lamford, on Jan 8 2010, 03:16 PM, said:
The chance of the 3-3 heart break has dropped to 7/18*6/17*5/16*11/15*10/14*9/13*COMBIN(6,3) which I make 31%, so this seems to be the rough chance of playing for hearts 3-3. This chance goes up when you require West to have at least one of the minor-suit honours - to around 34%.
It's lower than that, because we can be fairly sure that East doesn't have a singleton in a minor. That may affect the chances for the other lines as well, of course.
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I still do not understand your line 2. West would only play a third diamond if East is ruffing, and therefore you cannot throw a spade on this trick.
Yes. That's why I said "(2) ... needs diamonds 3-3". Line (2) is clearly inferior to the others, but is also what someone might choose instinctively.
Lamford said:
I now believe I underestimated your line 3; if West has the ace, king of clubs, you make regardless of where the ace of diamonds is, whether or not East plays a club through.
East wins the second diamond and plays a club to the queen and king. West exits with his remaining spade and waits to score
♣A10.
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When West has all three minor-suit honours, however, the 3-3 heart break has gone up to 39%, and when he has two, it is around 36.5%, so line 1 is back in front again.
You can't do that, can you? You have already included the cases where West had three hearts and both club honours in your 31% or 34% for a 3-3 break.
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Also many Easts would not overcall 2S with just QJxxxx and out.
Possibly true, but let's not overstate this effect. It could be as good as QJ108xx.