[lamford]

You have AQ6 in dummy opposite J9543 in hand. You lead the three to the two, queen and seven. You cannot afford a loser, but have a quick entry back to hand in a side-suit. What next?

[Fluffy]

lamford, on 2013-January-23, 07:42, said:

What next?

count vacant spaces?

[lamford]

Fluffy, on 2013-January-23, 07:48, said:

count vacant spaces?

There is nothing to guide you. The opponents have passed throughout, and there is no guide to distribution from the play to trick one.

[PhilKing]

I think I may need to know whether the suit is clubs, diamonds, hearts or spades.

I'm not sure how easy it is for West to play the 8 from K82 with appropriate frequency, since the wrong hand is exposed and the eight could theoretically cost a trick. Even so, playing a safe 2 makes us too predictable. I think Wirgren said each defender should play middle half the time from three even when that will occasionally cost and we should vary whether to pin or cash to avoid being owned. The article is from about four years ago - I will try and find it.

I would tend to go for the pin against most players, the drop against very creative types and just balance my strategy if they are genuinely World Class (if the suit is black I go for the drop and the pin if it is red).

[gnasher]

Against perfect defenders who know my holding in the suit, I play the ace. The jack gains against Kxx-10x (three combinations); the ace gains against Kx-10xx and x-K10xx (six combinations).

(If you prefer to think in restricted-choice terms, it's 0.5 combinations to 2 x 0.5 combinations.)

[the_clown]

gnasher, on 2013-January-23, 09:20, said:

Against perfect defenders who know my holding in the suit, I play the ace. The jack gains against Kxx-10x (three combinations); the ace gains against Kx-10xx and x-K10xx (six combinations).

(If you prefer to think in restricted-choice terms, it's 0.5 combinations to 2 x 0.5 combinations.)

Since you cant afford the loser I dont think x-K10xx is relevant at all.

[PhilKing]

the_clown, on 2013-January-23, 09:29, said:

Since you cant afford the loser I dont think x-K10xx is relevant at all.

Maybe they will unblock the king.

[lamford]

PhilKing, on 2013-January-23, 08:29, said:

I think I may need to know whether the suit is clubs, diamonds, hearts or spades.

I'm not sure how easy it is for West to play the 8 from K82 with appropriate frequency, since the wrong hand is exposed and the eight could theoretically cost a trick. Even so, playing a safe 2 makes us too predictable. I think Wirgren said each defender should play middle half the time from three even when that will occasionally cost and we should vary whether to pin or cash to avoid being owned. The article is from about four years ago - I will try and find it.

I would tend to go for the pin against most players, the drop against very creative types and just balance my strategy if they are genuinely World Class (if the suit is black I go for the drop and the pin if it is red).

My view is that against almost all players I would pin. If West had played the eight, East would need to falsecard half the time from 1072 as well. So, whenever it goes 8, Q, 7, you know someone has correctly false-carded, but do not know who. So, I would play for the drop if East plays the 2, the pin if West plays the 2, and judge which one has falsecarded if neither do! I would play the person who was more World Class to have falsecarded, in practice.

Of course the extra undertrick would play a part if East could duck from K10xx, but let us assume it is the setting trick in 6NT, which it was, so few will duck here!

[gnasher]

the_clown, on 2013-January-23, 09:29, said:

Since you cant afford the loser I dont think x-K10xx is relevant at all.

Sorry, I should read the question more carefully. Still, I may save an undertrick.

[JLOGIC]

The 8 never costs since even if partner has T9 doubleton they will just play for T9x. I wonder if anyone has ever gone for a pin after 8 Q 9 heh.

It is an interesting theory that RHO might play the 8 or the 7 from T8x since they're equals, but LHO will never play the 8 or the 7 from K72 or K82 since they are not equals. I suppose this is true vs some people, I like it. That said, I would be scared that LHO is giving suit preference or if they're really bad count.

Against good players I would always play for the drop, I think this is a well known enough scenario that good players do a good job with both Kxx and Txx of playing a random spot.

[jallerton]

lamford, on 2013-January-23, 07:42, said:

You have AQ6 in dummy opposite J9543 in hand. You lead the three to the two, queen and seven. You cannot afford a loser, but have a quick entry back to hand in a side-suit. What next?

I look to see whether or not I have a second entry back to hand.

[lamford]

JLOGIC, on 2013-January-23, 13:12, said:

Against good players I would always play for the drop.

Against good players the two relevant variations are symmetrical, and it is as much a guess as KJT opposite A98x without any other information. If the two is played by either side, there are two possibilities:
a) they are not strong enough to find the falsecard from H(8/7)x
b) they are strong enough and this is the 50% where they chose to play the small card.
If they would find the falsecard at least 50% of the time, it does not matter what you do, so you do not lose by playing restricted choice.

[PhilKing]

lamford, on 2013-January-24, 05:53, said:

Against good players the two relevant variations are symmetrical, and it is as much a guess as KJT opposite A98x without any other information. If the two is played by either side, there are two possibilities:
a) they are not strong enough to find the falsecard from H(8/7)x
b) they are strong enough and this is the 50% where they chose to play the small card.
If they would find the falsecard at least 50% of the time, it does not matter what you do, so you do not lose by playing restricted choice.

Statement b is erroneous. They can falsecard 100% or 0% as appropriate.

I assume you are playing for the drop if the two has not appeared? After all, East has the easier falsecard. (If your answer is no, at least you will sometimes make the contract, but it means you may as well not have looked at the spots in the first place).

Against this strategy the defence can simply withold the two from both sides when the king is not dropping and you go down 100% of the time. East plays the 2 only from T72 and T82, eschewing the more obvious falsecard in the main variant.

It is a game theory catastrophe when they counter with an unbalanced strategy. Perhaps Rodwell is reading this thread and will now own your soul.

The Anders Wirgren article is in the July 2008 Bridge World for any one interested.

[lamford]

PhilKing, on 2013-January-24, 06:56, said:

I assume you are playing for the drop if the two has not appeared? (If your answer is no, at least you will sometimes make the contract, but it means you may as well not have looked at the spots in the first place).

Against your strategy the defence simply withold the two from both sides when the king is not dropping and you go down 100% of the time. East plays the 2 only from T72 and T82, eschewing the more obvious falsecard in the main variant.

It is a game theory catastrophe when they counter with an unbalanced strategy. Perhaps Rodwell is reading this thread and will now own your soul.

No, when the two does not appear, the only relevant position is when one or other has falsecarded. Let us say that West plays the eight and East the seven. So, either West falsecarded with K82 or East with T72. Now I agree that game theory is to play for the drop exactly half the time, and to pin half the time, in which case the opponents' strategy is irrelevant. Varying it will not change their expectancy. If the two does not appear, and West is a client playing with Rodwell, then I will play that Rodwell has falsecarded, rather than the client has. If the client plays the two, then I play him for H8x, as he will find the falsecard less than half the time. It is only when Meckwell are together that it does not matter. And then game theory says that you should play for the drop half the time, using some factor that is random.

[PhilKing]

lamford, on 2013-January-24, 07:34, said:

No, when the two does not appear, the only relevant position is when one or other has falsecarded. Let us say that West plays the eight and East the seven. So, either West falsecarded with K82 or East with T72. Now I agree that game theory is to play for the drop exactly half the time, and to pin half the time, in which case the opponents' strategy is irrelevant. Varying it will not change their expectancy. If the two does not appear, and West is a client playing with Rodwell, then I will play that Rodwell has falsecarded, rather than the client has. If the client plays the two, then I play him for H8x, as he will find the falsecard less than half the time. It is only when Meckwell are together that it does not matter. And then game theory says that you should play for the drop half the time, using some factor that is random.

Your example of the two not appearing and West being a client misses the point. Rodwell could play the two from T72 100% of the time, for instance, and West may also always play the two, but for different reasons. You have guessed that Rodwell is the falsecarder in an imaginary position that he can ensure never happens. This opens you up to exploitation.

Besides, my statement that b was incorrect stands since your answer is a red herring - I was not referring to clients who never falsecard. I was referring to this statement "If they would find the falsecard at least 50% of the time, it does not matter what you do, so you do not lose by playing restricted choice."

[lamford]

PhilKing, on 2013-January-24, 07:49, said:

Your example of the two not appearing and West being a client misses the point. Rodwell could play the two from T72 100% of the time, for instance, and West may also always play the two, but for different reasons. You have guessed that Rodwell is the falsecarder in an imaginary position that he can ensure never happens. This opens you up to exploitation.

Besides, my statement that b was incorrect stands since your answer is a red herring - I was not referring to clients who never falsecard. I was referring to this statement "If they would find the false-card at least 50% of the time, it does not matter what you do, so you do not lose by playing restricted choice."

The statement "it does not matter what you do" is better phrased as "your expectancy is the same for either play". If you always pin, disregarding the opponents' carding, your expectancy is to be right half the time. If you always play for the drop, disregarding the opponents' carding, your expectancy is to be right half the time. We are assuming that it is one of the layouts K?2 opposite T? or K? opposite T?2. If you take into account your opponent's carding, and they outwit you, of course you can be beaten. But there is no intrinsic advantage to the opponent, unlike the game where you write down head or tail and your opponent does. You win 2 units on two different, lose 1 unit on two heads and lose 3 units on two tails.

This two-person zero-sum game is balanced, but it is not necessary for the person considering the finesse or pin to adopt a mixed strategy, unlike the coin-writing game. Just ignoring the opponents' false-card by pretending there is a dim light, and you can only make out honour cards, produces the same result as looking at the opponents' carding. But only if they play perfectly. When Rodwell is partnering the client, there is nothing he can do to compensate for his partner's failure to false-card. When his partner has the two, he will play it, and Rodwell has to play the 7 or 8, whichever he has perforce. When his partner does not have the two, declarer will know that his partner's seven or eight is more likely to be from K7 or K8, and again there is nothing Rodwell can do to disguise the situation. It takes two to tango. Interestingly, and this surprised me, there is no need for the declarer to look at Rodwell's card (assuming the jack holds and no ten appears).

[PhilKing]

lamford, on 2013-January-24, 08:59, said:

When Rodwell is partnering the client, there is nothing he can do to compensate for his partner's failure to false-card. When his partner has the two, he will play it, and Rodwell has to play the 7 or 8, whichever he has perforce. When his partner does not have the two, declarer will know that his partner's seven or eight is more likely to be from K7 or K8, and again there is nothing Rodwell can do to disguise the situation. It takes two to tango. Interestingly, and this surprised me, there is no need for the declarer to look at Rodwell's card (assuming the jack holds).

Your new points make my case for me.

You originally you stated that if the two did not appear, you would assume the world class player had false carded! There is still a need to look at his card, since he should play the two 100% of the time (it is the card he is known to hold) but might forget on a bad day. Playing the two is his only viable strategy, albeit one the entitles him to less than GTO.

Regarding the always pin or always drop method, you are making a statement of the bleeding obvious - I don't get why you brought this up since you are trying to beat GTO yourself. To focus in on the relevant strategy, could you clarify what your strategy is when West plays the seven or eight and East the two? Not against this pair, but against two good players (say two Europeans you have never seen before in a strong pairs event). I think I am clear on what you do when neither player plays the two, which I hope you have reconsidered.

Anyway, I now have a huge headache, so take your time!

[lamford]

PhilKing, on 2013-January-24, 09:27, said:

You originally you stated that if the two did not appear, you would assume the world class player had false carded! There is still a need to look at his card, since he should play the two 100% of the time (it is the card he is known to hold) but might forget on a bad day. Playing the two is his only viable strategy, albeit one the entitles him to less than GTO.

I originally stated that if the two did not appear, I would play the player that was MORE World Class to have falsecarded. We know that someone has, so it is logical to play the stronger player to have done so. Not looking at his card ONLY applies when a World Class player is partnering a weak player. The two points were in different posts. There is no need to see the World Class player's card. Even if he forgets to false-card, it is not going to change your decision.

PhilKing, on 2013-January-24, 09:27, said:

Regarding the always pin or always drop method, you are making a statement of the bleeding obvious - I don't get why you brought this up since you are trying to beat GTO yourself. To focus in on the relevant strategy, could you clarify what your strategy is when West plays the seven or eight and East the two? Not against this pair, but against two good players (say two Europeans you have never seen before in a strong pairs event). I think I am clear on what you do when neither player plays the two, which I hope you have reconsidered.

Anyway, I now have a huge headache, so take your time!

I brought up the "always pin" or "always drop" method to refute what I perhaps mistakenly thought was your idea that this would be beaten by a "mixed strategy" by two experts. You wrote: "It is a game theory catastrophe when they counter with an unbalanced strategy. Perhaps Rodwell is reading this thread and will now own your soul." The unbalanced strategy in this example does not make an iota of difference. If you told them, "I am going to finesse the queen, and regardless of what falsecards you play, I will [cash the ace/run the jack]", they would not benefit. If you told them who you would play to have falsecarded, that would be a different matter. Also if they are prepared to adopt an inferior strategy on the basis that you might they can gain, but will lose if you discern it. In our example, they have to decide first, and that gives you a game theory advantage. If they find the strategy of false-carding exactly half the time with all relevant holdings, both sides have an expectancy of zero. If they vary from that you can improve if you discern it. You will be aware that we assume the game is played a large number of times, with you going second every time.

We know that perfect strategy is either drop or pin at random in all the outcomes (because in theory all three small cards are equals). All we can do is judge how likely each opponent would be to false card. I think that in practice virtually nobody plays correct game theory. The poor player will almost never falsecard and the very good player will do so too often. He or she will want to show that he or she knows that it is a false-card situation. I also think it is more likely that East has falsecarded if the two does not appear, as that false card seems easier.

But it has given me a headache too!

[JLOGIC]

lamford, on 2013-January-24, 05:53, said:

Against good players the two relevant variations are symmetrical, and it is as much a guess as KJT opposite A98x without any other information. If the two is played by either side, there are two possibilities:
a) they are not strong enough to find the falsecard from H(8/7)x
b) they are strong enough and this is the 50% where they chose to play the small card.
If they would find the falsecard at least 50% of the time, it does not matter what you do, so you do not lose by playing restricted choice.

All I meant is I always play for the drop since I save an undertrick, and I also don't have to cross back to the other hand and use an entry. If it's 50/50 then in real life this is always a concern, going down 1 less on KTxx offside always has some value even if it's not a priority.