[Stephen Tu]

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IMPS. This is trumps, south declarer. Need all 5 tricks to make game. No entry restrictions. When you play the K, West drops the 9.

1. What's the right play with no extraneous info?
2. What if West opened a weak two hearts, East raised, suit is almost certainly 6-3, does the right play change?

3. Is it ever right for West to drop the Q from QT or Q9, given he doesn't know if South holds the other of T/9?

[TimG]

When I next lead the Seven and East follows low, the important holdings are:

A) 9 QT62 (2.8%)
B) T9 Q62 (3.4%)
C) Q9 T62 (3.4%)

With A you want to run the Seven; with B you want to play the Jack; with C you want to play the Ace.

With B, West will play the T on the first round some of the time, reducing the 3.4% (in theory to 1.7%).

Since C is more likely than A, the second round play from hand should be the Ace.

When the hearts are known to be 6-3, the odds change to:

A) 9 QT62 (4.8%)
B) T9 Q62 (4.1%)
C) Q9 T62 (4.1%)

So, now running the Seven is the winner.

I used Pavliceck's Suit Break Calculator, I don't know how to adjust for empty spaces like this without an aid.

Spoiler

Suitplay runs the Seven. Don't know where I went wrong.

[Phil]

Tim, playing the 9 from 9x is a pretty routine play for many.

[Stephen Tu]

Phil, on 2012-August-29, 12:41, said:

Tim, playing the 9 from 9x is a pretty routine play for many.

In this case though, the T will show up from East on the 2nd round, and it's percentage to finesse. What do you do when East plays the 6?

[TimG]

Phil, on 2012-August-29, 12:41, said:

Tim, playing the 9 from 9x is a pretty routine play for many.

But, when East plays small to the second trick, there is no more spot for West to have an original holding of 9x, the only cards outstanding are the Queen and Ten.

[lamford]

TimG, on 2012-August-29, 13:36, said:

But, when East plays small to the second trick, there is no more spot for West to have an original holding of 9x, the only cards outstanding are the Queen and Ten.

This looks like one we had last night with Ax in dummy opposite QJ8xxx. When you cash the ace, the ten or nine drops on your left, and now it is right to to finesse the 8. LHO made a TO double of the suit but it would be right anyway. I am pretty sure this one is low to the 8 on the second round. I might even have it in my database. I don't but I think it is low to the 8 on the second round. You are going to lose to Q9 or QT anyway, and stiff 9 is more likely than T9 doubleton.

[aguahombre]

TimG, on 2012-August-29, 11:53, said:

When I next lead the Seven and East follows low, the important holdings are:

A) 9 QT62 (2.8%)
B) T9 Q62 (3.4%)
C) Q9 T62 (3.4%)

Since C is more likely than A, the second round play from hand should be the Ace.

Phil, on 2012-August-29, 12:41, said:

Tim, playing the 9 from 9x is a pretty routine play for many.

Stephen Tu, on 2012-August-29, 13:02, said:

In this case though, the T will show up from East on the 2nd round, and it's percentage to finesse.

Shouldn't East pop with the ten on "C"? Maybe Suitplay considered this, got a headache, and opted for running the 7.

[Stephen Tu]

aguahombre, on 2012-August-29, 19:11, said:

Shouldn't East pop with the ten on "C"? Maybe Suitplay considered this, got a headache, and opted for running the 7.

Yes. This is the key thing I think, after reflection. East has to pop T, and West has to pop 9 from 9x often enough to make declarer give up on Q9/qt and pick up the stiff honors instead.

A neat combo. How you play vs. beginners often a lot different from how one should play vs. experts.

Be sure not to play T from Tx TOO often though, lest you run into Kaplan's "deep 9" theorem.

[awm]

Tim's analysis is right (provided RHO follows small twice before you play ace) presuming that LHO will never play Q from QT or Q9.

If he will play Q from QT/Q9 fairly often, your best line is to play for his original honor to be stiff. This picks up all three stiffs (instead of two of three doubletons).

Should a good defender play Q from QT/Q9? I'll claim that he shouldn't. Supposing I hold QT tight, if I play the queen I will lose a trick any time partner has xxx (declarer plays ace next, planning to hook the ten later if I show out). Declarer won't play for the queen to fall when I play ten on the first round, because ten from Tx is a routine play. I will also lose a trick if partner has 98x (declarer has no way to go wrong). These two holdings combined are more likely than declarer having the eight but not the nine (there are three spot cards in each of partner's hand and declarer's, so they are equally likely to have the nine). So Q from QT/Q9 loses more positions than it wins (assuming I haven't seen declarer's hand).

[semeai]

TimG, on 2012-August-29, 11:53, said:

I used Pavliceck's Suit Break Calculator, I don't know how to adjust for empty spaces like this without an aid.

It's not so bad actually. You can use the regular "empty spaces principle" to figure out the relative likelihoods of A, B, and C above (with or without the 6-3 split). Here's how:

Without the 6-3 hearts: You're comparing a specific 1-4 split to a specific 2-3 split. This is the same as comparing where to place one extra card when you have a specific 1-3 split already in place. West has 12 empty spaces and East 10, so the ratio of the probability of a specific 1-4 split (placing the "extra card" in East) to that of a specific 2-3 split (placing the "extra card" in West) is 10:12.

[This doesn't match up exactly with the percentages you quoted because they were rounded. If you go back to Pavlicek and ask for more digits, you'll see this matches.]

With the 6-3 hearts: Now when we posit the specific 1-3 split, there are 6 empty spaces in West and 7 in East. Thus the ratio of the probability of a specific 1-4 to a specific 2-3 is 7:6.