[Rebound]

Opps, I dismissed the case where LHO goes up A right away too quickly. Fortunately, my reasoning still holds. The only possible remaining holdings are Jx - x and x - Jx, the others having already been eliminated. So again it's a 50-50 shot whether to play the Q the next time. Oh, and one other, hopefully minor, error. You can succeed with stiff A offside, but again you have to lead low to the 10 then low to the 9. That still doesn't make it worth it I don't think. So I believe I am still correct in essence.

[fred]

The answer to:

KQ10987

32

A few of you either got this right or came close to getting it right. Well done!

I am making the assumption that the defenders will always defend optimally.

The first problem is whether to play an honor from the dummy on the first round or finesse the 10. This is pretty much a math problem and since some of you did the math already, I am not going to go into it here. Playing an honor from the dummy on the first round is correct.

Now let's assume that this wins the trick and you travel back to you hand to play a 2nd round of the suit with LHO following small again.

At first glance this appears to be a pure guess. Playing the other honor is necessary when LHO started with Axx and playing the 10 is necessary when LHO started with Jxx. The odds of these 2 holdings are exactly the same so it seems that you might as well toss a coin.

Now let's back up for a minute and suppose that RHO had won the first trick with the Ace. This would appear to be a bad play from Ax since RHO could have ducked and given you the guess on the 2nd round that I referred to in the previous paragraph.

However, it would be necessary for RHO to win if he had AJ doubleton since this would be his only chance to win a 2nd trick on defense.

Therefore, it seems reasonable to conclude that if RHO wins the first trick with the Ace you should play him for AJ doubleton because we are assuming optimal defense.

But is that really optimal defense? Suppose that a tricky RHO figures this out and decides to win the first trick at least some of the time from Ax in an attempt to make it look like he has AJ.

The correct strategy for the declarer is to let him get away with this, to play him for AJ, and to go up with the other honor on the 2nd round (thereby failing to win the 5 tricks that are required).

In order to see that this is true, you have to understand something about the basic nature of suit combination problems. The general way to approach these problems is to come up with a set of holdings that the defenders can have for which success is possible regardless of the strategy that the defense chooses to adopt. Several of these sets can be constructed for most suit combinations - the one you are looking for is the set that has the greatest total probabality.

So before you play a single card you should think to yourself: I can come up with a plan that works whenever RHO has Jx or AJ (among other holdings which all cancel out): I will play low to the King and, regardless of whether that loses or not, I will play low to the Queen the second time.

The alternative plan is to play low to the King and, regardless of whether that loses or not, finesse the 10 the second time. This plan works whenever RHO has Ax but it loses to his AJ doubleton.

The odds of Ax and Jx are the same so the first plan is correct because it picks up one additional holding: RHO having AJ.

Do you find the part about "regardless of whether it loses or not" to be strange? Shouldn't the defenders plays impact your strategy?

No! They are not on your side!

Make your plan and stick with it.

I hope that the above explanation was coherant. These concepts are not exactly easy to explain, but I can tell you for sure that I know I am right

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

[Rebound]

I guess I should apologize for my long post since it turned out to be mostly irrelevant and fundamentally flawed. It is indicative of the main problem I have with bridge... the ability to discard the irrelevancies without going thru the complete line of reasoning. Sorry folks.

[fred]

You didn't do so bad rebound. You did figure out that it was wrong to finesse the 10 on the first round and you figured out that the 2nd round play appears to be a complete guess. I think it shows courage to attempt to solve a different problem in front of 100s of people and that there is absolutely no reason for you to apologize.

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

[mpefritz]

More later, but there may be some restricted choice on the spots when looking at the plays when EAST wins the first round with the A, when EAST also has a non-zero probability of playing the A from Ax combinations. Depending on his likelihood of playing the A from Ax, there may be a point at which playing for the AJ is wrong. (my gut say he has to be 75% likely to play A from Ax to not play for the AJ when the ACE is won on the first round)

Note that if you get all spots on the first round and as you lead to the board on the second round, this likelihood of playing the A from Ax by EAST also comes intio play, but there is no RC on the spots as you have seen them all.

fritz

[fred]

I am not going to do the math, but I am willing to bet (a lot!) that whatever restricted choice inferences existing on RHO's spot card play, they are cancelled out the restricted choice inferences on LHO's plays.

One way to deal with restricted choice is to not even thinka about it and to just enumerate all of the relevant holdings in which each line of play succeeds - the results will always be the same.

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

[Fluffy]

Back to the first case I just played a deal in BBO with same kind of guess

KJ9765432

void

Having ot guess wich honnor is singleton

[Stephen Tu]

Quote

Do you find the part about "regardless of whether it loses or not" to be strange? Shouldn't the defenders plays impact your strategy?

No! They are not on your side!

It depends on how well you think you know your opponents. Generally with suit combinations, there is a theoretical best strategy (possibly more than one with equivalent success rate) for declarer that will guarantee him a certain percentage of success against any defense, including the optimal defense. He basically chooses beforehand which suit combinations he will pick up, and ignores falsecarding if it is consistent with one of those holdings. If the defense is sub-optimal, declarer can take an alternate line to take advantage of this, and improve his score. However, if declarer is wrong about the opponents & they are actually defending optimally, he will get a worse score than the theoretical best.

Lately, particularly in pair events against unknown random opponents (at any level less than say at least a Blue Ribbon semi-final), I have started just playing them for being poor players & playing true cards, not randomizing / falsecarding appropriately, and not being good enough to duck when it's right, and my results have improved. I only revert to the theoretical best line against players whom I know and respect their play. Best against good defenders is not best against poor ones!

[shanbari]

fred, on Jan 5 2005, 08:22 PM, said:

..
Do you find the part about "regardless of whether it loses or not" to be strange? Shouldn't the defenders plays impact your strategy?

No! They are not on your side!

Make your plan and stick with it.

I hope that the above explanation was coherant. These concepts are not exactly easy to explain, but I can tell you for sure that I know I am right

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

it all makes sense, fred,

shan

[myfish]

hi,I want to ask how to play the following suit with 5 tricks

AQ763
K94

[firechief]

If the K9x is in the concealed hand, I might try the effect of leading the 9 towards the AQ7xx. Maybe my LHO is worried I'm about to run it, and will cover from JTxx (no 8). If I were to start with the ace, I would not hook the 9 after the jack or ten falls behind the K9x. I won't finesse because the opponents are supposed to play the jack or ten from JTx.
Joel