[antonylee]

You declare some contract with AK876 in your hand and Q54 on the board, the bidding having marked you with 5+ cards in the suit. When leading the 6, lefty puts in the jack. Do you finesse on the way back?

[karlson]

No?

[nate_m]

No.

Just think about what you pick up vs. what you lose to. If you hook every time you see an honor you blow to J9, 109, J10, and J109 offside while picking up J, 10, 9 offside. The particular honor played should not affect your decision.

[WesleyC]

The other reason you can't play for restricted choice on this layout is that LHO has an automatic falsecard holding ♠JTx.

However it gets more interesting if you change the layout to AK87 opposite Q65.

Now when you play a ♠A and ♠Q, if LHO plays two of the relevant honours: this IS a restricted choice situation (and actually a more powerful one than the traditional QJ case).

Holding JT9, LHO could play [JT, J9, T9, 9T, 9J & TJ] however, holding only Hh they have only 2 ways [hH, Hh]. So in this case, taking the finesse is significantly better than trying to drop HHH.

[1eyedjack]

WesleyC, on 2015-March-16, 20:58, said:

The other reason you can't play for restricted choice on this layout is that LHO has an automatic falsecard holding ♠JTx.

On the hand as stated, this falsecard is not going to provide declarer with any losing option. On the second round his partner will be forced to play one of the JT9 before declarer is forced to the choice, at which point rising is compulsory.

[helene_t]

Assuming he ddoesn't falsecard with j9 he has one third of jt9 plus half of jt which is odds 833/1000 by restricted choice which is just about compensated by the a priori bigger chance of a particular 3-2 split. So it must be very close. I would not finesse because he might have falsecarded.

Besides, if we sometimes finesse and he knows that then he should play jack from jt9 but that would destroy the rc argument.

[campboy]

1eyedjack, on 2015-March-17, 00:58, said:

On the hand as stated, this falsecard is not going to provide declarer with any losing option. On the second round his partner will be forced to play one of the JT9 before declarer is forced to the choice, at which point rising is compulsory.

True, but if LHO had JTx he wouldn't know that (you could have the 9) so he should still falsecard.

[campboy]

helene_t, on 2015-March-17, 03:16, said:

Assuming he ddoesn't falsecard with j9 he has one third of jt9 plus half of jt which is odds 833/1000 by restricted choice which is just about compensated by the a priori bigger chance of a particular 3-2 split. So it must be very close. I would not finesse because he might have falsecarded.

Besides, if we sometimes finesse and he knows that then he should play jack from jt9 but that would destroy the rc argument.

If you have no other information at all, P(JT9)/3+P(JT)/2 exactly equals P(J).

But, as you suggest, 1/3 might not be his optimal choice for the probability of playing the J from JT9.

[lackeman]

Hi!
In general we have more information that affekt how to play!
Whith this info only i still think that finesse is prob the best against most opps.
Seldome people play for ex Jxx like that. Say declerer have A9xxx or A10xxx from the defenders aspekt this can lose a trick. So when J comes IT is probably fr.o.m. J,JT,JTx,JT9,JT9x.. We can here then have many hands playing J. Here it is mathematically bad to finesse.
But the normal Way to play is lowest from sequence, that means à change in the "true" math. If for ex T comes he often have J.
Here "the math,restricted choose" say it is better to "play from top in trumf". But as i said we should not "turn of our senses" not leting us directing bye "everything else that happened and other factors that matters". from our experience we learn more and more and we have to let "statistik,random" play à less part in our play!
Random is not Random for ever that seamed so earlier may be understod better tan w math! But before we have understand that we can play "statistic bridge".
This is why there is no good computer (i don know of) in bridge compared w for example chess. For me this was a mystery before. Bridge is more like human "life" than for ex chess. Our brain are therfore developped to "work better". Life is observing the nature (oberving playing and bidding). Than based on the "history, and experience" the brain produced a play plan (a theory,"an Idea").
If we take chess for example "the right move" is only depended on "the actuall position" (and the experience of other chessgames").
The best to so in bridge changes therfore during a bord, more info comes in.
To value "prioritate" that right and then understand and Know how to do(better) is the factor limiting our understanding.

[lackeman]

Edit mean " in most cases i dont finesse against T9x after lho drop J"

[zillahandp]

No y on earth would you

[WesleyC]

helene_t, on 2015-March-17, 03:16, said:

Assuming he ddoesn't falsecard with j9 he has one third of jt9 plus half of jt which is odds 833/1000 by restricted choice which is just about compensated by the a priori bigger chance of a particular 3-2 split. So it must be very close. I would not finesse because he might have falsecarded.

Besides, if we sometimes finesse and he knows that then he should play jack from jt9 but that would destroy the rc argument.

The situation missing [♠JT9xxx] certainly isn't trivial, and there is some complex game-theory equilibrium of how often you should play the various honours to guarantee your side's best result.

However, I'm not sure that your maths analysis is correct. First, you can never afford to take a second round finesse (because playing an honour from JTx is a free falsecard). So wait until 2 rounds have been played before making a choice of whether to finesse the 3rd round or play for the drop. For clarity, lets consider the case where the opponent sitting behind the ♠AK87 plays ♠JT on the first two rounds.

Case 1)

They hold JT (roughly 48% chance)
They had no choice about cards to play in this scenario.

Case 2)

They hold JT9 (roughly 52% chance)

However in case 2 there were three different honour combinations (JT, T9 or 9J) which is where the restricted choice comes in.
Assuming they play each combination with equal probability, we need to divide the initial 52% chance by 3.

Normalizing this back to a comparative percentage gives:

3rd round finesse (wins on JT) ~74%.
Play for drop (wins on JT9) is ~26%.

So taking a 3rd round finesse is by far the better choice.

[helene_t]

Thanks, forgot about jtx. We are missing five cards so if he has jtx the nine will appear and it now requires his partner to play the nine on the second round from 9xx which may be pretty random while jtx requires a falsecard.

[lackeman]

The one played the J must have J,JT,JT9 or Sometimes J9. After taking the Q leading against the remaining AK8x rho then have shown the two X cards. If for ex lho have JTx, Jx,J9x,or Jx then rho must play some of the "high Cards T or 9". Then we easy take 5 tricks and obvious we cant finesse in trick 2.
Therfore we can be sure that lho 100% must have JT9,JT,J, or sometimes J9 from start. Lets say this happens 40 times ie that lho have JT9 10 times, JT 10 times, J 10 times and J9 10 times.
How often do we think the J is played? 10 times when he has only J, If J is played more than 10 Times from the other possible holdings we shall top, else finesse. That should be a personal choose.
Then IT has been a bidding, a lead, some carding, some knolidge of distribution the 3 other (cl,d,sp). Also we may have other factor that may influence our play.