[dburn]

Scoring: IMP

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You, South, open 1♦. You could have opened 2♦, natural and strong, but you decided against so doing. At this point I am well aware that 99.99% of the readership will not understand what I have wrtitten so far, but I cannot help that.

Your partner responds 1♠ and you bid 3NT, which in the modern style shows good diamonds and outside guards (but denies the ability to open a strong 2♦).

Your partner bids 4♣ (do you agree? would Ken Rexford agree?), you bid 4♦, partner bids 4♠. You can pass this, but you think that maybe that ace of hearts is worth a show with ♠Jx, so you bid 5♥ and pass partner's 6♦. Who knows how well you have bid this? But at least when the dummy goes down, it seems that partner has done well to remove 3NT.

The opening lead is the queen of hearts. You win the ace, and cash ♦AK on which LHO follows with the three and ten, RHO with the eight and jack. How do you continue?

[655321]

Ace of clubs, club finesse is near enough to 50%, and that is the line I would take.

Ruffing out the spades needs spades 3-2, and either (A) RHO having the doubleton (34%), or, (B) if LHO has the doubleton, you need the last diamond to be with RHO.

Restricted choice alone says that LHO is more likely to have the ♦Q. But, in addition, you could argue that RHO, holding QJx and seeing his partner play the ten, ought to play the Queen most (all?) of the time, so that declarer will be unsure who has the Jack. If we think that RHO would usually play the Queen from QJ8 for this reason, the odds of case (B) are much less than 50% of 34% - so our total odds for ruffing out the spades are 34% + not much = well under 50%.

Maybe a cunning East would play the Jack from QJ8 whenever they have the ♣Q, and play the Queen from QJ8 when they don't, but that is too deep for me, and I would pay off.

[bb79]

655321, on Sep 21 2008, 07:51 PM, said:

Restricted choice alone says that LHO is more likely to have the ♦Q. 

Can you elaborate this? I can't see how RC applies when QJT is missing and each opp had at least one of them. Thanks.

[han]

From Q10x most opponents would always play the 10, from QJx many could play either.

[pclayton]

bb79, on Sep 21 2008, 05:13 PM, said:

655321, on Sep 21 2008, 07:51 PM, said:

Restricted choice alone says that LHO is more likely to have the ♦Q. 

Can you elaborate this? I can't see how RC applies when QJT is missing and each opp had at least one of them. Thanks.

(edited)

For the spade to work, I need the suit 3-2. If RHO has the 3rd trump, I always make. If LHO has the 3rd trump, he needs to hold the 3rd spade.

The club hook isn't a 50-50 prop. 7-0 or 6-1 clubs kills it.

I'm playing spades.

Post-edit: Spades looks even better since LHO is odds on to hold the 3rd trump.

[SlickRicky]

Hi Phil,

That is true, but on this hand RHO played the jack, and that was after LHO had played the ten. So if LHO had QTx they did not have a "free" falsecard.

Ricky

[655321]

pclayton, on Sep 21 2008, 08:53 PM, said:

bb79, on Sep 21 2008, 05:13 PM, said:

655321, on Sep 21 2008, 07:51 PM, said:

Restricted choice alone says that LHO is more likely to have the ♦Q. 

Can you elaborate this? I can't see how RC applies when QJT is missing and each opp had at least one of them. Thanks.

It doesn't. Once RHO sees the J from pard, the Q is a free play.

No, RHO played the 8 then the J. LHO played the 3 then the 10.

Defending a slam as West, personally I would never play the trump Q from QTx when declarer, on my right, cashes the AK.

[pclayton]

SlickRicky, on Sep 21 2008, 05:55 PM, said:

Hi Phil,

That is true, but on this hand RHO played the jack, and that was after LHO had played the ten. So if LHO had QTx they did not have a "free" falsecard.

Ricky

Yes, sorry. I'll re-look at this.

[y66]

I think RHO is more likely to have the DQ for the reason given by 65'.

I'll play for spades to split 3-2 or 2-3.

[655321]

y66, on Sep 21 2008, 09:03 PM, said:

I think RHO is more likely to have the DQ for the reason given by 65'.

I'll play for spades to split 3-2 or 2-3.

Mm, yes, but I am claiming that LHO (not RHO) is much more likely to have the queen.

[awm]

Playing the spades has a couple ways to win. Either:

(1) Spades are 3-2 with RHO having the doubleton.
(2) Spades are 3-2 with LHO having the doubleton but only two trumps.
(3) Spades are 4-1 or worse, but the person with short spades has only two trumps, and the club hook is on.

However, because of restricted choice RHO is only about 1/3 to hold the ♦Q (if he had QJ8 he might have played queen on the second round, but LHO would never play queen from QTx on the second round).

Estimating probabilities at 2/3 for spades 3-2, we get:

(1) 1/3
(2) 1/3 * 1/3 = 1/9
(3) 1/3 * (1/2)(2/6 + 1/6) = 1/12

Total 19/36

The club finesse is slightly less than half because there might be a 6-1 break.

So I'd play on the spades. Obviously this is not some super-accurate probability calculation (I've assumed that holding length in one suit and shortage in another is independent, and have rounded off the chances of a 3-2 break). But they're not really that close together.

[655321]

On further reflection, my idea that East has an automatic play of the Queen from QJ8 seems wrong. Playing the Jack makes declarer think West probably has the Queen (i.e. declarer is likely to misguess), but playing the Queen means declarer has no indication.

On that assumption, awm's line does look correct (I make it 51.7%). So, whichever trump honor East plays, ruffing out spades is best.

But is there anything in the idea that East, holding QJ8, will play a different honor according to his holdings in the black suits? For example, holding a singleton spade East might try to tempt declarer into ruffing out the spades by playing the ♦Q (now West is only 50% to hold the last trump). Whereas, holding a doubleton spade and the club queen, East could play the ♦J, making it more likely that West has the last trump (although, as awm mentioned, ruffing out the spades is still percentage). The maths here is too tough for me, but it does seem possible that it could affect the odds.

[gnasher]

If you play on spades, what will you do if the queen appears on the first round?

[pclayton]

gnasher, on Sep 21 2008, 11:31 PM, said:

If you play on spades, what will you do if the queen appears on the first round?

By whom?

[y66]

Quote

Mm, yes, but I am claiming that LHO (not RHO) is much more likely to have the queen.

Whoops. Right. Thanks. Still think it's right to play spades. A lot closer though.

If SQ shows up on first spade, I'll stubbornly continue spades. Would rather go down there on a bad break than be swindled into taking a losing club finesse.

[dburn]

In simple terms, it seemed to me that East would hold two spades a little over 34% of the time (the a priori chance is a little less than 34%, but this increases slightly once diamonds are known not to be 5-0 or 4-1). East would by the same token hold three spades a little over 34% of the time, in which case I would need her to hold ♦Q. Given the diamonds played by the defenders, she would hold this card one third of the time. East would hold four spades and three diamonds around 3.5% of the time (a priori the chances of this holding are around 11%, but this must be adjusted because of the restricted choice implications in diamonds) and West would hold four spades and three diamonds around 7.5% of the time; in either of the last two cases I would need the club finesse.

The total chance of success by playing on spades thus seemed to be 34% (East has two spades) + 11.3% (East has three spades and three diamonds) + 5.5% (spades 4-1 but the second high spade is not ruffed and the club finesse works).

Having performed these cerebrations, I played on spades. Both defenders followed to two rounds, but when East produced the 13th spade I feared the worst. When West did not produce ♦Q, however, I could claim my contract. Of course, West had ♣Qxx, so absolutely anything I did within reason would have worked.

Like other contributors, though, I had wondered whether the defenders could meaningfully affect the issue on a different layout by selecting their plays in diamonds. Certainly, if East had played the queen on the second diamond I would have had nothing to guide me as to the position of the jack, and playing on spades would have been clearly the better chance. Perhaps, then, West with ♦J10x, a doubleton spade and ♣Q should always play the ten, not the jack, under the king - a case where one ought not to select randomly from equals as a defender.