Best percentage play

[lakers1]

[hv=d=n&v=n&n=sakjxhakqxdxxxcax&s=sxxxxhdakqtct9xxx]133|200|Scoring: IMP[/hv]

 

Auction 2N-3C-4C (44M max)-4H(transfer)-4S-5D-5H-6S.

 

After CK lead, what is the best percentage play to make the contract?

[JLOGIC]

Feels very right to just finesse a spade.

 

After cashing the SA, cashing the kings win on:

 

Qx of spades anywhere or

3-2 spades without the queen dropping and 3-3 diamonds or

3-2 spades without the queen dropping and Jx of diamonds with the short spade.

 

After cashing the SA, hooking a spade wins on:

 

Qx or Qxx of spades on

Qxxx of spades on with 3-3 diamonds or

Qxxx of spades on with Jx of diamonds having the short spade

 

I won't bother to do the math but someone else can

 

Also just as a side note, there is a small extra chance of RHO having a stiff club and Qx of spades, and we successfully pick up diamonds (presumably hooking through RHO).

[JLOGIC]

I started doing some crude math and I think playing AK is right now lol, I was just rounding though so I could be off but probably hooking is a little worse. Not sure what odds are of short DJ with short spades.

 

Also not sure how much it impacts us that RHO can have a stiff club.

 

In other news I don't know how to do math either so maybe someone can help.

 

Maybe a way to simplify it is playing for the drop:

 

1) Wins outright on Qx of spades off

2) Puts you on the diamonds with Qxx on

3) Puts you on the diamonds with Qxx off

4) Loses outright to Qxxx of spades on

 

Playing for the finesse

 

1) Wins outright on Qxx of spades on

2) Puts you on the diamonds with Qxxx of spades on

3) Loses outright to Qxx off unless RHO has a stiff club and we pick up D

4) Loses outright to Qx off unless RHO has a stiff club and we pick up D

 

If we know what the odds of the various spade holdings are, and the odds of diamonds coming in without them ruffing, and we know what % the possibility of a stiff club with RHO adds, we can figure this out.

[JLOGIC]

Hmm so that doesnt even look that close. Being on diamonds coming in on two Qxx holdings is about equal to making always on one Qxx holding and going down always to another Qxx holding.

 

Making always on Qx offside is far better than making sometimes on Qxxx onside.

 

So according to that without doing any math, playing AK of spades is much better and it's not close at all.

 

Sorry for the rambling.

[pooltuna]

gut feeling is that after A♣, A♠,A♦, the ♠ finesse will produce best odds rather than A♣, A♠, K♠, 4 rounds of ♦ for a ♣ pitch. Probably the hand holding Jx♦ has the ♠Q and reduces the latter line to needing 3-3♦ quite often.

[kayin801]

I tried to roughly calculate the chances (but probably failed). Damn you Jeff Rubens!

 

Drop succeeds = (spade Q dropping, spades 3-2) + (spade Q not dropping, spades 3-2)*((diamonds 3-3)+(Diamonds 4-2)*(diamond J dropping)*(spade Q w/ 4 diamonds))

 

= 68%*40% + (68%*60%)*(36%+48%*(1/3)*(1/2)) = 27% + 17.5% = 44.5%ish

 

Finesse succeeds = (spade Q onside)*(spades 3-2) = 50%*68% = 34%

 

I excluded spades 4-1 and diamonds 5-1 since in most cases the hand will succeed or fail regardless of playing for the drop or finesse (I think) and the percentages end up relatively insignificant, and I ignored the fact that having length in a suit changes these calculations to some extent. Hence rough calculations. Maybe I can't do that. Oh well!

 

If this is wrong maybe someone who doesn't suck at math can correct me.

[kayin801]

If you want to make a correction for the major additional chance afforded by the finesse, which is Qxxx of spades onside and diamonds cooperating, that should be roughly:

 

(1/2*4/5*28%)*(36%+48%*(1/3)*(1/2)) = about 5%, so I guess that's significant, but still only puts it up to about 40%. That should also take care of part of the overestimation of diamonds being with spades in the drop calculation.

[ceeb]

Drop succeeds = (spade Q dropping, spades 3-2) + (spade Q not dropping, spades 3-2)*((diamonds 3-3)+(Diamonds 4-2)*(diamond J dropping)*(spade Q w/ 4 diamonds))

 

= 68%*40% + (68%*60%)*(36%+48%*(1/3)*(1/2)) = 27% + 17.5% = 44.5%ish

Agree closely. My automated calculation includes the above, also the negligible considerations of J alone of diamonds and the opening leader's presumed KQ of clubs.

 

Finesse succeeds = (spade Q onside)*(spades 3-2) = 50%*68% = 34%

 

I excluded spades 4-1 and diamonds 5-1 since in most cases the hand will succeed or fail regardless of playing for the drop or finesse (I think) and the percentages end up relatively insignificant, and I ignored the fact that having length in a suit changes these calculations to some extent. Hence rough calculations. Maybe I can't do that. Oh well!

 

If this is wrong maybe someone who doesn't suck at math can correct me.

♠Qxxx onside is more significant than we intuit. It occurs over 11%, and so even considering the necessary diamond luck you've shortchanged the finessing line by up to 6.6% (if my club-lead logic is fair).

 

In summary I concur with the well yclept JLOGIC at 44.1% to 41% -- plus some singleton ♠Q cases adding the same 1+% to both numbers.

[JLOGIC]

Hah I was hoping ceeb would come in here and school us.

 

I think the important thing is even if you know no math or percentages you can figure out which is the percentage line using logic and elimination though. We are not all balla like ceeb :)

[ceeb]

Hah I was hoping ceeb would come in here and school us.

 

I think the important thing is even if you know no math or percentages you can figure out which is the percentage line using logic and elimination though. We are not all balla like ceeb ;)

Is "balla" Indian slang?

 

I of course agree completely about logic. Detailed computation is nothing -- neither mathematics nor related to at-the-table bridge -- though I am somewhat proud of my program. The beauty of mathematics is in finding simple and sometimes surprising ways to see things. This principle is important to playing bridge because, I believe, thinking leads to mistakes. The more thoughts I churn, the greater the chance one is wrong. Therefore it's really beneficial not merely to be able to solve bridge problems but to have economical thought processes for doing so.

[ONEferBRID]

You are playing for a 3-2 split in trump no matter what.

 

So, banging down the A, K first and then running Diams has better odds.

 

   West with Q x x of Sp occurs 30% of the time .

 

    The 3-3 Diam split occurs 35.5% of the time... as well as the added chance of the  J x doubleton with the short trump.

 

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Edit....

The Q x trump doubleton chance has to be added in somehow also

... Apriori, East has Q x doubleton 20 % of the time....

( hence the "ever" part of "eight ever, nine never " when only looking for the Q ).