[dicklont]

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Playing 4♥ this is the trump suit.
You know from the bidding that RHO has a weak 2 in spades and LHO holds 2 spades.

On the King both follow.
Do you play A and Q now, or does the knowledge of the spade suit make the finesse the better choice?

[effervesce]

You know RHO to have 6 spades, and LHO 2 spades. So, RHO has 7 non-spades, LHO has 11 non-spades. So for any particular non-spade card, there is a 11:7 ratio of probability LHO has it over RHO.

The default probability that the suit splits 3-2/2-3 is 68% (from memory I think). This probability is reduced since they're less likely to split given the preempt - perhaps 55-65 percent as a guesstimate.

I'm guessing the odds are better for running the 10. Lets test this out-

There is a suit break calculator at http://www.rpbridge.net/xsb2.htm
which calculates how suit break odds change given the number of spaces in each hand.

So given west has 11 spaces and east 7, it says the probability of a 3-2 break is 63%. You'll always pick up a 1-4 split too, so the overall % is 67% or so for playing for the suit to break.

Using the calculator there, a 3-2 break is 40%, of which the hook is 60% odds on to work.
A 2-3 break is 22%, of which the chances of the hook working is 40%.
A 4-1 break is 27%, for which the hook is 100%.
A 1-4 break - 4.5%, you'll always pick this up as you won't hook, so 100%.

So the overall probability for hooking is 0.24+0.09+0.27+0.045 = 65%

Meh-guess I'm wrong. Better to play for the drop.

Also see http://www.rpbridge.net/7z75.htm for an interesting analysis on how odds change.

So in this particular case, where you know a suit is 2-6 and have 5 cards in a suit you're interested in, you still play for the drop, although it is extremely close. Using the calculator, if you know a suit is 2-7 (instead of a 2-6 suit) then its enough that hooking is better.

[Mbodell]

Maybe you aren't allowed to use the fact that both players have hearts when you calculate your vacant spaces (and I see that maybe this volunteered info isn't the best based on the rp link), but if I count how many hands are possible treating all minor cards as equals and using the fact that both have at least 1 heart I get:

West's original hearts:

4 - 1716 hands
3 - 3861 hands
2 - 2145 hands
1 - 286 hands

Assuming we finesse we'll pick up all of the 4's, 60% of the 3's, 40% of the 2's, and all of the 1's (as we'll switch strategies and cash the A and finesse back). That adds up to 5176.6 hands or 64.64%.

Assuming we play for the drop by playing ♥K then ♥A then we'll pick up none of the 4's but all of the 3's, 2's, and 1's (on the 1's we'll finesse the 3rd round obviously). That is 6292 or 78.57% of the hands.

So playing for the drop is significantly better.

[Mbodell]

effervesce, on Sep 13 2009, 01:56 AM, said:

So in this particular case, where you know a suit is 2-6 and have 5 cards in a suit you're interested in, you still play for the drop, although it is extremely close. Using the calculator, if you know a suit is 2-7 (instead of a 2-6 suit) then its enough that hooking is better.

I don't think so, since really we are interested in the 3 card split when both follow to the K (so eliminate the 5-0 and 0-5 and remove 1 vacant space from each hand [although maybe from the rp link I'm wrong to remove the vacant spaces we've discovered]). I get that if it is split W has 2 spades and E has 7 spades then the finesse is 67% to succeed and the drop is 73.6% likely. Only if W has 2 spades and E has 8 do we favor the finesse to the drop (70.3% versus 67%).

Obviously, if we could find out more information in other suits first that would be helpful.

[maggieb]

Interesting thread, I like to think I knew how to do this when I was young.

Quote

Assuming we play for the drop by playing ♥K then ♥A then we'll pick up none of the 4's

I think you forgot about the stiff jack!

[effervesce]

maggieb, on Sep 13 2009, 06:34 AM, said:

Interesting thread, I like to think I knew how to do this when I was young.

Quote

Assuming we play for the drop by playing ♥K then ♥A then we'll pick up none of the 4's

I think you forgot about the stiff jack!

True... lets just assume the J isn't stiff for this question

[Mbodell]

maggieb, on Sep 13 2009, 03:34 AM, said:

Interesting thread, I like to think I knew how to do this when I was young.

Quote

Assuming we play for the drop by playing ♥K then ♥A then we'll pick up none of the 4's

I think you forgot about the stiff jack!

Well, I'm assuming that the two hearts played on the K are not the J. That was what the numbers in all my calculations were, they assume that on the K both players followed low because that was what the OP specified. So we know that the J isn't stiff.

[aguahombre]

the fact that the stiff jack did not appear affects the math by eliminating one setup from the base, doesn't it?

[Jlall]

Play for the drop, you need very significant empty space info to do something different. A teammate of mine had a situation like this but knew RHO was 7 and LHO was 1 in a suit. He took the hook which seemed right, especially since there was 1 other minor inference.

Anyways, 6-2 is not nearly enough.

[Mbodell]

aguahombre, on Sep 13 2009, 09:25 AM, said:

the fact that the stiff jack did not appear affects the math by eliminating one setup from the base, doesn't it?

It doesn't effect my math, because I did it after the first round of hearts.

[gnasher]

This is easier if you use one of Pavilcek's other calculators:

http://www.rpbridge.net/xcc1.htm

Filling in Axx opposite KQ109x and 11-7 for available space, I get:
Jxxx-x   21.57
xxx-Jx   16.18
xx-Jxx   13.48
Hence the finesse loses more often than it gains.

If you knew that the spades were 1-7, the available space figures would be 12-6, and the odds would be:
Jxxx-x   27.73
xxx-Jx   15.41
xx-Jxx   9.24
Hence the finesse would now be better.