[frank0]

Q8765
T432
3 tricks, infinite entries.
South leads 2 and West follows 9, which card should I play from dummy?
2-2 split: doesn't matter
Other cases
E----W--play small----play Q
AK9--J---2tricks---3 tricks(6.22%)
AJ9--K---3tricks---2 tricks(6.22%)
KJ9--A---3tricks---2 tricks(6.22%)
9----AKJ 2tricks---2 tricks(6.22%)
AKJ9void2tricks---2 tricks(4.78%)

so small should be better but SuitPlay tells me to play Q, do I miss something?

[gwnn]

I think from HJ9 LHO should play the J to force you to guess (this is not a mathematical argument).

[MrAce]

frank0, on 2012-July-07, 10:18, said:

Q8765
T432
3 tricks, infinite entries.
South leads 2 and West follows 9, which card should I play from dummy?
2-2 split: doesn't matter
Other cases
E----W--play small----play Q
AK9--J---2tricks---3 tricks(6.78%)
AJ9--K---3tricks---2 tricks(6.78%)
KJ9--A---3tricks---2 tricks(6.78%)
9----AKJ 2tricks---2 tricks(6.78%)
AKJ9void1tricks---2 tricks(4.78%)

so small should be better but SuitPlay tells me to play Q, do I miss something?

1-3 3-1 splits are 6.22, not 6.78

But that doesnt seem to affect your claim, it really looks wrong result by SP. Very interesting. I maybe wrong.

Thinking about Csaba's deceptive J from HJ9, even if every opponent play J from HJ9, ducking will lose only to J-AK9. So if we always play small to Q and always duck when we see 9 or J it still comes to same % . In order to think that Q is correct play we have to totally rule out that LHO can have HJ9 and he never plays 9 from a HJ9 holding.

Frank you showed ducking when split is AKJ9-void takes 1 trick, while covering takes 2 tricks, why ? I think ducking still gets 2 tricks.

[manudude03]

I suspect there's also restricted choice with HJ9 (i dont think the J can cost)

[gwnn]

When I start thinking about falsecards and counter false cards my head starts spinning. But what are you saying MrAce? It seems like if LHO always plays the J from HJ9,we have to play the Q (HJ9 is impossible). The break even point is if LHO plays the J 66% of the time and 9 33% of the time. I don't know what the optimal % is for defenders but looks like Suitplay thinks it is >66%.

[MrAce]

gwnn, on 2012-July-07, 12:08, said:

When I start thinking about falsecards and counter false cards my head starts spinning. But what are you saying MrAce? It seems like if LHO always plays the J from HJ9,we have to play the Q (HJ9 is impossible). The break even point is if LHO plays the J 66% of the time and 9 33% of the time. I don't know what the optimal % is for defenders but looks like Suitplay thinks it is >66%.

I dont understand what you meant by HJ9 is impossible.

But look at SP probabilities, when SP sees the 9, it still thinks that LHO can hold HJ9 and gives it the full probability. This is why i am confused about the result.

If LHO played J, we could perhaps change our mind, but they didnt. I dont know how much of the time they do this or not but against real experts you are absolutely right. Because if we try to duck the J we lose to

AKJ-9
J-AK9

and win when

AJ9-K
KJ9-A

Same possibility, SP thinks (i assume) LHO play 9 or J randomly from those holdings since it doesnt matter and none of them can cost. But as you mentioned when it comes to humans it differs. In a weak field you expect much more 9 from HJ9 and in finals of a big event you almost always expect J from HJ9.

[Mbodell]

The encyclopedia says both low to the queen on the first round and duck one round then low to the queen give the same chances (and are best play). Should work for 3 tricks 53% of the time. Expected tricks 2.48.

But yeah, I think both suit play and the encyclopedia assume optimal defense.

[awm]

It seems like there are four relevant holdings for LHO here:

AJ9
KJ9
AK9
J

The right play would seem to be to play the jack from AJ9/KJ9 half the time. Then when you see the nine, it's equally likely to be AK9 or AJ9/KJ9 and you have an equal guess whether to play queen. Similarly, when you see jack it's equally likely to be from J stiff or AJ9/KJ9.

So optimal defense, it doesn't matter and suitplay is fine. But on realistic defense most opponents will play 9 from AJ9/KJ9 more often than jack (I think) so probably ducking the nine is better.

[gwnn]

MrAce, on 2012-July-07, 12:22, said:

I dont understand what you meant by HJ9 is impossible.

But look at SP probabilities, when SP sees the 9, it still thinks that LHO can hold HJ9 and gives it the full probability. This is why i am confused about the result.

I said if LHO never plays the 9 from HJ9, then HJ9 is impossible. If LHO plays the 9 only 1% of the time of HJ9, then it is almost impossible. And so on.

Yes, suitplay has an interesting way of presenting data. It shows a priori probabilities but its conclusions are more than just adding these up. For example just try AKT98 opp xxxx, it will cash the ace and then if RHO (dummy is AKT98) drops an honour, suitplay will give:

Jxx Q 6.22%
xx QJ 6.78%

But then goes on and finesses the T anyway, because suitplay knows about restricted choice and will assume that RHO will play the Q less than 91.7% of the time (incidentally, I think optimum from QJ tight is anywhere between 8.3% and 91.7%).

Quote

If LHO played J, we could perhaps change our mind, but they didnt. I dont know how much of the time they do this or not but against real experts you are absolutely right. Because if we try to duck the J we lose to

AKJ-9
J-AK9

and win when

AJ9-K
KJ9-A

Same possibility, SP thinks (i assume) LHO play 9 or J randomly from those holdings since it doesnt matter and none of them can cost. But as you mentioned when it comes to humans it differs. In a weak field you expect much more 9 from HJ9 and in finals of a big event you almost always expect J from HJ9.

Suitplay thinks that defenders play optimally. Unfortunately I don't know what % LHO should play the J from HJ9 although it seems that careful analysis would be able to find it out. I think it might be something like 33%-66% but sorry I'm not gonna think it all over now.

[frank0]

MrAce, on 2012-July-07, 11:49, said:

1-3 3-1 splits are 6.22, not 6.78

But that doesnt seem to affect your claim, it really looks wrong result by SP. Very interesting. I maybe wrong.

Thinking about Csaba's deceptive J from HJ9, even if every opponent play J from HJ9, ducking will lose only to J-AK9. So if we always play small to Q and always duck when we see 9 or J it still comes to same % . In order to think that Q is correct play we have to totally rule out that LHO can have HJ9 and he never plays 9 from a HJ9 holding.

Frank you showed ducking when split is AKJ9-void takes 1 trick, while covering takes 2 tricks, why ? I think ducking still gets 2 tricks.

I edit the original post. Thanks

[JLOGIC]

gwnn, on 2012-July-07, 17:31, said:

I said if LHO never plays the 9 from HJ9, then HJ9 is impossible. If LHO plays the 9 only 1% of the time of HJ9, then it is almost impossible. And so on.

Yes, suitplay has an interesting way of presenting data. It shows a priori probabilities but its conclusions are more than just adding these up. For example just try AKT98 opp xxxx, it will cash the ace and then if RHO (dummy is AKT98) drops an honour, suitplay will give:

Jxx Q 6.22%
xx QJ 6.78%

But then goes on and finesses the T anyway, because suitplay knows about restricted choice and will assume that RHO will play the Q less than 91.7% of the time (incidentally, I think optimum from QJ tight is anywhere between 8.3% and 91.7%).

Suitplay thinks that defenders play optimally. Unfortunately I don't know what % LHO should play the J from HJ9 although it seems that careful analysis would be able to find it out. I think it might be something like 33%-66% but sorry I'm not gonna think it all over now.

How hard is it, it's obviously 50 %.

All,

Here is how you can think about this.

As Declarer

You can decide that you will pick up AK9 onside, or stiff J onside, and never let what the play affect you. So, if they play the 9, you play the Q, and if they play the jack you play the queen. This means regardless of what strategy the opponents are employing, you will be unexploitable, you are simply always losing to HJ9. This is an optimal strategy.

You will notice AK9 and stiff J are 2 combos, and so are KJ9 and AJ9. They are equally likely. Ergo, in this case you can also decide to ALWAYS pick up KJ9/AJ9.

This means ducking the 9, and also ducking the jack. In this way you pick up AJ9/KJ9 no matter how the opps play. This is also an optimal and unexploitable strategy.

This is recommended if you think the opps are better than you at these games. They can be altering their percentages from optimal in order to try to exploit you by winning the guessing game of how they are deviating from optimal (ie, playing the J too often or too infrequent from optimal).

Now, the FUN thing to do is to try to outguess them. The first level of this against say bad players would be to always cover the jack, and to duck the 9. This would be exploiting the tendency of playing the J too infrequently from HJ9, indeed most people will never do this. So this is a good play against bad players, you will pick up stiff J and KJ9/AJ9, a full extra combo.

Now, if you were wrong about this, and they knew your strategy, they would ALWAYS falsecard from HJ9 and thus you would only pick up stiff J, and lose to AK9 and HJ9, losing 1 full combo from optimal play.

I am happy to admit that I will ALWAYS play the J from HJ9 vs basically everyone. This exploits the declarers playing for a never falsecard as discussed above. To exploit me if you knew my strategy, you would DUCK the jack, and go up on the 9. You will win on AK9 and HJ9 now, losing only to stif J, picking up an extra combo from optimal play.

As Defender

Your goal is to make their play irrelevant. We have seen the optimal solutions involve them picking up 2 combos of KJ9, AJ9, J, and AK9. Assume that you play the 9 from KJ9 100 %, but the J from AJ9 100 % (this is for simplicity, is the equivalent of playing the J and 9 50 % of the time from KJ9/AJ9).

When you play the 9, declarer can cover and will pick up AK9, but he will lose to KJ9. Likewise if he ducks, he will lose to AK9, but pick up AJ9.

When you play the J, declarer can cover and pick up stiff J, but lose to AJ9. Likewise, he can duck and pick up AJ9, but lose to stiff J.

So, whether you play the J or the 9, declarers play is completely irrelevant, you are unexploitable. But again, that means you can't exploit! If you think you can outguess declarer, try to exploit.

Level 1 of doing this is doing what I suggested earlier, always play the J from HJ9. If declarer doesnt know this falsecard, or doesnt think you are capable of it, you will win all of KJ9, AJ9, and AK9! Of course, if declarer picks you off, you can be exploited and only win stiff J.

Level 2 would be to always play the 9 from HJ9. This would require playing a declarer who thinks you would always falsecard from HJ9, and thus will duck your jack, and pop on your 9. Now you are winning your stiff J and HJ9 combos again. TBH there is no one I would go to this level against, they have to be very good and know your game very well, if I thought level 1 wouldn't work I would attempt to go the unexploitable route unless I knew the person quite well and felt confident.

These situations are very easy to analyze for unexploitable play, the fun and edge comes in winning the battle of exploiting someone who is trying to exploit you. This is very much like rock paper scissors, either player can decide to play an unexploitable 50/50 style, however it can be a great and strategic game when 2 players are trying to exploit the other.

There are many other suit combinations in bridge like this.

[JLOGIC]

Here is another one of the same nature that many players would be surprised by.

How do you play xx opp KQT9xx when you lead low to the king and it goes low, and and then you play low up to the QT and they play low against optimal defense?

Many would be surprise to learn that this seemingly 50/50 situation has a correct answer, you play the queen! Why is this, surely optimal defense will always include ducking Ax on our right, right?

Well, in that case, say you lead low to the king and RHO wins the ace. What do you do? Well, you thought the other situation was 50/50, meaning RHO will ALWAYS duck Ax. In that case, when RHO wins the ace, we should play him for AJ doubleton and drop the queen.

Now, this is where many people get lost, thinking about the percentage of time that RHO should duck Ax now etc. If you are looking for an optimal solution, you don't need to get into that.

Look at it this way, we are deciding to lose to Ax on our right. We are choosing to pick up Axx on our left, and AJ doubleton on our right. This is an optimal solution, because it makes their play with Ax completely irrelevant. If they win it with Ax, they score 2 ticks, and if they duck it with Ax, they get 2 tricks! But we always pick up Axx on our left, and AJ doubleton on our right, and their strategy with Ax on our right cannot alter that.

If you try any other strategy, you can be exploited by their Ax play. Say you play low to the king, planning to play low to the ten next if it holds. Well, now they can always win with Ax on your right, which means you cannot pick up AJ doubleton (because if they win the ace, you have to hook next since Ax is more likely than AJ doubleton). Using this strategy you will pick up only Jxx onside.

As is often the case, when you are declarer and need an optimal strategy in case of a falsecard or wahtever with some combination, you can just play to lose to that combination making the opps play irrelevant so they cannot ***** with you. As defender you will have to do more work.

Now, in practice, we can try to exploit their weak tendencies. Many people will win with Ax offside. If they do this, you can play low to the king and low to the queen if they duck, and low to the king, low to the ten if they win. If they say win 100 % of the time with Ax, you are now picking up Ax off AND Jx off, a big improvement from the optimal solution wehre we pick up Jx off and AJ off, because there are THREE combos of Ax and only one combo of AJ. You have added two combos to your win rate.

Of course if they knew that you did this they could simply duck with Ax, and now you are picking up only Jx off, losing you a combo.

As defender, you might think you should win Ax 33.333% of the time, and duck 66.666% of the time, to protect your AJ. Your thought process is that AJ is 1/3rd as likely as Ax, so when it goes low to the king and ace, you have 1/3rd of your Axs, and all of your AJs, so it is neutral whether they hook or go for the drop now.

That is true, but look at their guess now when it goes low to the king and low, and they lead back up again. The queen is now a percentage play, because you have only 2/3rds of your Axs, and all of your Jxs. Effectively, you have just made it go from a 50/50 guess (if you duck 100 % of Axs) on this guess, to a 50/50 guess on low to the K and A and then low up. You did not gain annything. If declarer was going to alter his strategy now, and say play low to the king, low to the queen if the king won, but play low to the king and low to the ten if you won the ace, he is now picking up Jx and 1/3rd of Axs, which is the same as picking up Jx and AJ. This is a longwinded version of saying that you can win the A from Ax 0-33.3 % of the time, but if you win more often you can be exploited.

[blackshoe]

JLOGIC, on 2012-July-07, 23:07, said:

sigh double post

That's okay, Justin, it's worth reading twice.

[gwnn]

JLOGIC, on 2012-July-07, 22:42, said:

How hard is it, it's obviously 50 %.
(very long post)

Clearly, pretty hard but thanks for this explanation, now my head is spinning slower than before.

[gwnn]

Coincidentally, after exactly two years this thread has been dormant, I have been reading Roy Hughes' "Card by Card" when he discusses the same combination on page 95. There appears to be a typo on his winning cases in that he writes 9 for east as a winning case instead of AK9.

He has
Txxx
Qxxxx, i.e., you play from dummy and East is first to play one of the J or 9 to make the board interesting.

He names four possible strategies for South: always Q, always x, Q-on-J and Q-on-9 and two possible strategies for East: J (always play the jack if you have it) and 9 (always play the 9 if you have it).

After going through the necessary preamble about how usually ceteris are not paribus,
you have the following winning cases (note that whenever east has AKJ/AK9 he has to play low to give us a problem):

          EJ            E9
SQ   AKJ, AK9, J    AKJ, AK9, J
Sx   AJ9, KJ9       AJ9, KJ9
SQ-J J, AKJ         AJ9, KJ9, J, AKJ
SQ-9 AK9, AJ9, KJ9  AK9

or just the numbers:

     EJ E9
SQ   3  3
Sx   2  2
SQ-J 2  4
SQ-9 3  1

Now what he did is exclude strategy Sx since it is dominated by SQ and SQ-J and exclude SQ-9 because it is dominated by SQ. So you get:

     EJ E9
SQ   3  3
SQ-J 2  4

And in this case, East clearly has to go for EJ since that dominates E9. Then S gets to choose again and he will go for SQ.

So according to this reasoning, S should go up with the queen no matter what and east play the jack no matter what, and this is the equilibrium, no mixed strategies are involved. Is there anything wrong with this argument? Certainly there does not appear to be a good deviation for either party from it. In real life, indeed a lot of Easts will play the 9 from HJ9 but that's just an error, not them trying to punish a perceived strategy of "Q<-9" which nobody is doing. Q<-J is a good choice as it punishes this error but pays off to the apparently optimal pure strategy of always sticking in the J. Or am I misunderstanding something again?

[gwnn]

If we allow for the 50-50 random play for east as a third possibility, we have the following payoff matrix (east just gets the average between EJ and E9 should they be different):

     EJ E9 ER
SQ   3  3  3
Sx   2  2  2
SQ-J 2  4  3
SQ-9 3  1  2

SQ still dominates Sx and SQ9:

     EJ E9 ER
SQ   3  3  3
SQ-J 2  4  3

And it still looks like EJ is better than E9 or ER, no? Then we have

     EJ
SQ   3
SQ-J 2

And then declarer can still play for SQ and east's best try was to stick to EJ all along. Is this wrong somewhere?

edit2: Justin makes no mention of AKJ onside, I think that's where the difference is coming from.

This post has been edited by gwnn: 2014-July-08, 07:05