A Useful Theory?

[Califdude]

Having majored in math in college, I''ve long been intrigued by the so-called Principle of Restricted Choice. (If you are not familiar with that concept you might want to brush up on it before continuing.) Lately I've been toying with the idea of a possible cousin to that principle.

 

Assume you are declarer and Spades are trumps. The opponents have not bid. The opponent on your left leads a small club as the opening lead. During the play you can see no special reason for selection of a club by that player, i.g. it was not the top of a sequence, not a singleton etc..

 

During the play, the location of the king of hearts becomes the key to making the hand. Your count of the distribution of the opponents' hands gives no clue, your best guess is that hearts are divided three and three. The high cards played by the opponents combined with their bidding also does not give a clue as to the location of the king of hearts, i.g. if this opponent held the king of hearts in addition to the other high cards shown, he would have bid, does not apply.

 

OK, here's the theory I'm asking you to think about. Given that opening leaders generally try to avoid leading away from kings not part of a sequence, does the fact that the opening leader led clubs make it more likely that he holds the king of hearts? Is there a kind of restricted choice operating here, that if he did not hold the king of hearts he might have led hearts instead of clubs, so the fact that he did not makes it more likely he did not have that choice? What do you think?

[rbforster]

Yup.

[OleBerg]

The theory is sound.

 

It is very rare in the pure form you describe, but the general principel is on the repertoire of the expert player.

 

How many misspellings in the sentence above? :)

[Lobowolf]

Having majored in math in college, I''ve long been intrigued by the so-called Principle of Restricted Choice. (If you are not familiar with that concept you might want to brush up on it before continuing.) Lately I've been toying with the idea of a possible cousin to that principle.

 

Assume you are declarer and Spades are trumps. The opponents have not bid. The opponent on your left leads a small club as the opening lead. During the play you can see no special reason for selection of a club by that player, i.g. it was not the top of a sequence, not a singleton etc..

 

During the play, the location of the king of hearts becomes the key to making the hand. Your count of the distribution of the opponents' hands gives no clue, your best guess is that hearts are divided three and three. The high cards played by the opponents combined with their bidding also does not give a clue as to the location of the king of hearts, i.g. if this opponent held the king of hearts in addition to the other high cards shown, he would have bid, does not apply.

 

OK, here's the theory I'm asking you to think about. Given that opening leaders generally try to avoid leading away from kings not part of a sequence, does the fact that the opening leader led clubs make it more likely that he holds the king of hearts? Is there a kind of restricted choice operating here, that if he did not hold the king of hearts he might have led hearts instead of clubs, so the fact that he did not makes it more likely he did not have that choice? What do you think?

This is actually a fairly well-known application of Restricted Choice (though you might want to be careful about the assumption that opening leaders generally try to avoid leading from kings, particularly if the auction suggests an agressive opening lead). I think the standard example is declarer is missing the Q of trump in a slam and gets a non-descript side suit lead and draws the inference that LHO might have led a trump from xx, but never would have from Qxx, etc.

[Guest Jlall]

This is standard.

[rogerclee]

This theory is very useful. Whether it is an advanced/expert theory is another question...

[Echognome]

This theory is very useful. Whether it is an advanced/expert theory is another question...

Shh. I'm still working on the Principle of Restricted Choice.

[rbforster]

A better example is where you find that opening leader has in fact underlead his king from Kxx(x), but might or might not have another suit with (K?)xxx. Since he clearly chose to underlead a king, he's more likely not to have the other Kxxx since if he did, he might have underlead that one instead.

 

There are other more exotic applications, such as this one where a preemptor leads a singleton against your slam. With no other suit inferences for choosing his lead, like:

 

(3♣)-X-(P)-6♠

 

obvious singleton ♦ lead

 

you proceed through the play and conclude that opener had 3118 or 3217 with a bad suit. In the end position you play him for 3217 because, among other things, if he had 2 choices of singleton he might have lead the other one.

[mikeh]

I'm not sure what the OP is getting at, but the proposition as stated is far too simplistic.

 

The topic of drawing inferences during the play has been the subject of at least two good books, albeit almost certainly long out of print. I think the first one I read was by Jannersten and the second by Lawrence. And, of course, the topic is usually addressed in any good book on either declarer or defensive play.

 

The difficulty I have with the OP, is that in my view these types of inferences are bound up in a host of factors, and are rarely, if ever, as simple as 'he led a club, therefore he is likely to hold the heart king'.

 

For one thing, as already mentioned, the defender may be under the impression, accurately or otherwise, that the auction called for an aggressive lead, and then the inference might well be the exact opposite of the one suggested by the OP.

 

For another, I continue to be surprised (altho I should know better by now) that so many players dislike underleading Kings on opening lead. Yes, there are auctions that suggest staying off that lead, but at least this player routinely underleads Kings on opening lead... and while this may say more about the poor level of the rest of my game than it does about my leads, the opening lead is one of the better parts of my game.

[EricK]

A better example is where you find that opening leader has in fact underlead his king from Kxx(x), but might or might not have another suit with (K?)xxx. Since he clearly chose to underlead a king, he's more likely not to have the other Kxxx since if he did, he might have underlead that one instead.

It's tricky though. If opening leader has a choice of two unbid suits and the one he leads turns out to be from Kxx(x). Is it not now more likely that he has the other King - so that he had no choice in underleading a king.

[cherdano]

The principle is sound, of course.

Let's take a different example: If you find out that Mikeh has led from ♣xxx, and you need to guess whether he has ♥Kxx or ♥Jxx or ♥xxx, then he is most likely to have ♥Jxx, and least likely to have ♥xxx. If, on the other hand, he led from ♣Jxxx, his hand is probably x Jxxx Jxxx Jxxx.

[awm]

There is a nice book called "Dormer on Deduction" about this kind of thing.

[OleBerg]

This theory is very useful. Whether it is an advanced/expert theory is another question...

My partner can confirm that at least one intermidiate player knows enough about it, to discuss it on the internet.

[Stephen Tu]

The inference on underleading Ks depends quite a bit on the player. Mikeh admitted to underleading Ks and I do also, I probably do so too often esp. MP but I can't stop myself :(

 

 

As for RC on opening lead, there's a good article by Phillip Martin called "The Monty Hall Trap" in Granovetter's "For Experts Only" article compilation book.

[mikeh]

The principle is sound, of course.

Let's take a different example: If you find out that Mikeh has led from ♣xxx, and you need to guess whether he has ♥Kxx or ♥Jxx or ♥xxx, then he is most likely to have ♥Jxx, and least likely to have ♥xxx. If, on the other hand, he led from ♣Jxxx, his hand is probably x Jxxx Jxxx Jxxx.

Damn, now I have to find a different approach to opening leads :(

[Finch]

The principle also works on length leads as well, of course.

If you bid 1NT - 3NT and LHO leads a 4-card minor against this, you can be certain that he doesn't have a 5 card suit elsewhere.

 

And as others have pointed out, you may need to interrogate oppo about their opening lead style in detail before deciding what deductions to make about restricted choice on lead.

[Rossoneri]

Rarely so clear-cut, but useful principle, might just push you into one direction instead of the other.

 

Now to find that Granovetter book!

[han]

You can also keep this in mind when you are looking for the trump queen and a trump lead might have been preferable to the actual lead.