[foo]

Unless I am playing rank novices, I always assume an opponent is =capable= of falsecarding.

What I don't assume is that the chance of said falsecard is so high that I should automatically change my plans based on that possibility.

Probability, not possibility, should dictate the best plan for playing the hand unless some non mathematical factor weighs in. As Dorothy Truscott once said "all the math in the world is not worth an opponent's hitch telling you what they have."

So many players "grow up" these days without playing much money bridge that it seems the value of Table Feel and Partnership Management is not nearly as appreciated as it used to be.

IME, Table Feel matters more than math in deciphering what to do vs these potential mandatory Falsecard situations ATT.

Unfortunately, I do not seem to be making that point as clearly as I wish to.

[Stephen Tu]

Quote

Unless I am playing rank novices, I always assume an opponent is =capable= of falsecarding.

What I don't assume is that the chance of said falsecard is so high that I should automatically change my plans based on that possibility.

No, of course you shouldn't automatically change. You have to estimate the probability that an opponent is capable of falsecarding, and if he is capable, the frequency of which he will actually do so, and then compare to the alternative line. If you don't always assign probabilities to what card an opponent will choose when he has legitimate choice of plays, your analysis will be garbage.

The point of the matter is that stiff J is very rare, only 2.6% a priori. It's only 1.1% more frequent than you would expect the J to be played from JT doubleton (where the drop is superior).

On the other hand, JTx at 10.2% is quite common in comparison. Now, only an expert opponent is going to falsecard all the time, and only half the time he'll play the J. But 5.1 >>> 1.1. So against an expert it's clear to play for the drop. Now against a lesser player, maybe he'll remember to do so less than half the time, so maybe only 2% out of the original 10.2% he'll play the J. That *still* makes the drop better than the hook. Only against the people that have no clue that they are supposed to do this, so that the chance it's a falsecard is < 1.1/10.2, would the hook be better.

You are saying you shouldn't play for the drop since the possibility of a falsecard is low. But the possibility of stiff J is ALSO very low, and in fact the hook will be worse than the drop if you think your opponent is capable of playing the J even just 1/8 of the time he has that holding.

You can't make your points clearly because you are simply wrong. If you were right, you could identify the flaws in everyone else's logic better than we have with yours. Foo you'd be better off not trying to use math in your arguments, if you just argued that most people are idiots and would never falsecard your argument would be stronger. Once you start throwing out bogus numbers like "23% it's a falsecard" it undermines you.

Quote

Table Feel matters more than math

You seem to be contradicting yourself. First you say you should follow the numbers. Now you want to back table feel, since we've shown that your numbers are ridiculous.

Table feel can be quantified and treated mathematically to make a decision. You simply use table feel to adjust the probability you assign to the choice of plays. If your feel tells you your opponent is weak and would never falsecard, that the J is stiff, then you've just assigned 0% to the falsecard chance and you can justify taking the hook. But if you are playing against an expert, this would be a big mistake. Your prior claim was that the hook is better vs. all players and this is simply not true no matter how you analyze it.

[foo]

Let's try this again.

"All the math in the world is not worth an opponent's hitch telling you what they have."

IME, Table Feel matters more than math in deciphering what to do vs these potential mandatory Falsecard situations ATT.

IOW, I disagree with you that the math generates significant enough numbers that you should be assuming the opponents have Falsecarded unless you have additional evidence to support that hypothesis.

[matmat]

Quote

Play the odds. Not the opponents. Unless you are very confident of your table feel
xx
+
AKQ9xx

Quote

OW, I disagree with you that the math generates significant enough numbers that you should be assuming the opponents have Falsecarded unless you have additional evidence to support that hypothesis.

do you read what you write?

[foo]

matmat, on Nov 20 2007, 02:28 AM, said:

Quote

Play the odds. Not the opponents. Unless you are very confident of your table feel
xx
+
AKQ9xx

Quote

OW, I disagree with you that the math generates significant enough numbers that you should be assuming the opponents have Falsecarded unless you have additional evidence to support that hypothesis.

do you read what you write?

Yep. Those advocating the play for drop against the expert but the play for split honors vs a non expert are basically saying that the expert is predictable enough that you should =trust an expert to always Falsecard=.

I've been saying all along that one should not trust an opponent to have Falsecarded without additional evidence to back it up.

The numbers involved are single digits of percentages that are very easily tipped in either direction.

I've been saying all along that Table Feel is a more reliable indicator of whether a Falsecard has taken place than just this math unless this math is backed by more confirmatory evidence.


As an aside, let's say random expert notices that all his opponents automatically play him to Falsecard 100% of the time when a Falsecard situation exists.

So he tweaks things so he plays a completely random card from the "mandatory falsecard" holding every time the the situation comes up.

Now when the card that hits the table is one that =could= be a Falsecard, the opponents can not so easily assume that the expert has Falsecarded. After all, sometimes he does and sometimes he doesn't...

Since this strategy rates to work more often than either never Falsecarding or always Falsecarding, it would seem clear that an expert's defense will indeed evolve in this direction.

[the hog]

Justin isn't this a restricted choice situation as well? I must admit I have never fully understood the rationale behind restricted choice, but if lho drops the J or T doesn't restricted choice suggest you should hook?

[Gerben42]

Yes in principle, but no because RHO may drop J or T from JTx as well to confuse you.

[the hog]

Jlall, on Nov 20 2007, 04:39 PM, said:

The_Hog, on Nov 20 2007, 03:50 AM, said:

Justin isn't this a restricted choice situation as well? I must admit I have never fully understood the rationale behind restricted choice, but if lho drops the J or T doesn't restricted choice suggest you should hook?

The classic restricted choice holding is AKT9x opp xxxx. When you play the ace the queen drops behind you. The reason you should hook is that the possible options are

QJ tight
Q stiff

QJ tight is slightly more likely (since a specific 2-2 combo is more likely than a specific 3-1 combo), however the Q will be played from only half the QJ tights combos, so stiff Q is much more likely than half of the QJ tights.

In this case the possible options when the jack drops are:

J
JT
JTx(3)

Since there are 3 combos of JTx and one of JT, thats a total of 4 combos that playing for the drop wins against. However, as you noted, restricted choice applies, and the jack will only be played half the time from JTx and JT. Half of the 4 combos still leaves 2 combos. This is still (much) greater than the one combo that hooking wins against.

If you can rule JTx out because your opponent is not capable of dropping the jack from that holding you're again reduced to a situation analagous to my first example.

J
JT

The same restricted choie argument would now argue for a finesse.

Thanks.

[foo]

Justin's post on Restricted Choice should be pinned.

Nice job Justin.

[glen]

even better he should blog it

[han]

Yes, very nice explanantion. Perhaps correct spelling before stickying it

[Stephen Tu]

Quote

Yep. Those advocating the play for drop against the expert but the play for split honors vs a non expert are basically saying that the expert is predictable enough that you should =trust an expert to always Falsecard=.

No, to prove the drop is superior, it is sufficient to trust the expert to falsecard *enough*, here playing the J at least ~1/9 of JTx and playing randomly from JT tight, *always* is not necessary. But an expert really ought to always play either the J or the T here. Why would a known expert ever not want to falsecard vs. a person like you? *It is a ZERO COST play, and he gets an extra trick from you every time he does it!* Experts don't pass up freebies. Against the people like me who know that he is an expert, and will play for the drop, he has lost nothing, because if he doesn't falsecard I was still going to pick up the suit. And he picks up massively vs. people like you who don't know how to analyze the situation, and laughs when you insult him and hook into his T when the suit was 3-2 all along.

*On this layout (JTx behind declarer, xx in dummy), there is never an advantage in not falsecarding by playing x*. Falsecarding anything less than the maximum only reduces the # of tricks vs. mistaken declarers. Not falsecarding never takes more tricks on this layout. If you play x, everyone from rank novice to expert is playing the drop.

Vs. me, it doesn't matter what he does, I pay off to stiff J.
Vs. you, who is picking up stiff J, why would he not want to falsecard all the time to counter this?

There do exist suit combinations where best defense involves falsecarding less than 100% of the time, where doing it too often is exploitable just like not doing it often enough. THIS IS NOT ONE OF THEM.

Quote

Now when the card that hits the table is one that =could= be a Falsecard, the opponents can not so easily assume that the expert has Falsecarded. After all, sometimes he does and sometimes he doesn't...

Never helps him on this layout. If it could be a falsecard with any reasonable frequency I am supposed to play for the drop, so this layout I pick up JTx & Jx, lose to stiff J. You on the other hand want to hook, so you pick up stiff J, lose to JTx/JT playing the J, so the opponent maximizes his advantage by playing the J as often as he can.

Even if defender is falsecarding much less than always for no particular reason, it doesn't have to be much for the drop to be superior because there are just so many more JTx combos than J stiff combos. They have to falsecard w/ J ~< 1/10 of the time, (~ < 1/5 time overall including falsecards w/ T) for hooking when an honor appears to the left to be better.

Quote

Since this strategy rates to work more often than either never Falsecarding or always Falsecarding, it would seem clear that an expert's defense will indeed evolve in this direction.

On some combos, yes. For example QJ doubleton tight behind declarer. Playing the Q all the time is as exploitable as playing the J all the time, it is right to mix it up.

BUT THIS COMBO IS NOT THE SAME. Best defense from JTx is to mix it up between playing the J & playing the T, BUT YOU NEVER HAVE TO PLAY THE x to be optimal here.

[Blofeld]

Hence the term, "mandatory falsecard".

[skjaeran]

Stephen Tu, on Nov 19 2007, 02:39 AM, said:

If you want to throw in the Jx/Jxx combos

Jxx can't come into play either, since the T will then show up when you play a small from xx (originally) after laying down the ace.

[Edmunte1]

Jlall, on Nov 20 2007, 04:39 AM, said:

The_Hog, on Nov 20 2007, 03:50 AM, said:

Justin isn't this a restricted choice situation as well? I must admit I have never fully understood the rationale behind restricted choice, but if lho drops the J or T doesn't restricted choice suggest you should hook?

The classic restricted choice holding is AKT9x opp xxxx. When you play the ace the queen drops behind you. The reason you should hook is that the possible options are

QJ tight
Q stiff

QJ tight is slightly more likely (since a specific 2-2 combo is more likely than a specific 3-1 combo), however the Q will be played from only half the QJ tights combos, so stiff Q is much more likely than half of the QJ tights.

More, for understanding the restricted choice, here are the probabilities for the holdings:
23 - QJ holding is 40.7% / 6cases = 6.78%
23J - Q holding is 49.7%/8 cases = 6.21%

So it seems that playing for the drop is more likely, and most of the people don't understand that explanation that holding QJ tight the defender has to choose from playing either the Jack or the Queen because they don't think about another case

23Q-J holding is 49.7%/8 cases = 6.21%

I'll try to explain it differently.
Suppose that your general strategy in 100 boards when you hold AKT9x opp. xxxx (or similar holdings) after cashing Ace, and the QUEEN drops - to play for the drop, you'll win in 52/100 boards (6.78/(6.78+6.21).

BUT this strategy doesn't take into account the case when you cash the Ace and JACK drops.

If we consider a general strategy when we cash the Ace and a Honour drops (from our point of view Jack and Queen are equals, we can call them Q1 and Q2) then:

- playing for the finesse will win in (6.21 (Q1 drops)+6.21(Q2 drops))/(6.78+6.21+6.21)=64.7%
- playing for the drop will win in 6.78/19.2 =35.3%

[lilboyman]

In "Bridge Odds fot Practical Players", by Kelsey & Glauert, it is written on page 24 that "If two honour cards in a suit are missing,there is a 52% chance that they will be split between the opponents, a 48% chance that the same opponent will have them both." Contining to to page 95 where the authors discuss restricted choice it is written, "When a defender follows suit or wins a trick with one of two equivalent cards, the probability of his having both cards is halved." Hence, it would seem that there is only a 24% chance that LHO has the ten and the finesse should win 76% of the time.

[Stephen Tu]

Oh wonderful, another person who can't count ...

It is true, *before we play any cards*, that LHO will have J+T only 24% of all possible times. But once we play a round and RHO follows & LHO plays the J, the sample space collapses. All the hands where RHO might have J disappear. The possibility RHO is void disappears. The possibility RHO has stiff T disappears. Also, your reasoning presumes that LHO will play the J whenever he has it, even when he started with irrelevant holdings like JTxx, Jxx, Jx, where it won't matter what we do and the opp wouldn't do it anyway.

The ONLY holdings where it matters are JTx, JT, J, to do the analysis you halve the first two because of restricted choice principles. And you multiply the first one by an estimate of whether your opponent knows this is a mandatory falsecard situation, if an expert this would be 100% or close to it, if a novice you might be close to 0%.

The odds of LHO having J and T having no prior knowledge, is not the same as asking how often LHO has the T already knowing that he has the J and either chose or was forced to play it.

[gwnn]

"Even though while I read through the thread I saw many many words I didn't really understand, let me just write down what I think is right. After all, all that incomprehensible talk about falsecards and Latin words and "%" signs might just be nonsensical"