[mr1303]

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You need to bring this suit in for 1 loser in no trumps. What is the correct way to play the suit against genuine experts? No outside entries.

[Apollo81]

lead the 9
duck if W plays low
cover if W plays the J
duck if W plays the K

[mr1303]

OK, you lead the 9. All follow and you're still in hand.

Next play? LHO follows with a low card on your second round

[BillHiggin]

mr1303, on Mar 17 2007, 05:32 AM, said:

OK, you lead the 9. All follow and you're still in hand.

Next play? LHO follows with a low card on your second round

You have now seen all the low cards.
You need to win the rest of the tricks in this suit (no way to get there if you lose one now)
There are two (well three) possibilities:
LHO started with Jxx and RHO smoothly held up the K from Kx. So you can rise with the ace and run the suit when he swears at you.
LHO started with KJxx and RHO played his only card in the suit under your 9. And no matter what you do, LHO will still stop the run of the suit.
Absurd possibility - LHO started with xx, and RHO has taken perverse delight in ducking with KJx - so he cost himself a trick, but you still cannot run the suit.

Absolutely clear to make the only play that can work. Play the ace!
At this point, percentages have nothing whatsoever to do with solving the problem.

[mr1303]

Could LHO not have Kxx and RHO ducked with Jx?

[Apollo81]

mr1303, on Mar 17 2007, 09:37 AM, said:

Could LHO not have Kxx and RHO ducked with Jx?

If RHO is good enough to duck with either holding, then it's a 50-50 guess. I think that Kx is a more obvious duck than Jx, so I would play the ace.

[pclayton]

Rosenberg made this play a few years ago - ducking with Jx. Personally I think its no big deal but its hard to duck smoothly.

Enough of have ducked with Kx to make the play.

To me what is interesting is if you lose to the J, do you still hook? If RHO is supposed to duck with Jx and that leaves KJ dub offside as the relevant combo.

This is similar to KQT9xx in dummy and RHO wins the 1st trick with the Ace. You are supposed to drop AJ now.

Back to the original - holding KJ dub RHo really should win the King, no?

My head is now hurting.

[Halo]

If you just play the percentages, nothing clever, noone can really do better. Even Michael Rosenberg, without the Jack, won't be able to fool you - and you won't be embarassed when you futilely try to catch him out.

[mr1303]

Well, that was exactly what happened to me.

I led the 9, all followed, then continued with the ace, and dropped RHO's Jack.

In the analysis afterwards in the pub, RHO did say he'd duck with Kx as well, so there wasn't much in it.

[FrancesHinden]

I agree that more people will duck with Kx than with Jx, though obviously it should be 50:50.

[awm]

Relevant positions for RHO are:

1. Kx (3 ways)
2. Jx (3 ways)
3. KJ (1 way)
4. K (1 way)
5. xx (3 ways)

If RHO has any other holding and your plan is to play the nine and duck a low card, cover the jack, or duck the king from LHO, then you will either always make (RHO Jxx) or always fail (others).

In position 1, RHO should always duck (if he wins you cannot go wrong). Now you make only if you play ace the second round.

In position 4, RHO has no choice but to win king. Now you make only by finessing second round.

In position 5, RHO has no choice but to duck. Now you make only if you finesse when LHO plays jack second round.

In position 2, RHO has the choice of ducking or winning. Say he ducks with probability p. In position 3 he has the choice of cards to win with, say he wins jack with probability q. In position 1, LHO has a choice in the second round; say he plays low with probability s and otherwise jack.

Say LHO were to play jack on the second round (after the nine wins first round). Now if we ace, we win 3(1-s) and if we queen we win 3 (position 5). So we're always better off to play the queen if the 9 wins and then the jack is played by LHO. Since we're always doing this, it's best off for the opposition to set s=0 (now we never pick up Kx offside).

Say RHO wins the king first round. On the next round LHO follows low. If we finesse then we win 1 (singleton king). If we play from the top we win 1-q (KJ tight). So we may as well finesse. Now the opponents do best to set q=0 (we never pick up KJ tight).

Say we play the nine and it wins. Now suppose we play another small card and LHO plays low. If we play ace, we win 3s. If we queen, we win 3p. But s=0, so we should play the queen.

Say RHO wins the jack first round. On the next round LHO follows low. If we finesse then we win 3(1-p). If we play ace, we win q. Since q=0, we should finesse.

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So our best strategy is:

Start by leading the nine. If LHO plays low let it ride; else cover the jack or duck the king. If the nine holds, play to the queen (or win LHO's king of course). If the nine loses to the jack, finesse LHO for the king on the second round. If the nine loses to the king, finesse LHO for the jack on the second round.

The best strategy for the opponents is the following: Holding KJ tight, RHO should always win the first trick with the king. Holding Jxx, LHO should always play the jack on the second round. Holding Jx, RHO should win the jack on the first round. Our best strategy will pick up the suit regardless of his play but by winning the jack he gets the defense a trick in the suit and therefore saves 1 imp presumably.

Of course, all of this assumes everyone is playing an optimum strategy and has a full count on the hand, there's no information from tempo, etc. It's not clear these assumptions are warranted even against expert opposition.

[Fluffy]

nice analsis, but just eb careful not to win K with KJ when declarer has 3 cards and only 2 stoppers in partner's 5 card suit