It came to me in a dream...

[Guest Jlall]

OK heres the position (it literally came from a dream).

 

You have KJT9 of diamonds in dummy, and Axx of diamonds and a master club club(trump) in your hand. You have already ruffed a spade and a heart both in your hand so the defenders know you're out. The 8 cards the opponents have left are 5 diamonds, 1 spade, and 1 heart, and 1 club. You KNOW the spade is on your right, but don't know where the heart is. You lead a club from your hand, lho pitches following, and RHO pitches a diamond.

 

What's going on? Does RHO have xx or Qxx?

 

Assume first RHO is a palooka, second hes advanced, third hes expert, and fourth hes meckstroth. How does this affect your answers?

 

Extra credit: what if RHO pitched a heart and was an expert? what if meckstroth pitched a heart?

 

No wonder I don't get much sleep.

[andych]

whenever RHO (palooka/adv) doesnt pitch his known ♠, I assume he is sleeping and finesse LHO for the Q, no matter he pitches ♥ or ♦.

 

Against meckstroth I take a toss.

[Guest Jlall]

mis read

Sorry probably my fault...that was not the easiest post to follow :)

[Winstonm]

Against an expert, if RHO pitches the card he is not known to hold - here the heart - he is trying to help me count his shape and I play him for the Q.

 

If Meckstroth makes this play, it may be a double cross and more likely is a double cross as the first play is too smarmy for him - but then it may be a triple cross, too: ugh. Maybe the key issue here is having the reputation for being able to play this well - then you can do whatever you feel like at the time and the opp won't have a clue.

 

Seriously, though, I'd have to think at this point it's pychological and have to determine what Meckstroth thought of me. If he thought me alert enough to suspect a double cross, he'd probably go for the triple cross so I'm back to playing him for the Q.

 

Against a run-of-the-mill expert who pitched a diamond, I'd play him for the Queen; against a more substantial opponent, I'd play for the double cross and finesse his partner.

 

It seems it's only those considered world class that you start thinking about the triple and quadruple cross.

 

Canasta anyone? :P

 

Winston

[andych]

The problem is difficult ....

 

I think RHO is still possible to have Qx or XXX. He is not necessarily holding xx or Qxx to discard a D.

 

It appears to me that whatever RHO discard on C, he does not lose anything. If he discard D from Qx or XXX, he just let us know the result sooner.

 

If RHO has xx or Qxx, we still have a pure guess if we start with DA and small D. Results known after guessing the 2nd D play.

 

So no psychology involved?

 

 

:P :D

[Guest Jlall]

I think you are missing the problem.

 

For starters Qx is simply impossible. We might have misguessed diamonds by playing ace and low, or we might have guessed by leading the king then jack, but pitching from Qx gives us no guess at all. Whichever way we go the Q will drop on the first round.

 

With xxx we also cannot misguess if he pitches from that holding. When we lead the king then jack, when RHO follows on the second one, we know he has a spade so it is 100 % to drop the queen. Had he not pitched from xxx, we would have just been 50/50 to guess it.

 

Sure it's possible that they are idiots, but both of those holdings are now irrelevant after their mistake because we will pick them up 100 %. The only RELEVANT holdings are an original xx and Qxx.

[andych]

I think you are missing the problem.

 

For starters Qx is simply impossible. We might have misguessed diamonds by playing ace and low, or we might have guessed by leading the king then jack, but pitching from Qx gives us no guess at all. Whichever way we go the Q will drop on the first round.

 

With xxx we also cannot misguess if he pitches from that holding. When we lead the king then jack, when RHO follows on the second one, we know he has a spade so it is 100 % to drop the queen. Had he not pitched from xxx, we would have just been 50/50 to guess it.

 

Sure it's possible that they are idiots, but both of those holdings are now irrelevant after their mistake because we will pick them up 100 %. The only RELEVANT holdings are an original xx and Qxx.

 

We know for always D is either LHO 3 RHO 2 or LHO 2 RHO 3. We shall not see DQ on 1st round if RHO doesnt discard D.

 

 

 

Let say RHO holds Qx and did not discard D

 

We play A, LHO play small D. 2nd D, LHO low -> pure guess

 

 

DK, small D from table, RHO DQ -> no guess (RHO Qx)

 

small D from hand, small D from LHO, DJ (pure guess), DQ from RHO -> results known

 

.......

 

Every D play we either face with pure guess or see the DQ and no guess.

 

Similar development if RHO start with XXX and didnt discard D

 

DA, LHO small D, Dx, LHO DQ -> no guess (RHO xxx)

 

DK, small D from table, RHO small D -> pure guess

 

 

low D from hand, LHO low D, DK, RHO low D, Dx from table, RHO low D, pure guess

 

 

Also same - either we have pure guess, or see the Q (no guess), if RHO start with xx or Qxx.

 

 

:ph34r: :ph34r:

 

 

 

 

P.S. Edited a few times for complexity. But hope you get my idea/reasoning (though I am not sure if I am right).

 

 

Enjoyed the problem!!!!

[inquiry]

-> pure guess

I think, the question raised here is why an "expert" in EAST would show you his heart with a heart discard, instead of throwing a spade.

 

This leaves you with the following infomation. EAST has two diamonds WEST has three. The "pure guess" is now a no longer an issue. You know that WEST is 3/5th chance to hold the diamond queen, East 2/5th. Instead of a blind guess you are a 3/2 favorite if you hook WEST. The question is, why didn't EAST discard his known spade. Now EAST could have three diamonds west two, or the other way around. You can't know.

 

Did East share this "data" with you so you could calculate the odds favor finessing his partner? Why would he do that? To help you out? Maybe you think he did it so you would finessee his parner becasue he has Qx of diamonds. In that case, you go against the odds. But, maybe he did it because he knew you were good enough to realize he wouldn't be wanting you help you get the count, so he is pretending to have Qx doubleton so you will not hook his partner.

 

This is a mind game. I think that is the point. If EAST is that good, just go with the odds and play the man with three diamonds to have the queen.

[andych]

-> pure guess

I think, the question raised here is why an "expert" in EAST would show you his heart with a heart discard, instead of throwing a spade.

 

This leaves you with the following infomation. EAST has two diamonds WEST has three. The "pure guess" is now a no longer an issue. You know that WEST is 3/5th chance to hold the diamond queen, East 2/5th. Instead of a blind guess you are a 3/2 favorite if you hook WEST. The question is, why didn't EAST discard his known spade. Now EAST could have three diamonds west two, or the other way around. You can't know.

 

Did East share this "data" with you so you could calculate the odds favor finessing his partner? Why would he do that? To help you out? Maybe you think he did it so you would finessee his parner becasue he has Qx of diamonds. In that case, you go against the odds. But, maybe he did it because he knew you were good enough to realize he wouldn't be wanting you help you get the count, so he is pretending to have Qx doubleton so you will not hook his partner.

 

This is a mind game. I think that is the point. If EAST is that good, just go with the odds and play the man with three diamonds to have the queen.

If the Expert RHO show me his Heart, he tells he has 2 Dia and LHO has three D.

 

But did he lose anything? No....

 

We can say that LHO is more likely to have the DQ before playing any D.

 

When we start with DA and small D, what D to play from dummy is pure quess.

 

Even we start with low D to dummy DK, we have not gained anything. Or we have not lose anything comparing with playing DA and small D. We just know the result sooner. Either RHO drops DQ at 2nd D, or we are going to lose a D to LHO if RHO doesnt drop DQ.

 

 

Agree??

 

We should start with DA and small D after we know RHO has 2 D? It seems so only. Playing small D to DK in 1st trick is just as good.....

 

 

 

 

P.S. Again edited a few times for complexity. Interested parties pls reread.....

[pclayton]

I think this is an interesting problem presented in an interesting format.

 

I've gotta run out to a meeting. Could someone post the hand diagram with the relative info? Its easier to digest instead of reading a recital of what has happened.

[Blofeld]

-> pure guess

I think, the question raised here is why an "expert" in EAST would show you his heart with a heart discard, instead of throwing a spade.

 

This leaves you with the following infomation. EAST has two diamonds WEST has three. The "pure guess" is now a no longer an issue. You know that WEST is 3/5th chance to hold the diamond queen, East 2/5th. Instead of a blind guess you are a 3/2 favorite if you hook WEST. The question is, why didn't EAST discard his known spade. Now EAST could have three diamonds west two, or the other way around. You can't know.

 

Did East share this "data" with you so you could calculate the odds favor finessing his partner? Why would he do that? To help you out? Maybe you think he did it so you would finessee his parner becasue he has Qx of diamonds. In that case, you go against the odds. But, maybe he did it because he knew you were good enough to realize he wouldn't be wanting you help you get the count, so he is pretending to have Qx doubleton so you will not hook his partner.

 

This is a mind game. I think that is the point. If EAST is that good, just go with the odds and play the man with three diamonds to have the queen.

Agree with Ben's analysis but not with the final conclusion.

 

If we don't think we can beat East at mind games, I think from a game theoretic point of view we should take the hook against West 60% of the time and against east 40% of the time. Otherwise East will do best by only dropping the heart when he holds Qx.

[andych]

-> pure guess

I think, the question raised here is why an "expert" in EAST would show you his heart with a heart discard, instead of throwing a spade.

 

This leaves you with the following infomation. EAST has two diamonds WEST has three. The "pure guess" is now a no longer an issue. You know that WEST is 3/5th chance to hold the diamond queen, East 2/5th. Instead of a blind guess you are a 3/2 favorite if you hook WEST. The question is, why didn't EAST discard his known spade. Now EAST could have three diamonds west two, or the other way around. You can't know.

 

Did East share this "data" with you so you could calculate the odds favor finessing his partner? Why would he do that? To help you out? Maybe you think he did it so you would finessee his parner becasue he has Qx of diamonds. In that case, you go against the odds. But, maybe he did it because he knew you were good enough to realize he wouldn't be wanting you help you get the count, so he is pretending to have Qx doubleton so you will not hook his partner.

 

This is a mind game. I think that is the point. If EAST is that good, just go with the odds and play the man with three diamonds to have the queen.

Agree with Ben's analysis but not with the final conclusion.

 

If we don't think we can beat East at mind games, I think from a game theoretic point of view we should take the hook against West 60% of the time and against east 40% of the time. Otherwise East will do best by only dropping the heart when he holds Qx.

After RHO discards his Heart, we could say so LHO is 60% having the DQ.

 

But it does not make finissing LHO for DQ in favor of dropping RHO DQ.

 

 

Hand LHO Dummy RHO

DA Dx D9 Dx

Dx Dx ??

 

Pure guess.

The last D from LHO (his 3rd) is 50% DQ.

The last D from RHO (his 2nd) is 50% DQ.

 

We are not better off.

 

Whatever card RHO discards on C is irrelevant......

Whatever RHO is (expert/idiot??) is irrelevant.....

[Guest Jlall]

Pure guess.

The last D from LHO (his 3rd) is 50% DQ.

The last D from RHO (his 2nd) is 50% DQ.

 

We are not better off.

 

Whatever card RHO discards on C is irrelevant......

Whatever RHO is (expert/idiot??) is irrelevant.....

Sorry I don't believe in pure guesses this late in the hand :ph34r:

 

Ben has it right, this is a mind game. I'm just curious about general thoughts people have, this is obviously very situational as to what you actually do.

 

We do have information though. If we choose to completely disregard everything, maybe it is a pure guess, but bridge is about filtering through the information.

[inquiry]

Could someone post the hand diagram with the relative info? Its easier to digest instead of reading a recital of what has happened..

 

[hv=n=shdkjt9c&w=shdxxxcj&e=sah3dqxc&s=shdaxxca]399|300|Position one. East thows ♥x on club. He is know to hold the 13th spade[/hv]

 

[hv=n=shdkjt9c&w=shdxxxcj&e=sah3dqxc&s=shdaxxca]399|300|Position one. East thows ♥x on club. He is know to hold the 13th spade[/hv]

 

[hv=n=shdkjt9c&w=shdxxxcj&e=sah3dqxc&s=shdaxxca]399|300|Position one. East thows ♥x on club. He is know to hold the 13th spade[/hv]

 

In the first two cases EAST dicards a heart on the club ACE. That tells you 100% certainy about the diamond distribution (three with WEST, two with EAST). How do you play?

 

In case 3, EAST discards the "Expected" 13th spade. Now you have no idea who has three diamonds, and who has the 13th hearts. Equally, you don't know who has the diamond queen either. In this third case, finding the queen is 50-50, you will get it right half the time (assume no other clues). Pitching the heart (cases one and two) however can give you additional infomation. The only question is can you trust it.

 

Lets assume EAST never throws a heart (case three). You wil be right half the time (either way you go... to keep it simple, you will hook WEST all the time, but you can hook either randomly).

 

Lets assume EAST thows the heart giving you count. IF he only does this while holding the diamond queen, you would have 100% line by playing him for the queen. If he only does this while not holdling the queen (double cross), you will have a 100% line playing his partner for the queen. IF he does this 1/2 the time while holding the queen, your best chance is to play his partner for the queen. If he does this exactly 60% of the time holding the queen and 40% of the time not holdign the queen, you will be right half the time if you hook WEST.

 

There are some players (lets call them "bright experts") who;s style might be to "help" you by pitching the heart 100% when holding the Qx. They are actually more helpful if you know their style than those who throw a spade. I think this is where Justin was going. And if the match their percentage up exactly right with their heart discard? You are back to square one, just as if they discarded the spade

[andych]

Could someone post the hand diagram with the relative info? Its easier to digest instead of reading a recital of what has happened..

 

Dealer: ????? Vul: ???? Scoring: Unknown

♠ [space] ♥ [space] ♦ KJT9 ♣ [space] ♠ [space] ♥ [space] ♦ xxx ♣ J ♠ A ♥ 3 ♦ Qx ♣ [space] ♠ [space] ♥ [space] ♦ Axx ♣ A

Position one. East thows ♥x on club. He is know to hold the 13th spade

 

Dealer: ????? Vul: ???? Scoring: Unknown

♠ [space] ♥ [space] ♦ KJT9 ♣ [space] ♠ [space] ♥ [space] ♦ Qxx ♣ J ♠ A ♥ 3 ♦ xx ♣ [space] ♠ [space] ♥ [space] ♦ Axx ♣ A

Position two. East thows ♥x on club. He is know to hold the 13th spade

 

Dealer: ????? Vul: ???? Scoring: Unknown

♠ [space] ♥ [space] ♦ KJT9 ♣ [space] ♠ [space] ♥ (X) ♦ (Q)xx ♣ J ♠ A ♥ (3) ♦ (Q)xx ♣ [space] ♠ [space] ♥ [space] ♦ Axx ♣ A

Position three. East thows the known ♠ on club, the location of the 13th ♥ is unknow

 

In the first two cases EAST dicards a heart on the club ACE. That tells you 100% certainy about the diamond distribution (three with WEST, two with EAST). How do you play?

 

In case 3, EAST discards the "Expected" 13th spade. Now you have no idea who has three diamonds, and who has the 13th hearts. Equally, you don't know who has the diamond queen either. In this third case, finding the queen is 50-50, you will get it right half the time (assume no other clues). Pitching the heart (cases one and two) however can give you additional infomation. The only question is can you trust it.

 

Lets assume EAST never throws a heart (case three). You wil be right half the time (either way you go... to keep it simple, you will hook WEST all the time, but you can hook either randomly).

 

Lets assume EAST thows the heart giving you count. IF he only does this while holding the diamond queen, you would have 100% line by playing him for the queen. If he only does this while not holdling the queen (double cross), you will have a 100% line playing his partner for the queen. IF he does this 1/2 the time while holding the queen, your best chance is to play his partner for the queen. If he does this exactly 60% of the time  holding the queen and 40% of the time not holdign the queen, you will be right half the time if you hook WEST.

 

There are some players (lets call them "bright experts") who;s style might be to "help" you by pitching the heart 100% when holding the Qx. They are actually more helpful if you know their style than those who throw a spade. I think this is where Justin was going. And if the match their percentage up exactly right with their heart discard? You are back to square one, just as if they discarded the spade

Still I believe I am correct.....

 

 

The expert RHO holding Qx doesnt hurt you or himself by discarding H.

 

Yes you know LHO has 3 Dia and expert RHO has 2 Dia.

 

Also you play 1st round DA and collect 2 low D from opps. It is irrelevant. You know it before playing any D.

 

2nd D from hand LHO low ... <====== problem comes only until this point of time. At this point of time, both LHO/RHO has 1 D left. You have to determine who has the DQ.

 

You can forget anything before the hand.... anything about the D distribution.....

 

It is the same problem as if you are playing 7C holding

 

 

Your hand

S -----

H -----

D Axx

C AKQJT98765

 

 

RHO hand

S AQKQJT9

H AKQJT

D Qx

C -----

 

or RHO hand

S AKQJT9

H AKQJT

D xx

C -----

 

 

:ph34r: :ph34r:

 

Happy to see more response .....

[han]

I completely agree with Ben's last post (and I didn't read most others). Note that Meckstroth can play the heart more or less often while maintaining the pure guess, as long as he throws the heart 3/2 as often while holding the queen. For instance, he could throw it 90% of the time when he has the queen, and 60% of the time when he doesn't. Or he could never throw a heart. The point is, when playing against a top expert, it is still close to a 50/50 guess, while against a beginner you might gain by drawing the right inference.

[Al_U_Card]

Mindgames only work if you let them. Once you see the pitches (whatever they may be) expect deception and finesse thru the expert or the person you like the least as this causes the least pain and gets you a better story to tell when it works and if it doesn't well then, hey, a WC fooled you, way to go!

[inquiry]

2nd D from hand LHO low ... <====== problem comes only until this point of time. At this point of time, both LHO/RHO has 1 D left. You have to determine who has the DQ.

 

You can forget anything before the hand.... anything about the D distribution.....

Er.. no.

 

Your right up implies after WEST play a low diamond on the second roudn and before EAST plays each have one diamond remaining, so the odds are equal you will drop the queen if you go up or if you hook.

 

This is not true in this setting, mathematically (before mind games). For jsut as you note on the first diamond, EAST will paly low. If you known diamonds to be 3-2, WEST will play low on the second round. This is a certaintly. But there were more chances the queen was with WEST, and these more chances still exist after he plays low twice.

 

Let's take your statement. "EAST with Qx can discard a heart without hurting himself" to mean you suggest with Qx it will occur to him to throw a heart, but with xx it will not. Now you play east for the heart, and you are right 100% of the time. Or lets assume you meant it as EAST will throw a heart from any doublton diamonds. Now you will play WEST for the heart and be right 60% of the time.

 

So if EAST adopts a play a heart strategy anytime holding doubleton or anytime holding Qx specifically, it is a losing one in the long run. Becasue if he simply played a spade you would have had a 50=50 chance to get the ending right.

 

Now EAST will NEVER have the oppotunity to play a heart if he didn't have one. Which means he has three diamonds, and thus a 60% chance to hold the diamond queen. So if EAST always plays a heart when he has one, the fact that he didn't play one also has an effect on your play.

 

Does your head hurt yet? This third possibility actually changes the rate at whcih the heart should be discarded. If you play it 60% of the time you have three hearts, that menas you only play it 30% of the time overall. GACK, so 70% of the time you dont;s play, you will have three hearts 35% of the time, and the queen 60% of that. It is not a dream, it is a nightmare.

[Al_U_Card]

Does your head hurt yet? This third possibility actually changes the rate at whcih the heart should be discarded. If you play it 60% of the time you have three hearts, that menas you only play it 30% of the time overall. GACK, so 70% of the time you dont;s play, you will have three hearts 35% of the time, and the queen 60% of that. It is not a dream, it is a nightmare.

3 hearts? If you don't mean 3D then my head REALLY hurts....

[mikeh]

I am late to this thread, so apologize for repeating what others have said :ph34r:

 

Pitch a ♦

 

A palooka is more or less random, but is more likely to pitch a ♠ from 1=0=Qxx=0 than a ♦, so I cash A and hook LHO

 

An expert is more likely to reduce to Qx and a good ♠ because he will feel much better beating you 2 tricks on the mindgame. This factor of how do you feel after a certain line, when an alternative was equivalent, is a real factor.

 

Meckstroth (or clone) is going to randomize his pitch with 1=0=3=0 regardless of his exact ♦ holding.

 

 

With a ♥ pitch, the palooka was just throwing an idle card without realizing that the ♥ and the♠ were not equivalent, so I would hook LHO

 

With the expert, the expert was giving me too much info, so I hook him unless he is a real expert and thinks that I can play, in which case I hook LHO, on the basis of relative emotional cost/benefit analysis.

 

With the Meckstroth, I mentally flip a coin.

 

The emotional cost benefit analysis is real:

 

My real life partner and I bid to a slam in a long auction in which it wsa clear that he lacked a ♠ control and that I held the K♠ but not the A.

 

A real expert on lead led a small ♠ in normal tempo and dummy was KJ10 opposite xx.

 

My bet is that 60% or more of experts would play the King in this situation. I'd like to predict 80%, but prediction is a risky business. All opps would lead a ♠ on our auction, but only agood player would underlead an Ace smoothly.

 

If the K lost, well, you went down making an expert play and paying a compliment to your expert opp. If the J lost to the Queen, you have given LHO a good story: a story of how he outwitted you on opening lead. The decision is not even close.

 

PS partner went right when he popped the K.

 

PPS I appreciate the elaborate analysis of others and I am not arguing with them, but I would not try to delve that deeply into mind games at the table: I'm too lazy and if I did, I'd be letting them win by draining my energy anyway :ph34r:

[Guest Jlall]

Not surprisingly, all of my conclusions were the same as Mike's.

 

A bad player will never pitch from the DQ so just finesse their pard.

 

An "expert" is probably pitching from the queen trying to mess with you, so hook them for it.

 

As for Meckstroth, I think it does depend what level he thinks you're operating at and he would not "randomize" his carding if he thinks you are some intermediate level player. He would probably have the queen thinking you are not deep enough to figure it out. If he thinks you are a good player, I agree he will probably be randomizing it.

 

Anyways in my dream, I snickered at Meck for even thinking I would fall for this discard. Clearly he knew I would see right through it if he was pitching from the queen, and he knew that I knew that. Thus he thought I would play him to be pitching from xx, and was executing a standard triple cross by actually having the queen. I immediately hooked him out of his queen and made my grand to win a close final of the spingold...

 

Then I woke up.

[han]

Nicely done Justin, you showed him!

[Guest Jlall]

Nicely done Justin, you showed him!

yeah what a fish :(

[Fluffy]

When I do this kind of things on my dreams LHO low ♦s are the 5 and 4, while I also have the 4 on my hand, then the hand gets averaged :/