[han]

---

When you cash the ace, west drops the 10. You cross to dummy and play a low one up, east plays low.

What is the best play in theory? Does this differ from your play in practice?

Beginner/intermediate please hide your answer.

[Grady]

Does the bidding tell you anything? If not, then you play the K, hoping to drop the Q; provided you have another entry to the board so that you can lead toward your holding again. If you have no other entry to the board, play the J rather than the K.

[han]

The idea of a suit combination is that you consider it in isolation, without regard to the rest of the hand. YOu have unlimited entries to both hands.

I forgot to mention, but in this particular case you have to make 5 tricks. (of course, playing to the 8 guarantees 4). I think it is a hard problem.

[Blofeld]

I'm assuming that when you said "West plays low" you meant East.

I think:

If the Q is tripleton or more offside then the contract has no play.

So playing the K now picks up QT precisely offside.

Playing the J now picks up just T9 onside.

Playing the 8 picks up T singleton offside.

Restricted choice says that we shouldn't play for T9 offside. a priori, QT should be slightly more likely than T singleton. However, with this holding I think our opponent does best to sometimes play the Q, which would tip us towards playing for the T singleton.

There's almost certainly a mistake there.

[cherdano]

It is not so clear what LHO should do from QT. If we had AKJ9x, playing the Queen would look pretty silly. (It would only be correct if we had just two cards in dummy.)
If he knew that we have AKJ8x exactly, he should occasionally play the Queen, and most of the time (more than 2/3) the T, and the same from Q9. This way, we can only pick up Q or T or 9 singleton.

However, if LHO doesn't know which of the two we have, it seems still wrong to play the queen, since it loses with certainty of the AKJ9x cases against a perfect declarer (if he drops the T, I think we always have to finesse the jack next round for restricted choice reasons), and only some of the cases (depending on our strategy) against AKJ8x. Since it is even more wrong to play the Queen if we don't have the 8 (here the problem would be a little different if dummy had 876), I think he just shouldn't play it. Which means it is right for us to play him for QT when he drops the T here, and for the singleton Q if he had dropped the Q.
We payoff when he incorrectly drops the Q from QT, but that is made up for by the cases when we have AKJ9x.

Now in practice: It is clear to go for the queen drop against beginners. However, advanced and expert players might err by dropping the Queen some of the time. Will they make this mistake 16% of the times? Possibly, then we should take the double finesse against them. And pretend we are playing against beginners when we are playing against bridge gods...

Arend

[han]

Blofeld, on Oct 26 2005, 05:41 PM, said:

I'm assuming that when you said "West plays low" you meant East.

Yes thanks, I'll correct it.

Your analysis looks good to me. Justin pointed out to me that nobody play the Q from Q10 in practice east might plays the 9 from 9xx on the second round, which also makes Q10 doubleton less likely. I hope I didn't misunderstand his comments and made him look bad now.

[han]

cherdano, on Oct 26 2005, 06:06 PM, said:

It is not so clear what LHO should do from QT. If we had AKJ9x, playing the Queen would look pretty silly. (It would only be correct if we had just two cards in dummy.)
If he knew that we have AKJ8x exactly, he should occasionally play the Queen, and most of the time (more than 2/3) the T, and the same from Q9. This way, we can only pick up Q or T or 9 singleton.

However, if LHO doesn't know which of the two we have, it seems still wrong to play the queen, since it loses with certainty of the AKJ9x cases against a perfect declarer (if he drops the T, I think we always have to finesse the jack next round for restricted choice reasons), and only some of the cases (depending on our strategy) against AKJ8x. Since it is even more wrong to play the Queen if we don't have the 8 (here the problem would be a little different if dummy had 876), I think he just shouldn't play it. Which means it is right for us to play him for QT when he drops the T here, and for the singleton Q if he had dropped the Q.
We payoff when he incorrectly drops the Q from QT, but that is made up for by the cases when we have AKJ9x.

Now in practice: It is clear to go for the queen drop against beginners. However, advanced and expert players might err by dropping the Queen some of the time. Will they make this mistake 16% of the times? Possibly, then we should take the double finesse against them. And pretend we are playing against beginners when we are playing against bridge gods...

Arend

Maybe south was dummy?

[cherdano]

Hannie, on Oct 27 2005, 01:14 AM, said:

Maybe south was dummy?

Well, your original problem implicitly said that North was dummy.

Anyway, it doesn't really change my analysis, because (assuming defender can read the distribution) we are exactly as likely to have the 9 in hand as his partner. So there is nothing for him to gain by playing the Queen.

Arend

[inquiry]

Gosh.. ok, as instructed....

Spoiler

Sadly, I lead low to the eight on the second round. This will lose to T9 doubleton or QT doubleton, but will pick up all other doubletons. And, a good player with Tx might play the ten to try to talk you out of the hook of the jack. (well, i have no idea what a good player might do... which is why i am following the instruction to hide this response... cute joke btw).

Ben

[cherdano]

Ben, West can't have Tx as RHO didn't follow with the 9.

Arend

[Blofeld]

Ben, that was my initial thought, but LHO can't have Tx, as RHO has played two x's already.

Arend, if declarer holds the 9 then he won't be applying restricted choice, so I'm not sure that it's so suicidal to play the Q from QT. "Not sure", mind - I could still be convinced either way on this. Need to think about it a little more

[cherdano]

Blofeld, on Oct 27 2005, 01:33 AM, said:

Ben, that was my initial thought, but LHO can't have Tx, as RHO has played two x's already.

Arend, if declarer holds the 9 then he won't be applying restricted choice, so I'm not sure that it's so suicidal to play the Q from QT. "Not sure", mind - I could still be convinced either way on this. Need to think about it a little more

When declarer has AKJ9x and the queen drops, he can just safely cash the king and win against both Q singleton (LHO shows out, so lead low from dummy and finesse the 9 on the 3rd round) or any 3-2 split (both follow, so just cash the J).

Arend

[Blofeld]

Oops.

I knew that I needed to think about it some more.

[Echognome]

For best play in theory, we only need to consider 4 cases.

--W----E---Ex-Ante%---Conditional %
--T--Q9xx---2.83---------21.7
-T9---Qxx---3.39---------26.1
-QT---9xx---3.39---------26.1
QT9----xx---3.39---------26.1


Although I had to look up the percentages, the idea without the exact numbers is straightforward enough. You have seen 3 cards and that only leaves the holdings above as possibilities. Finessing the 8 gains on the first layout. Finessing the J gains on the second layout. Playing the K gains on the third layout. Nothing helps you on the last layout. The question you ask next is, would West play the T from each of those holdings. With the first holding, he has no choice. From the second holding he plays the T half the time and 9 half the time. From the 3rd holding he'd play the T most of the time. From the last holding he'd probably play the T or 9 equally as likely, but it's not really relevant since 5 tricks just aren't there. So my thinking is that since playing for either case 2 or case 3 is theoretically better than case 1 AND in case 2 West will falsecard more often, then I will play for case 3 and play for the drop.

[han]

Echognome, on Oct 26 2005, 11:05 PM, said:

So my thinking is that since playing for either case 2 or case 3 is theoretically better than case 1

I don't understand the meaning of the word "theoretically" in this sentence.

[Echognome]

Main Entry: the·o·ret·i·cal·ly
Pronunciation: -ti-k(&-)lE
Function: adverb
1 : in a theoretical way
2 : according to an ideal or assumed set of facts or principles : in theory

Assumed set of facts... see above.

Seriously though, I just mean that by the odds, Q9xx is less likely than either Qxx or 9xx. So one should play accordingly.

Should I define accordingly?

[Echognome]

It's an interesting question. Suppose West play's the 10 and East plays the 9. One of them is false-carding but whom? West from 10x (ok he may think he's giving count for some reason) or East from 9xx. Then I'd like to know which hand is dummy as the 10 is a much easier falsecard seeing AKJ8x than it is seeing xxx.