to insert the King...

Yeah, I found the diagram a bit confusing, too, though it is perfectly obvious once you figure it out.

The hand with ♦AQTxxxx is the dummy (north). You are west and hold the ♦Jx. You know your partner holds the stiff king, the object is to play the ♦J or ♦2, whichever will convince declarer to take the finesse.

[hrothgar]

Sorry in advance about the formatting. I think that this analysis is correct, but I didn't get nearly enough sleep last night.

A priori, their are 8 distributions that we need to consider

KJ2 - Void = 11%
KJ - 2 = 13%
K2 - J = 13%
J2 - K = 13%
K - J2 = 13%
J - K2 = 13%
2 - KJ = 13%
Void - KJ2 = 11%

Two of those distributions are intrinsically uninteresting.
If a player holds either a Void or a Stiff King under the 7 card suit, things are pretty dull.

Excluding those two cases leaves

KJ2 - Void = 14.47%
KJ - 2 = 17.11%
K2 - J = 17.11%
J2 - K = 17.11%
2 - KJ = 17.11%
J - K2 = 17.11%

Lets start by considering the following "pure" strategy.
The Defender will always play his lowest card.

In this case, Declarer will always

1. Cover the King with the Ace
2. Cover the Jack with the Queen
3. Cover the 2 with the Queen

If you compare the Strategies "Cover the 2 with the 10" and "Cover the 2 with the Queen", Cover the 2 with the 10 "wins" against the KJ2 distribution, but loses against K2 - J. Since KJ -2 is more common than KJ2, "Cover the 2 with the Queen" is superior.

Returning the the original question:

Regardless of whether the Declarer sees the 2 or the Jack, he should still insert the Queen. Accordingly, the Defender can't gain by randomizing his play from J2. Then again, the Defender also can't lose.

[TimG]

hrothgar, on Aug 7 2004, 12:22 PM, said:

Sorry in advance about the formatting. I think that this analysis is correct, but I didn't get nearly enough sleep last night.

A priori, their are 8 distributions that we need to consider

KJ2 - Void = 11%
KJ - 2 = 13%
K2 - J = 13%
J2 - K = 13%
K - J2 = 13%
J - K2 = 13%
2 - KJ = 13%
Void - KJ2 = 11%

Two of those distributions are intrinsically uninteresting.
If a player holds either a Void or a Stiff King under the 7 card suit, things are pretty dull.

Excluding those two cases leaves

KJ2 - Void = 14.47%
KJ - 2 = 17.11%
K2 - J = 17.11%
J2 - K = 17.11%
2 - KJ = 17.11%

Eight cases minus two cases is six cases. Though I imagine you just forgot to include teh 6th in the post since the five percentages shown add up to ~17.11% short of 100%.

I also think your conclusion is right, though how you got there isn't quite explained.

[1eyedjack]

hrothgar, on Aug 7 2004, 12:22 PM, said:

Returning the the original question:

Regardless of whether the Declarer sees the 2 or the Jack, he should still insert the Queen. Accordingly, the Defender can't gain by randomizing his play from J2. Then again, the Defender also can't lose.

OK, if we assume that declarer plays perfectly, neither side gains regardless of what card the defender plays.

That being the case, declarer's optimal play must be on the assumption that declarer plays imperfectly.

The most obvious imperfect play that declarer might make, as you have pointed out, is to cover the 2 with the 10 rather than with the Q.

So it must be right to play the 2. ie an automatic non-falsecard.

Open to conviction otherwise.

[hrothgar]

TimG, on Aug 7 2004, 09:06 PM, said:

hrothgar, on Aug 7 2004, 12:22 PM, said:

Sorry in advance about the formatting.  I think that this analysis is correct, but I didn't get nearly enough sleep last night.

A priori, their are 8 distributions that we need to consider

KJ2 - Void = 11%
KJ - 2 = 13%
K2 - J = 13%
J2 - K = 13%
K - J2 = 13%
J - K2 = 13%
2 - KJ = 13%
Void - KJ2 = 11%

Two of those distributions are intrinsically uninteresting.
If a player holds either a Void or a Stiff King under the 7 card suit, things are pretty dull.

Excluding those two cases leaves

KJ2 - Void = 14.47%
KJ - 2 = 17.11%
K2 - J = 17.11%
J2 - K = 17.11%
2 - KJ = 17.11%

Eight cases minus two cases is six cases. Though I imagine you just forgot to include teh 6th in the post since the five percentages shown add up to ~17.11% short of 100%.

I also think your conclusion is right, though how you got there isn't quite explained.

I corrected the original post and added the J - K2 distriubtion.

>I also think your conclusion is right, though how you got there isn't quite explained.

"The proof is left as an exercise to the reader" ???

More seriously:

The only hand that's at all interesting is the one in which defend holds J2 under AQT9876. In this case, the Defender has three viable Strategies:

The "pure" strategy of always playing the 2
The "pure" strategy of always playing the J
The mixed strategy of playing the 2 with probablity X and the J with probability (1-X)

I'm going to start by looking at the set of pure strategies.
In this case, I'm going to assume that the defender ALWAYS plays his lowest card.

Distribution: J2 - K Frequency = 17.1%
Defender's Strategy = Always play 2
Declarer's Strategy 1 = Always play Ace, Payoff = 13 tricks
Declarer's Strategy 2 = Always play Queen, Payoff = 12 tricks
Declarer's Strategy 3 = Always Play 10, Payoff = 12 tricks

Distribution: KJ2 - Void Frequency = 14.47%
Defender's Strategy = Play 2
Declarer's Strategy 1 = Always play Ace, Payoff = 12 tricks
Declarer's Strategy 2 = Always play Queen, Payoff = 12 tricks
Declarer's Strategy 3 = Always Play 10, Payoff = 13 tricks

Distribution: K2 -J Frequency = 17.1%
Defender's Strategy = Play 2
Declarer's Strategy 1 = Always play Ace, Payoff = 12 tricks
Declarer's Strategy 2 = Always play Queen, Payoff = 13 tricks
Declarer's Strategy 3 = Always Play 10, Payoff = 12 tricks

Distribution: 2 - KJ Frequency = 17.1%
Defender's Strategy = Play 2
Declarer's Strategy 1 = Always play Ace, Payoff = 12 tricks
Declarer's Strategy 2 = Always play Queen, Payoff = 12 tricks
Declarer's Strategy 3 = Always Play 10, Payoff = 12 tricks

Distribution: J - K2 Frequency = 17.1%
Defender's Strategy = Play J
Declarer's Strategy 1 = Always play Ace, Payoff = 12 tricks
Declarer's Strategy 2 = Always play Queen, Payoff = 12 tricks
Declarer's Strategy 3 = Always Play 10, Payoff = 12 tricks

Distribution: KJ -2 Frequency = 17.1%
Defender's Strategy = Play J
Declarer's Strategy 1 = Always play Ace, Payoff = 12 tricks
Declarer's Strategy 2 = Always play Queen, Payoff = 13 tricks
Declarer's Strategy 3 = Always Play 10, Payoff = 12 tricks

Now lets consider Declarer's optimal response to this strategy:

If the Defender plays the Jack, then Declarer should insert the Queen.
This strategy breaks even if Defender played Jack from KJ and breaks even if the Defender played from the stiff Jack.

If the Defender plays the 2, then Declarer has three reasonable options:

Declarer can always play the Ace:
Declarer can always play the Queen:
Declarer randomly play either the Ace or the Queen.

Declarer's expected payoff against Defender's pure strategy is indentical with any of these choices. The easiest way to progress to an equilibirum is to note that if Declarer choses to ALWAYS insert the Queen, regardless of what card the Defender plays he won't be any worse off and can't be "fooled" by a false card.

[Trpltrbl]

Not sure what the problem is, 12 tricks are there.

Mike

[luke warm]

i'm with mike, i don't see the problem.. am i right that i have the long diamonds and my rho leads one? if so, just play the A, regardless of the card played... either lho shows out or not.. either way, the slam is home

maybe i missed something...

[1eyedjack]

I think it is just the overtrick up for grabs. Pershaps it's MP

[EricK]

It doesn't matter which card you play as long as you play it quickly (OK, I mean "in tempo").

This is the only holding in which you may have a genuine reason to hesitate, so if you do hesitate, declarer may draw the right conclusion and make the overtrick. And if you hesitate without this holding and declarer guesses wrong, you may find the TD adjusting the score.

Eric

[inquiry]

I would have tended to play the jack witout thuoght because you will have figured this out as soon as the dummy hit. But after reading Richards post, I think it really doesn't matter whch you play. I think he got it right.

Ben

[luke warm]

1eyedjack, on Aug 8 2004, 09:02 AM, said:

I think it is just the overtrick up for grabs. Pershaps it's MP

ok, this is the only reason to get stressed over this... i think, even at mp, i'm playing the ace... i figure rho isn't leading from K,x so i'm losing a trick anyway unless K is stiff on my left... if i'm wrong, it won't be the last time

[pclayton]

Did I format this hand incorrectly?

You lead a spade (opening lead), and you see dummy on your left.

OK?

I get the impression that some of the posters thought I am holding 3rd hand and dummy is on my right.