[l milne]

Assuming expert (even double-dummy if you like) defense:

---

You start with a small card to the King.
What do you play next if:
a] West plays small, East wins the Ace;
b] West and East both play small.

[jschafer]

What would you call 'double dummy defence' from East if he is holding ATxx?

[TimG]

l milne, on 2010-December-25, 18:44, said:

a] West plays small, East wins the Ace;
b] West and East both play small.

On the second round, Suitplay plays:

a] Jack from hand;

b] low to Jack.

SuitPlay is free, more info here.

[JLOGIC]

TimG, on 2010-December-26, 07:57, said:

On the second round, Suitplay plays:

a] Jack from hand;

b] low to Jack.

SuitPlay is free, more info here.

How is this helpful? I think lmilne was trying to offer a good beginner/int suit combo for the beginner/ints to work on, not just hoping someone would post a result (after using a computer program). The point of this suit combo is: why is it not just 50/50 what to do, as most people would think it is?

[awm]

For [b] it seems you are trying to pick up ATxx held by one of the opponents. Either opponent is equally likely to have ATxx, but it's conceivable that sometimes East would have won the ace over the king from this holding at the first trick in the suit. If he would never do this (i.e. always duck) then it's equal odds, but otherwise playing to the jack next is better. It follows we should play to the jack next in case [b].

Assuming the above strategy, consider case [a]. If our plan is to play the queen next, then we lose to singleton ace in the East. If East has ATxx, then he should duck the first trick to put us in case [b] above. So playing the queen next will actually never help us against best defense. Playing the jack next helps us in the case where East has singleton ace, so we should go with that approach.

[l milne]

I don't even know if this is beginner stuff, to me it's more top of the intermediate scale. I didn't learn about restricted choice on "irrelevant" spots until quite recently. (oops, little hint there for those having problems with this)

TimG, I have Suitplay, as well as "Bridge Odds for Practical Players" by Kelsey & Glauert. If you really think this is simple and non-interesting, then perhaps reflect on why Kelsey & Glauert recommend the Queen on the second round for a] (they don't consider b] fwiw). Also, look at the 6 layouts Suitplay considers on the second round. Only two of these depend on the line of play. Notice anything interesting?

Jschafer, very good question. Obviously, double-dummy in one trial it doesn't matter what East does. Over an extended sample with player histories, East would duck sometimes and win sometimes, probably in the ratio of 3 to 1 if my instincts serve me well! If playing against Suitplay, it doesnt matter as Suitplay always loses to ATxx offside no matter what. If playing against Kelsey, duck 100% would work better, as it gives him some chance to go wrong.

[TimG]

l milne, on 2010-December-26, 16:28, said:

(oops, little hint there for those having problems with this)

Sorry, I didn't understand this to be a quiz, I thought you genuinely wanted to know the answer. Which is why I added the suitplay link -- I thought I was being helpful rather than spoiling, not everyone knows about SuitPlay. And, of course, SuitPlay's answer did not preclude further discussion.

[l milne]

TimG, on 2010-December-26, 17:29, said:

Sorry, I didn't understand this to be a quiz, I thought you genuinely wanted to know the answer. Which is why I added the suitplay link -- I thought I was being helpful rather than spoiling, not everyone knows about SuitPlay. And, of course, SuitPlay's answer did not preclude further discussion.

Sorry, should've made it clearer that this was a quiz.
I am starting to think Suitplay's answer is incorrect, as it has been known to be in the past. Sacrilege, I know.

[han]

Just thought about it for a bit so this may be way off:

You always pick up all 3-2 splits, 5-0 splits and stiff 10's. Whatever way you play you will pick up either A10xx on your left or on your right, but not both. The only holdings that are relevant are the stiff aces.

By playing low to the king, and then the jack (or equivalently, low to the jack), you pick up both singleton aces. If you play this way regardless of whether RHO plays the ace or not, then there is nothing the opponents can do to prevent you from winning against all 3-2 and 5-0 splits, singleton 10's, A10xx on your left and both singleton aces. Against good defense you cannot do better than this.

[kgr]

awm, on 2010-December-26, 11:26, said:

For <b> it seems you are trying to pick up ATxx held by one of the opponents. Either opponent is equally likely to have ATxx, but it's conceivable that sometimes East would have won the ace over the king from this holding at the first trick in the suit. If he would never do this (i.e. always duck) then it's equal odds, but otherwise playing to the jack next is better. It follows we should play to the jack next in case [b].

Adam,
([b]=both small)
I don't understand this:
If east would sometimes win the ace with ATxx, but he didn't play the Ace isn't it then less then 50% that East had ATxx (because East would have played the Ace sometimes and West being before KQ would never play the Ace). And therefore I would think it is more likely that West has ATxx?

[jschafer]

I think that is what he said (or how I understood it at least), after all why else would he play the Jack next?

[kgr]

jschafer, on 2010-December-27, 06:07, said:

I think that is what he said (or how I understood it at least), after all why else would he play the Jack next?

Yes, rereading what he said: you are right

[kgr]

awm, on 2010-December-26, 11:26, said:

For <b> it seems you are trying to pick up ATxx held by one of the opponents. Either opponent is equally likely to have ATxx, but it's conceivable that sometimes East would have won the ace over the king from this holding at the first trick in the suit. If he would never do this (i.e. always duck) then it's equal odds, but otherwise playing to the jack next is better. It follows we should play to the jack next in case [b].

After rereading I think that I agree.
...Any idea why suitplay also says that J is best? How does suitplay that into account that East would sometimes plays the A?...or is it best to play sometimes the Ace as East??

[jschafer]

deleted nonsense.

This post has been edited by jschafer: 2010-December-27, 11:35

[vuroth]

My take on it is:

a) While I'm not 100% on 3 card RC, east seems to be favourite to have a low card or two, so I think 1-4 is more likely then 4-1, so I'll play the queen next.

I may be falling victim to the opponents I play against, but I'll play west for not being single. I think east ducking is a bit less likely than west ducking, but I can't fully explain why, so who knows?

[cherdano]

Jschafer something is wrong with your math. Maybe it's because "ATxx-x or x-ATxx" is six times as likely as "Txxx-A", not three times as likely?
Kgr, read han's post (and give it an upvote). Suitplay doesn't consider psychological probabilities, but analyzes strategties, and han's post tells everything you need to know that there is no better strategy.

[jschafer]

cherdano, on 2010-December-27, 08:15, said:

Jschafer something is wrong with your math. Maybe it's because "ATxx-x or x-ATxx" is six times as likely as "Txxx-A", not three times as likely?

I'm confused now

[han]

Hey I didn't know about upvoting. I gave cherdano my first upvote for his excellent suggestion.

[dburn]

Put simply: if you lead to the king and it holds (but the ten does not drop), then either: the suit is 3-2; or someone has ducked with A10xx.

If you lead the queen next, you lose when West has ducked with A10xx, which he will always do.

If you lead to the jack next, you lose when East has ducked with A10xx. How often will he do this? Well, he cannot do it more often than always, but he can do it less often - some players are firmly convinced that aces are meant to take kings.

So, you had better lead to the jack next because this loses less often than leading the queen next.

By the same token, if East wins the king with the ace, you had also better lead to the jack next. East will always win with the singleton ace, and while he cannot win with A10xx more often than always, he can win with it less often.

How often "should" East duck with A10xx? It doesn't matter. Against declarer's optimum stratgey (low to the jack on the second round) East will win two tricks with A10xx whether he wins or ducks. What you must not let him do is deprive you of a trick by winning the king with the singleton ace.

[TimG]

jschafer, on 2010-December-27, 07:56, said:

Duck 100% of time: Declarer will make 50% of ATxx-x vs x-ATxx and 100% of Txxx-A = 4.24% + 2.83% = 7.07% (of total layouts)
Duck 66% of time: Declarer will make 60% of ATxx-x vs x-ATxx and 50% of Txxx-A = 5.09% + 1.42% = 6.50% (of total layouts)

This isn't the best declarer can do, is it? If declarer sticks to his original line of play he can always make half of the ATxx-x/x-ATxx splits and 100% of Txxx-A regardless of a defender's duck percentage, can't he?