Card combination

[CSGibson]

I was playing family bridge with my mom at Christmas, and we had the following situation come up:

 

[hv=n=sx&w=sx&e=sxx&s=saqj]399|300|[/hv]

 

Playing trump from the dummy, 3 cards out including the king, RHO plays small, is it right to finnesse vs play for the drop? Why?

 

The only relevant cases are for RHO to have 2 trump remaining and LHO have 1, when RHO plays small, each have one unknown card left, is playing for the drop the same percentage as taking the finesse?

[CSGibson]

Whoops, meant to post this in B/I, sorry for the misplacement.

[gwnn]

with 2 small RHO will play (theoretically) randomly. with Kx, RHO will obviously NOT play randomly :P and will always play the x, so with Kx his choices are restricted and with xx his choices are free. Thus it's a more successful line to play him for Kx. Only if RHO is known to play his spots up-the-line will we get a break-even point when we see the smallest spotcard show up. I think Fred wrote in Learn to Play Bridge that it's never good to play your opponents to make a mistaken play (in the context of Axxx in dummy, Kxx in your hand, Q appearing from declarer), so it's basically a finessing situation.

[Fluffy]

This is plain wrong, the percentages depend on how many cards opponents STARTED with, not how many they have left, you can't calculate anything from a later position.

 

If you had 10 trumps at the start, look at Csaba's post about why fienese the king is always better when opponents have more than 2 cards left.

[Trumpace]

the percentages depend on how many cards opponents STARTED with, not how many they have left, you can't calculate anything from a later position.

Err.. you can calculate the correct percentages only after taking into account the later positions (not sure what you mean exactly by "later positions" though). Basically as you see the cards which fall, you gain information. For instance in ten card trump suit siuation, when LHO plays x, you can rule out the singleton K with him, plus Bayes rule always is a factor (for instance restricted choice).

 

Another example:

 

[hv=n=sakqt&w=s&e=s&s=s432]399|300|[/hv]

 

You cash the AK and both follow suit. Now from south hand, you lead low and West follows with some card which is not the J. Do you go for the finesse or drop?

[CSGibson]

let me clarify by saying that I know the finesse is the right play, I just couldn't explain why, which was bugging me. Thank you for the replies.

[Echognome]

the percentages depend on how many cards opponents STARTED with, not how many they have left, you can't calculate anything from a later position.

Err.. you can calculate the correct percentages only after taking into account the later positions (not sure what you mean exactly by "later positions" though). Basically as you see the cards which fall, you gain information. For instance in ten card trump suit siuation, when LHO plays x, you can rule out the singleton K with him, plus Bayes rule always is a factor (for instance restricted choice).

 

Another example:

 

[hv=n=sakqt&w=s&e=s&s=s432]399|300|[/hv]

 

You cash the AK and both follow suit. Now from south hand, you lead low and West follows with some card which is not the J. Do you go for the finesse or drop?

So in this case, we have one missing card.

 

The ex-ante probability of a 4-2 split (four on the left) is about 24.2%. The ex-ante probability of a 3-3 split is about 35.5%. So using conditional probabilities:

 

Pr(4-2)

-------------------

Pr(4-2) + Pr(3-3)

 

=0.242/(0.242 + 0.355) = 0.405 or about a 40% chance that the finesse works and a 60% chance that the drop works.

[Echognome]

Ok. I'm told that's not quite right, because it's a specific 4-2 and a specific 3-3. Namely Jxxx vs xxx.

 

So using the modified calculations it's

Pr(xxx) = 17.76%

Pr(Jxxx) = 16.15%

 

So Pr(Jxxx)/(Pr(xxx) + Pr(Jxxx)) = 16.15/(17.76 + 16.15) = 47.6% For the finesse and 52.4% for the drop.

[rogerclee]

If you don't want to read all of this stuff below, I think, if you are missing the K, 3, and 2, that you should play for the drop if the spot card is the 2 OR if you're playing against good opponents. You should finesse if the spot card is the 3 and your opponents are not that good.

 

I think it may depend, if you're playing against opponents assumed to follow up the line. However, this sounds sort of crazy to me, so somebody should definitely smack me on the head and tell me why I'm wrong.

 

Let's say you're missing the K, 3, and 2. There are eight possible divisions, all with approximately equal probability.

 

K32 --

K3 2

K2 3

K 32

-- K32

2 K3

3 K2

32 K

 

Let's say you're playing against someone who always follows up the line and the 2 is played. Then the possible divisions are

 

K3 2 - both lines lose

K 32 - drop wins

-- K32 - both lines lose

3 K2 - finesse wins

 

This is that 52.4-47.6 split that favors the drop.

 

If the 3 had been played, then there would be only two possibilities.

 

K2 3 - both lines lose

2 K3 - finesse wins

 

So in this case, you should finesse!

 

If you're playing against someone who plays 2 or 3 randomly from 23, then it's 52.4-47.6 by the same logic for the drop.

 

Notice that all of this is on the assumption that dummy actually only had one trump to lead; that is, there was no double-hook available. If a double-hook is available, then obviously you should be finessing.

[matmat]

I has assumed we were playing with a deck where cards are marked:

 

A,K,Q,J,T,x,x,x,x,x,x,x,x