gnasher, on May 26 2009, 07:17 AM, said:
kenrexford, on May 26 2009, 12:01 PM, said:
I'm not sure which wins most often. Probably easy to calculate.
Yes, very easy. In fact, I thought that's what I'd already done.
If clubs are 3-2:
- Playing clubs from the top loses if RHO has three clubs and
♠A is offside.
- Starting with a low club loses if RHO has
♣Q and
♠A is offside.
These two cases are equally likely.
The difference between the lines is when clubs are 4-1. Suppose that
♣10 is never a falsecard, and that you always guess correctly whether it is from Q10 or singleton 10. Your line gains when clubs are 10xxx-Q. My line gains when clubs are Q10xx-x. That's three times as many combinations, and I haven't had to do any guessing.
I think you are oversimplifying things.
First, as to the 3-2, you are missing a bit. If clubs are 3-2 with RHO having three and the spade Ace offside, you do not go down by cashing and then changing tacks if you see the 10 when LHO has Q10 tight. So, that was errant. Second, the Ace being offside is more likely when RHO has three cards than when he has 2.5 cards on average in clubs, albeit slightly, such that low works slightly less often than would seem obvious. On the flip-side, my line fails when RHO only has two cards, specifically the Q10, with the spade Ace offside.
So, the two 3-2 scenarios might not actually be equal.
As to the 4-1, you have a point, I think.
I think the odds still favor your line, but I don't think it is as easy to calculate as you suggest.
"Gibberish in, gibberish out. A trial judge, three sets of lawyers, and now three appellate judges cannot agree on what this law means. And we ask police officers, prosecutors, defense lawyers, and citizens to enforce or abide by it? The legislature continues to write unreadable statutes. Gibberish should not be enforced as law."
-P.J. Painter.