[awm]

There are some interesting observations about all this. If declarer basically ignores the defense and determinedly plays to the nine (or beats an honor with the ace and then plays to the nine the next round) then he will win precisely when the ten and one of the K or Q is onside. This is 37.5% or thereabouts.

If we always play low from KQx, KTx, QTx... then this is basically the best declarer can do. The same applies if we always play high the first time and duck the second.

However, there is a psychological ploy here. Most weaker players would never consider to play the king or queen from KTx or QTx. However, they might play an honor from KQx. Of course, playing this way is exactly wrong; declarer can then play to the jack on the second round every time you play an honor and pick up KQx as well as KTx/QTx for a roughly 50% success rate (if you always split from KQx) or in any case better than 37.5% (assuming sometimes split and sometimes not). On the other hand, this assumes declarer is aware of this tendency.

So the psychological ploy, against someone who doesn't think you're capable of such things, is to play an honor from KTx/QTx and play low from KQx. Of course this doesn't really work either, in the sense that if declarer knows you do this he can succeed roughly 50% of the time. But declarer is more likely to assume that you wouldn't think of this -- if he plays you to do exactly the opposite (split KQx, low from KTx/QTx) then he will succeed only when all three honors are onside (something like 12.50%)! If declarer assumes you play randomly or ignores you honor plays, he's still only 37.5% likely to succeed. Only if he guesses that you are playing "backwards" can he improve his success rate.

[pclayton]

Hannie, on Apr 26 2006, 12:02 PM, said:

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Why do I have visuals of Richard and Matt standing on the 2nd floor of a dormitory in New. Engalnd in January scribbling these formulas on a window pane in crayon and talking to imaginary people? tongue.gif tongue.gif

Hard to say without knowing you better Phil. Perhaps it is because you don't understand them and prefer to think of people you don't understand as being lunatics who have no idea what life is about? Perhaps because in most of the Western world intellectuals are often seen this way? I'm just guessing here, as I said, I can't read your mind from such a distance.

Blame it on Einstein I guess; great minds are often portrayed as eggheads having poor hygiene and dress strangely.

But Han, I totally respect and can barely comprehend the inner workings of a lot of the posters around here, especially Matt's and Richard and even yours. At least when it comes to non-bridge issues

Just kidding .

[han]

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At least when it comes to non-bridge issues tongue.gif

Now that was funny!

[jdeegan]

awm, on Apr 27 2006, 03:43 PM, said:

So the psychological ploy, against someone who doesn't think you're capable of such things, is to play an honor from KTx/QTx and play low from KQx. Of course this doesn't really work either, in the sense that if declarer knows you do this he can succeed roughly 50% of the time. But declarer is more likely to assume that you wouldn't think of this -- if he plays you to do exactly the opposite (split KQx, low from KTx/QTx) then he will succeed only when all three honors are onside (something like 12.50%)! If declarer assumes you play randomly or ignores you honor plays, he's still only 37.5% likely to succeed. Only if he guesses that you are playing "backwards" can he improve his success rate.

In a game where RHO knows my habits, I'm going to have to split from KQx at least part of the time. What are the odds now, Prof. Bayes?