[TimG]

I found it unnatural that the cards in a suit shifted left to fill up the space left by a selected card; it seems natural to me that to enter AQ I would click the Ace and then move two spaces to the right to click the Queen. But, maybe after using it a bit this way will seem natural.

Nice feature to have available, I'm glad you mentioned it in this thread or I would not have know it was there.

[dellache]

fred, on Dec 25 2009, 04:36 PM, said:

As some of you pointed out, it is not very difficult to do a rough estimate of the odds of success of both lines. However, when the numbers are almost the same and you really care which line is "better" (which as a practical matter is not exactly important), you need to be more careful. In particular:

1) Rounding (like using 68% for the odds of a 3-2 break or 40% for the odds of a 2-2 break) will sometimes result in you getting the wrong answer.

2) Not taking dependent probabilities into account will sometimes result in you getting the wrong answer. For example, ignoring point 1) above, multiplying 68% and 40% does not given you the proper odds of hearts breaking 3-2 and spades breaking 2-2. That is because the way that one suit breaks has an impact on the odds of various possible breaks in the other suit.

Note that points 1) and 2) imply that, unless you are Rainman, there is no way you are going to be able to confidently solve this problem in your head (at least not at the table where time constraints matter).

I am not confident enough in my math to present it here (at least not yet), but so far my conclusion is that drawing one round of trump and, assuming no 4-0 spade break, playing on hearts is marginally better than relying on the club finesse.

As a practical matter, even if at the table you somehow knew the odds of success of the two lines were very close, I would strongly suggest you ignore the math and rely on those inferences I was trying to get you not to think about in order to break the virtual tie. Consider relying on your world famous table presence as well - that rates to be worth more than the small % difference between the two lines.

Fred Gitelman
Bridge Base Inc.
www.bridgebsae.com

Hi Fred, I definitely agree with your conclusion and I guess Jeff Rubens would too (for those who like these kind of problems, "Expert bridge simplified" is a "Must have").

Here's an alternative way for deciding for the best line AT THE TABLE between :
- line A : club finesse ;
- line B : establish hearts, fall back on line A if possible.
- line B': line B but cash High trump first.

1. This is a good case for differential computing
- Line A fails, AND line B works : CA East (50%), Sp. 2-2 (40%), He 3-2 (68%) = 13.5%
- line A works, AND line B fails : CA West (50%), HE 4-1 (28%) = 14%

So A > B, but by a non significant margin (so A = B practically speaking).

2. Computing B' Vs A :
When you cash one High Spade and spades are not 4-0, you don't need to recompute the differences : you just have to perform some kind of "first order" adjustment. When you remove the 10% cases where the Spades don't break 4-0, you just multiply by 1.1 the probability of the 2-2 distribution used in the first difference computed above.
So the 13.5% becomes 13.5 *1.1 = 15%
Now we have B' > A (your conclusion), by a non significant margin.

3. Nitpicking.
The dependencies that we could (and didnot) take into account when multiplying Sp2-2 * He3-2 are of *very low order* in general (less than 1% over the overall result) and are of no practical use. Also, using more than 2 significative digits for computing these simple results at the table is of no practical use.

4. So your conclusion remains : it's VERY easy to compute the relative merits of A and B' at the table and see that they are PRACTICALLY equal. Then all what remains is to judge the inferences to be taken from the lead (as in Justin very good post).

Best regards,

[eyhung]

dellache, on Dec 27 2009, 12:34 PM, said:

1. This is a good case for differential computing
- Line A fails, AND line B works : CA East (50%), Sp. 2-2 (40%), He 3-2 (68%) = 13.5%
- line A works, AND line B fails : CA West (50%), HE 4-1 (28%) = 14%

So A > B, but by a non significant margin (so A = B practically speaking).

I like this method. But isn't hearts 0-5 also a failing case for line B? (We can assume hearts are unlikely to be 5-0 because of the failure to Lightner double). Even if we don't do the first order trick you talked about (eliminating 2% of hands doesn't change things much), that means the failing case for line B is

West CA (50%) and HE 1=4, 4=1, 0=5 (30%) = 15%. which means A ~== B'.

[dellache]

Yep.

[Cyberyeti]

Isn't there a much more important consideration here as the percentages are very close.

If the hearts don't break and a ruff is taken, you're going down.

If the club king loses to the ace, you're not down yet if you haven't cashed a high trump first. While I think it is in fact correct to return a club in all conceivable hands for declarer, if you think RHO might return a trump (or a heart) even a pretty small fraction of the time then the play of the club goes well ahead.

Stiff ace of clubs offside also allows you to try the hearts if you haven't cashed the top spade honour first.

[nige1]

At pairs, the ♥-establishment line is clearly better because it gives you a chance to beat pairs in 6N (or 6♠ on ♣A lead).

Even at teams, however, when the odds are close, it pays to take over/undertricks into account. Here there isn't much in it. If you adopt the ♥-establishment line and both lines work then you make an overtrick; but if neither work then you may lose an extra undertrick.