[catch22]

benlessard, on 2013-April-01, 20:49, said:

I complelty forgot about this one but it seemes we still got no answer for this one ?

A priori playing the K seems right so what the catch ?

I thought Steve Moe answered it

QT-A954
Q9-AT54

is the difference. But this is a priori, so if you lead the 2 and west follows with the 4 then both lines are the same

[PhilKing]

benlessard, on 2013-April-01, 20:49, said:

I complelty forgot about this one but it seemes we still got no answer for this one ?

A priori playing the K seems right so what the catch ?

The catch is that against a declarer that believes playing the king is correct, we can simply play low in second seat from QTx or Q9x and go in with the ten from ATx. When we play the ten(or 9), if declarer just counts combinations believing us incapable of such a play, he will now play the jack since that caters for QT/Q9. We will own him both ways. Three ways if we add in the play of the Q from QT/9.

By falscarding with the correct frequency, we force declarer back to the correct a priori strategy of always playing the jack or just getting destroyed. Declarer loses out on the stiff queen offside, but correct defensive strategy forces this.

[benlessard]

PhilKing, on 2013-April-02, 17:54, said:

The catch is that against a declarer that believes playing the king is correct, we can simply play low in second seat from QTx or Q9x and go in with the ten from ATx. When we play the ten(or 9), if declarer just counts combinations believing us incapable of such a play, he will now play the jack since that caters for QT/Q9. We will own him both ways. Three ways if we add in the play of the Q from QT/9.

By falscarding with the correct frequency, we force declarer back to the correct a priori strategy of always playing the jack or just getting destroyed. Declarer loses out on the stiff queen offside, but correct defensive strategy forces this.

I think you are right, if you plan low to K, you must be willing to play low to K even if a 9/T appear because falsecarding for ATx & A9x is a mandatory and free falscard.



According to suitplay the difference between low to king and low to J is a 3.0307 vs 3.0267 wich is 4/1000 of a trick (total average of tricks, not a specific number of trick needed). Imo this mean that there is another consideration that compensate elsewhere because ATx,A9x are much more frequent than the East holding stiff Q.

In line B playing low to K if it goes.. 2QK4, declarer should play low and not the jack a trick two wich I find weird since Q9 & QT are more likely than AQ (so this mean that with Q9,QT west will play the Q only 50% Wich i also find a hard to understand. Normally the defense should tend to a Nash equilibrium
that say that both options are equal not that one is only slightly better than the other.

In the end only 4/1000 trick it make me think its might be a rounding decimal error.
In the end I think the rounding error might make some sense

[PhilKing]

Just to clarify, does it play the jack when the nine or ten appears?

Also, I was thinking it might only be necessary to play the T(9) from ATx one time in four as a minimum. Not sure about the max without becoming exploitable. The fact it feels it is entitled to AQ worries me.

[manudude03]

I just checked it on Suitplay, it plays the jack unless A/Q pops on first trick.

[benlessard]

SP divide the group in 2 lines of play.

A - Low to J against small,low to J against Mid (9 ot T). Playing the J after xQKx) against falsecard of QT,Q9.

B- low to K against small or Mid. Not Playing the J after xQKx. (therefore playing against AQ). This probably mean that defender should falsecard close to 50% with QT or Q9.

If you need 4 tricks A is better if you need 3 B is better and for average A is 4/1000 better (probably a rounding error IMO).

West will always play the Q from AQ but for the rest

-------1
If West never falsecard...

When a small appear declarer should play the K it will win against East stiff Q.

when a mid appear declarer play the J and return the K. Even if west is holding AT or A9 it change nothing.

This will gain vs Q9 or QT.

When the Q appear he will play the K, and return low since AQ is the only case.

--------2---------

If west always falsecard with Q9,QT but doesnt falsecard with ATx.

When a small appear he should play the K it will win against East stiff Q.

When a mid appear he should play the K and return the J it will win against AT,A9 and T9.

When the Q appear you cover (east should always duck) and return low against AQ by West.




------------------------------------------------------------------------

If west never falsecard with Q9,QT but always falsecard with ATx but not with Qmx.

when a small appear declarer should play the K since Qmx is now more likely than Amx

When a mid appear he should play the K since Amx is a lot more likely than Qmx or Qm.

This mean that west falsecard with Amx too much he should falscecard with some Qmx too

Im going to stop here before I bury myself deeper.