A land of make believe...

[Jlall]

You are playing in a strange theoretical world where everyone plays optimally. You have this suit and need 3 tricks:

 

KT83

J652

 

You lead the jack, and it goes Q K A. The next time you lead the 6 and they follow. What do you play?

 

The next round you magically pick up the same suit. You lead the jack and it goes Q K small. You cross and lead the 6 and LHO follows. What do you play?

 

The next round you magically pick up the same suit. You lead the jack and it goes ace!, RHO follows small. You then lead up to dummy and LHO follows small. What do you play?

 

The next round you magically pick up the same suit. You lead the jack and it goes small small ace. You lead up to dummy again and LHO follows small. What do you play?

[Phil]

Does LHO know our suit length?

[Jlall]

Does LHO know our suit length?

They have seen our hand, we had a spill...every single round :P

[Hanoi5]

Ten, eight, ten, eight.

[Free]

I had a very similar hand yesterday: Jxx vs KT8x. RHO covered the J with the A holding AQx. LHO had 9xx. I thought that if he would've covered with the Q and ducked later on, that I'd lose 2 tricks.

 

Ok, for the hands in question:

1. with A9 RHO should take immediately because he hopes you finesse again. With Ax he could duck so you'd play small to the T. Against A9x you're hopeless, against Axx you'll see the 9 in the 2nd trick. So I'd say cash the T. Ofcourse, RHO may "falsecard" with Ax...

2. same logic as 1, but this time finesse the 8.

3. with Axx LHO doesn't have a reason to play the A. With Ax it's hopeless. So I'd say LHO has AQx and play the T.

4. 8 seems normal.

 

I didn't take 4-1 splits into account, I'm too lazy at the moment :)

[hanp]

Always play the 8, it wins if LHO has AQ9x (2 holdings), Q9x (2 holdings) or Q9xx (1 holding) and loses against Qxx (1 holding) and AQx (2 holdings). No other holdings are relevant, playing the 10 wins against the latter but loses against the former.

 

A strategy where you play differently depending on the opponent's carding will be abused by the perfect opponents.

 

For example, if you only consider the fourth case (where LHO follows low twice) you might think that the only relevant holdings are Qxx and Q9xx. Since the former is slightly more likely, you might think it is best to play the 10. However, if you play like this, the opponents can cover with Qxx and duck with Q9xx, and you will always go wrong.

 

This is of course backwards reasoning. You could correctly argue that it is the opponents who have to choose their strategy first, and that the above is therefore nonsense. However, it is easily possible for the opponents to choose a (mixed) strategy where you can do no better than always play the 8. Those who care should have no trouble computing such a strategy for the opponents.

 

Easily possible that I missed some holdings. LHO must have the queen and since with AQ, AQ9, Q9 and AQxx you are always beating it and you cannot beat Qx, the only relevant holdings are the ones I gave (I think).

[benlessard]

1&2 dont matter ! Because in a perfect both RHO and LHO will play their A in the correct ratio that will give you no advantage for winning against A9 or for guessing who has the A and who has the 9 and for beating AQ97----X. However if hes that perfect and know youre biased they will beat you.

 

In wich case the correct strategy is something like... further post to come

 

a third of the hands will fail because

AQ or A9x is in RHO

 

All 4-1 split are bad except

AQ9x

 

 

If JQKA shows up the only case that are relevant are

 

Q7x-----A9 (RHO will of course never duck with this holding)

Q9x-----A7 (RHO will duck g% of the times)

Q97-----Ax (RHO will duck g% of the times)

 

 

Q97x----A is not relevant because you are not going to finesse against the 7 (unless they spill their cards too)

 

If JQKx the relevant case are

 

AQx---97 (LHO will play the A vs the Q in H% of the times)

AQ7---9x (LHO will play the A vs the Q in H% of the times)

AQ97----x (LHO will play the A vs the Q in H% of the times)

AQ9x----7 (LHO will play the A vs the Q in H% of the times)

 

Q9x-----A7 (RHO will duck g% of the times)

Q97-----Ax (RHO will duck g% of the times)

 

 

IF declarer ALWAYS plan to finesse the 8 after the A show up and play the T when the A isnt played he will lose big time.

 

Im supposed to go to sleep now and this problem is driving me crazy...

 

However im sure you have to determine LHO mixed strategy before handling RHO strategy)

 

With

 

AQ7

AQx

AQ9x

AQ97

 

he will play the A or Q in a certain ratio

At first i was thing that he should always play the Q with those holding but he need to protect AQ9x and AQ97

 

The 4th case magically dont exist. Because LHO should always cover.

With Q97x he will always make 2 trick because you wont finesse against the 7 anyway and with Q?? he has to cover to give you the chance to go wrong.

[ron]

Always play the 8, it wins if LHO has AQ9x (2 holdings), Q9x (2 holdings) or Q9xx (1 holding) and loses against Qxx (1 holding) and AQx (2 holdings). No other holdings are relevant, playing the 10 wins against the latter but loses against the former.

 

A strategy where you play differently depending on the opponent's carding will be abused by the perfect opponents.

 

For example, if you only consider the fourth case (where LHO follows low twice) you might think that the only relevant holdings are Qxx and Q9xx. Since the former is slightly more likely, you might think it is best to play the 10. However, if you play like this, the opponents can cover with Qxx and duck with Q9xx, and you will always go wrong.

 

This is of course backwards reasoning. You could correctly argue that it is the opponents who have to choose their strategy first, and that the above is therefore nonsense. However, it is easily possible for the opponents to choose a (mixed) strategy where you can do no better than always play the 8. Those who care should have no trouble computing such a strategy for the opponents.

 

Easily possible that I missed some holdings. LHO must have the queen and since with AQ, AQ9, Q9 and AQxx you are always beating it and you cannot beat Qx, the only relevant holdings are the ones I gave (I think).

Han,

 

I am not convinced by your argument (although the conclusion may well be correct). If the opponents had the AQ942 instead of the AQ974, then your reasoning would certainly be correct. But in the given situation, playing the 8 loses to LHO's Q974 when LHO chooses to play the Q on the first round. It seems like this causes complications, but I may be missing something.

[Jlall]

Yeah you cannot pick up Q974.

 

Still AQ9x + Q9x > AQx + Qxx.

 

For some reason when I was explaining this to clee I thought there was only 1 combo of AQ9x (brain fart!) so I told him to play the ten in all cases (3 3-2 combos > 2 3-2 combos + a 4-1 combo).

 

Anyways, despite my small error and despite hans small error the methodology used is what's important. You must find a strategy where you neutralize what they do, aka if they know your strategy ahead of time they cannot game you in any way. People get very confused by this type of problem but it's actually pretty simple.

 

For extra credit I was hoping someone would berate me for starting by leading the jack against such good opponents! Definitely lead small to the ten against good opps and pick up AQx + Qx onside :) As an added bonus you can lose 1 less trick to stiff Q and stiff A onside also!

[ron]

I guess the pedantic answer is 8,8,8, does not matter. Optimal defense with Q9xx/Qxx is to play so that when the fourth case occurs, either holding is equally likely from declarer's POV. They can duck any percentage of the time with Q9xx (including never), so long as they duck C times as often with Qxx (where C is prob(Q9xx)/prob(Qxx)). If they don't do that, they can be exploited.

[ron]

Sorry, what I wrote directly above is wrong, the pedantic answer is 8,8,8, does not exist. Covering is always right with Q9xx and Qxx.

[hanp]

I disagree that it is the methodology that matters Justin. :)

[JanM]

For extra credit I was hoping someone would berate me for starting by leading the jack against such good opponents! Definitely lead small to the ten against good opps and pick up AQx + Qx onside :) As an added bonus you can lose 1 less trick to stiff Q and stiff A onside also!

I gave this to Kit Woolsey last night, and his comment was "why did I lead the J?" :)

[H_KARLUK]

For extra credit I was hoping someone would berate me for starting by leading the jack against such good opponents! Definitely lead small to the ten against good opps and pick up AQx + Qx onside :) As an added bonus you can lose 1 less trick to stiff Q and stiff A onside also!

I gave this to Kit Woolsey last night, and his comment was "why did I lead the J?" :)

Funny, i was also unsure that could be the correct Jack lifting device and right tire to up.

[kgr]

For extra credit I was hoping someone would berate me for starting by leading the jack against such good opponents! Definitely lead small to the ten against good opps and pick up AQx + Qx onside :P As an added bonus you can lose 1 less trick to stiff Q and stiff A onside also!

I was verifying this with suitplay and it prefers to lead the J for 3 tricks. Aren't you forgetting?:

AQ9xx-v