What are the odds?

[steve2005]

ok looking for odds of making a slam depending on a side suit, assuming there is no ruff after losing ace of trump or opening lead.

you need to have 3 club high card tricks for one pitch and you only have one side entry to club suit.

 

need to pick of Q♣ with AJTxx opposite Kx

finessing would be 50% plus chance of singleton Q. though if Q singleton and ♣ led then lose A♠ ♣ ruff possible.

 

so what about going AK ruff a ♣?

works on any 3-3

or 4-2 with Q doubleton

 

what are the odds?

again half the singleton a ♣ ruff possible

[rhm]

Analyzing two lines of plays is often easier by comparing winning and loosing cases.

 

Win for finessing compared to ruffing the third round are Qxxx and Qxxxx on your left.

 

Qxxx on your left is 1/3 of all 4-2 breaks, that is 16%

Qxxxx on your left is a little bit less than half of 16%, roughly 6.5%

Total winning cases 22.5%

 

Win for ruffing the third round compared to finessing are

 

Qx and Qxx on your right

 

Qx on your right is 1/6 of all 4-2 breaks or 8%

Qxx on your right is 1/2 of all 3-3 breaks or 18%

 

Total winning cases 26%

 

You could also play 2 rounds of clubs and then a ruffing finesse in clubs, but this drops the winning cases to 24%

 

So your best bet is bringing down the queen of clubs in 3 rounds.

 

Rainer Herrmann

[barmar]

How much do those odds change depending on the distribution of the trump suit when you were drawing trumps? This changes vacant spaces, doesn't it?

 

I'm guessing it's less than the 4% difference between the two cases, so it doesn't affect the choice of lines.

[pigpenz]

should be able to plug this into Pavliceks suit odds calculator for each condition

[gnasher]

How much do those odds change depending on the distribution of the trump suit when you were drawing trumps? This changes vacant spaces, doesn't it?

 

I'm guessing it's less than the 4% difference between the two cases, so it doesn't affect the choice of lines.

We should be able to manage this one without Pavlicek's help.

 

Suppose that they had five trumps, and the hand over the AJ10xx (RHO) had two. We play ♣K, ♣A, ♣J, and RHO follows small. We've seen all the small clubs. The spades were 3=2 and the small clubs were 2=3. Hence each defender has the same number of vacant places, so it's evens whether to take a ruffing finesse or to play for the drop.

 

Next, suppose that trumps were 2=3. We play ♣K, club and LHO follows small. If we finesse, we gain against Qxxx-xx and Qxxxx-x, but we lose against xxx-Qxx and xxxx-Qx. Look at the symmetry in the distribution of the small cards. When the small clubs are divided xxx-xx, the vacant spaces are the same in both hands, so Qxxx-xx and xxx-Qxx are equally likely. When the small clubs are divided xxxx-x, RHO has more vacant spaces, so Qxxxx-x is less likely than xxxx-Qx. Hence it's still right to play to ruff out the queen.