Suit combo

[benlessard]

[hv=pc=n&s=s2hdc&n=skj8763hdc]133|200[/hv]

 

 

Acording to suit play low to the J is better. However I dont see a why its not equal to low to K. Since with both holding you have to play the 2nd honnor at trick 2 to crash a T or 9 doubleton.

 

Ax --- QT9x

 

playing the J = 4 losers while playing the K = 3 losers

 

Qx --- AT9x = if you guess wrong still 4 losers if you guess right 3 losers.

 

 

Its the same for a stiff honnoer in RHO.

 

Im probably too tired but I just dont see it.

[GreenMan]

I may be way off the wall, but ... maybe playing the J allows for the small but nonzero chance that LHO would go up ace if she had it. No LHO would play the Q voluntarily, so when she plays small, there's a very slight advantage to playing the J.

[Free]

I may be way off the wall, but ... maybe playing the J allows for the small but nonzero chance that LHO would go up ace if she had it. No LHO would play the Q voluntarily, so when she plays small, there's a very slight advantage to playing the J.

Suitplay doesn't account for falsecards, voluntary dumping honors,... It just looks at DD. However I can't think of a situation where the J wins with a similar situation where the K loses. Intuitively I would even think that playing the K is slightly better.

[PhilKing]

What has West followed with? If they have followed with a true 9 or T, then the jack is better.

[gwnn]

Suitplay doesn't account for falsecards, voluntary dumping honors,... It just looks at DD. However I can't think of a situation where the J wins with a similar situation where the K loses. Intuitively I would even think that playing the K is slightly better.

Suitplay assumes optimal defence (assuming defenders know the complete layout), which includes mixed strategies with a/the optimal % of mixing (for many layouts the optimal % is any one of a range of percentages, like for the classical "what to play from QJ doubleton?" the optimal % is I think anywhere between 10-90%). So it does account for falsecards and voluntary dumping of honours.

[SteveMoe]

Ben, it looks as if the solution is asymetric in an unexpected way. I find it fascinating.

 

Of the 64 cases, only 24 show a difference between the 2 lines of play. There are 12 cases each for leading to the J (call this "A") and leading to the K (Call this "B"). Of the 12 cases favoring A, 4 win 3 tricks for A to 2 for B. Of the 12 cases favoring B, 5 cases win 3 tricks to 2 for A. Thus A has ONE MORE CASE where it wins 4 tricks than B does. Note there are only 8 patterns comprising the cases for each line.

 

Hand tabulating the data from Suit Play shows:

................................TRICKS

West-East.......#.......prob....A...B

AQ-T9xx.........1.......0.0161..3...4

AT9xx-Q.........1.......0.0121..2...3

AT9x-Qx.........2.......0.0323..2...3

AT9-Qxx.........1.......0.0178..3...4

ATx-Q9x.........2.......0.0355..3...4

A9x-QTx.........2.......0.0355..3...4

Axx-QT9.........1.......0.0178..3...4

Ax-QT9x.........2.......0.0323..2...3

...............12.......0.1994

 

QT9x-Ax.........2.......0.0323..3...2

QT9-Axx.........1.......0.0178..4...3

QTx-A9x.........2.......0.0355..4...3

QT-A9xx.........1.......0.0161..4...3

Q9x-ATx.........2.......0.0355..4...3

Q9-ATxx.........1.......0.0161..4...3

Qxx-AT9.........1.......0.0178..4...3

Qx-AT9x.........2.......0.0323..3...2

...............12.......0.2034

 

All other cases result in equivalent results between A and B. Looks to me like the difference is in the QT-A9xx and Q9-ATxx instances.

 

The payoff table shows this is a close decision:

 

..............A.........B

P(4).......24.224.....22.609

P(3).......80.342.....81.553

P(2).......98.509.....98.509

 

E(Tricks)..3.031.......3.027

 

...a razor thin difference.......

[benlessard]

AQ-T9xx.........1.......0.0161..3...4

QT-A9xx and Q9-ATxx instances

 

 

These cases are irrelevant since an honnor appear at trick 1.

 

If you click a small card by West SP underline the J but not the K.

 

Also there is no difference between KJ87xx and KJ876x wich mean the 5th round of the suit is irrelevant

[SteveMoe]

AQ-T9xx.........1.......0.0161..3...4

QT-A9xx and Q9-ATxx instances

 

 

These cases are irrelevant since an honor appear at trick 1.

 

If you click a small card by West SP underline the J but not the K.

 

Also there is no difference between KJ87xx and KJ876x wich mean the 5th round of the suit is irrelevant

 

Trying one more time...

................................TRICKS

West-East.......#.......prob....A...B

AQ-T9xx.........1.......0.0161..3...4

AT9xx-Q.........1.......0.0121..2...3

AT9x-Qx.........2.......0.0323..2...3

AT9-Qxx.........1.......0.0178..3...4

ATx-Q9x.........2.......0.0355..3...4

A9x-QTx.........2.......0.0355..3...4

Axx-QT9.........1.......0.0178..3...4

Ax-QT9x.........2.......0.0323..2...3

...............12.......0.1994

 

QT9x-Ax.........2.......0.0323..3...2

QT9-Axx.........1.......0.0178..4...3

QTx-A9x.........2.......0.0355..4...3

QT-A9xx.........1.......0.0161..4...3

Q9x-ATx.........2.......0.0355..4...3

Q9-ATxx.........1.......0.0161..4...3

Qxx-AT9.........1.......0.0178..4...3

Qx-AT9x.........2.......0.0323..3...2

...............12.......0.2034

 

Where a trick difference exists, the grey cases are symmetrical - A replaces Q. The red cases are unique.

 

What SP underline depends on the line selected - A or B. A shows the J, B shows the K as long as the card played by West is smaller...

 

The 5th card is irrelevant because the 5-1 and 6-0 splits do not differentiate lines of play.

[gwnn]

Ha, this is strange, in line B suitplay wants to play

 

x-Q-K-x

8-?

 

but in line A he plays

x-Q-K-x

J-?

 

is this a bug??

 

Edit: of course it's not a bug, I think it just means that if LHO knows we want to play low to J, he can play the Q from Qx and should play it from QT/Q9.

[GreenMan]

West-East.......#.......prob....A...B

AQ-T9xx.........1.......0.0161..3...4

 

But in this case you will NEVER play the jack so it should not be included in the calculations. Right?

[gwnn]

But in this case you will NEVER play the jack so it should not be included in the calculations. Right?

Am I still on everyone's ignore list? :(

[PhilKing]

Trying one more time...

................................TRICKS

West-East.......#.......prob....A...B

AQ-T9xx.........1.......0.0161..3...4

AT9xx-Q.........1.......0.0121..2...3

AT9x-Qx.........2.......0.0323..2...3

AT9-Qxx.........1.......0.0178..3...4

ATx-Q9x.........2.......0.0355..3...4

A9x-QTx.........2.......0.0355..3...4

Axx-QT9.........1.......0.0178..3...4

Ax-QT9x.........2.......0.0323..2...3

...............12.......0.1994

 

QT9x-Ax.........2.......0.0323..3...2

QT9-Axx.........1.......0.0178..4...3

QTx-A9x.........2.......0.0355..4...3

QT-A9xx.........1.......0.0161..4...3

Q9x-ATx.........2.......0.0355..4...3

Q9-ATxx.........1.......0.0161..4...3

Qxx-AT9.........1.......0.0178..4...3

Qx-AT9x.........2.......0.0323..3...2

...............12.......0.2034

 

Given that West has followed small, the only non-symmetrical case appears to be stiff queen offside, making the king superior.

 

Strange. Presumably, the jack is a counter to a mixed strategy whereby West splits more often with QTx and Q9x than with ATx A9x, although I had no idea the program was that sophisticated before seeing Gwnn's post.

[benlessard]

My obscure hypothesys so far is ...

 

LHO must play the Q from AQ because if he play the A = only 2 losers.

 

he must play the Q from Q9 or QT some amount of times to protect some AQ holdings and East must duck sometimes with Amxx to protect some AQ --- T9xx.

 

When a M appear it seems that AM is slighty more probable than QM since with some QM hes playing the Q. Therefore there is a small cost here. However if defender know that declarer is always playing J at trick one if a low appear LHO can pitch the Q from Qx at free cost to protect some AM cases ! This mean that whne a small appear Ax is tiny more likely than Qx.H

 

However in theory LHO should always mix his strategies ensemble so that KorJ remain a 50-50% proposition.

 

In the end the difference is so tiny that maybe its because of floating point limit.

[gwnn]

In the end the difference is so tiny that maybe its because of floating point limit.

Not according to Suitplay, according to it it is 24.2% vs 22.6% for 4 tricks... Sorry for not being more helpful but this is not a round-off error.

[GreenMan]

Am I still on everyone's ignore list? :(

 

I must be trailing behind everyone else's reasoning. I'll just sit back and watch now.

[PhilKing]

If West never falscarded (ie playing the T from ATx, for instance), declarer could gain a suit combination to which he is not entitled, namely stiff queen offside, since all the other combos balance out if West bovinely follows small.

 

Therefore, West has to occasionally play a such a falsecard to prevent declarer from getting more than his share. As long as he does so with the correct frequency, declarer has to revert to playing the jack, which caters for more holdings a priori. Nash is thus restored.

[Trinidad]

Am I still on everyone's ignore list? :(

Did you say something?

 

;)

 

Rik

[SteveMoe]

But in this case you will NEVER play the jack so it should not be included in the calculations. Right?

Look closely - this split is part of line B, low to K not J. Line B dominant shows more tricks for B.

[benlessard]

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 ?

[PhilKing]

It's a mystery.

[catch22]

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]

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]

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.