[benlessard]

---

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]

 GreenMan, on 2013-February-17, 21:43, said:

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]

 Free, on 2013-February-18, 02:46, said:

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]

 benlessard, on 2013-February-18, 23:15, said:

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]

 SteveMoe, on 2013-February-18, 23:59, said:

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]

 GreenMan, on 2013-February-19, 02:31, said:

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]

 SteveMoe, on 2013-February-18, 23:59, said:

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]

 benlessard, on 2013-February-19, 07:40, said:

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]

 gwnn, on 2013-February-19, 02:38, said:

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]

 gwnn, on 2013-February-19, 02:38, said:

Am I still on everyone's ignore list?

Did you say something?



Rik

[SteveMoe]

 GreenMan, on 2013-February-19, 02:31, said:

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.