Calculate the Odds

[HighLow21]

[hv=pc=n&s=sath75dkt972caq94&n=sq9432haqjt8dack5]133|200[/hv]

 

Forget the bidding -- it was atrocious. I was hurricaned into the NT small slam by a know-nothing partner.

 

My question is -- what are the odds of making the contract? How about 11 tricks? I tried for 12 and made a grand total of 10.

 

Note: the opening lead is a small club. I realize the odds go up if a spade is led, but it wasn't.

[helene_t]

South is declarer, right?

 

You win in dummy, unblock ♦A and play a low ♠ to the ten. If it forces the king you just need the heart finesse. If it loses to the Jack, you can be lucky that West started with Jxx or Txx of clubs so he can't play a club back. That would allow you to keep ♠Q as a menace. Otherwise you have to hope for ♠Kx with East, or some miracle in the minor suits.

 

Probably something like 25-30% in total, depending on how likely W was to lead a club from Jxx or Txx.

[HighLow21]

South is declarer, right?

 

You win in dummy, unblock ♦A and play a low ♠ to the ten. If it forces the king you just need the heart finesse. If it loses to the Jack, you can be lucky that West started with Jxx or Txx of clubs so he can't play a club back. That would allow you to keep ♠Q as a menace. Otherwise you have to hope for ♠Kx with East, or some miracle in the minor suits.

 

Probably something like 25-30% in total, depending on how likely W was to lead a club from Jxx or Txx.

Good response. Thank you for this. (Yes, South declares.)

 

I'm going to assume for the rest of this discussion that suit-by-suit probabilities are independent of each other (they are not, but it's not far off and it makes the math actually doable).

 

Your line is better than what I tried at the table. I completely spaced out on the possibilities in spades, because I was so upset about the bidding. The primary line I was going for was 5 tricks in hearts plus 3 tricks in diamonds (6-1 or 5-2 split with one or both honors in the short hand, OR 4-3 split with both honors in the short hand). This is about 26.8% for the diamonds, I believe. Your spades option seems like a little over 50/50 to me; much better.

 

So we are going for 7 tricks from the majors. By my count, being able to play ♥ for 5 tricks requires W to have Kxx♥ (17.8% of the time) or Kx♥ (16.1% of the time). This is 33.9% I think. Using the spade play you described, without a squeeze or error by the defense the slam is thus, I believe, half of this, or 17.0%. Add to this the possibility of dropping K♠ (either Kx♠ with East or KJ♠ with West -- by itself, 8.1% I think) adds another 2.7%. We're at 19.7% now.

 

Let's assume normal probabilities on the club lead for simplicity (though a decent defender is more likely to pick something else with Txx or Jxx, if there was any other choice, but there's a fair chance there wasn't a good choice, especially holding Kxx(x)♥). Txx or Jxx with West originally is 17.8%, so by my math this adds [(1 - 19.7%) x (17.8%) x (33.9%)] = 4.8%. We are now at 24.5%.

 

If W has the K♥ to 4 or more, the only way to get 5 tricks is via a squeeze--and there seem to be so many available. Which squeeze is best? And does that get us all the way up to 30%?

 

It should be noted that at the table I estimated about 15% for the slam, but that's because I was starting with the diamond play. It's still a bad slam, but not as terrible as I thought.

 

One consideration on squeeze play here: after the A♦ is unblocked and a heart finesse is taken, dummy will quickly become short of entries. Any clue how to figure out which squeeze play is best in light of this?

 

And feel free to correct me on any of my math here.

[rhm]

If W has the K♥ to 4 or more, the only way to get 5 tricks is via a squeeze--and there seem to be so many available. Which squeeze is best? And does that get us all the way up to 30%?

The odds are hard to calculate.

If West has the K♥ to 4 or more, your best chance is four tricks from spades, East having ♠Jxx or ♠Jx or ♠Kx or ♠KJx or erroneously plays an honor from ♠KJxx(x). (If the ♠T holds, cash the ♠A immediately)

A DD simulation shows that slam will make nearly 40% of the time and that is before the club lead, which will often but not always be the killing lead.

Since declarer plays single dummy chances are somewhat lower, but almost certainly above 30%, probably slightly better than a one in three chance.

For example one problem is that if the ♠10 looses to the king and a club comes back you do not know what to discard on the ♣Q and the ♦K when both follow with low cards to the ♠A

Squeeze chances are not good if the defense can return a club.

 

Rainer Herrmann

[helene_t]

Thinking more about it, I think it can't be wrong to play low at trick one, giving you an extra club trick if W started from Jxx or Txx.

 

The DD results presumably include some layouts where one trick needs to be set up in diamonds. You won't play for that in practice. Also, if W has Jx of spades you can set up a spade trick DD but not SD. Nevertheless, if DD gives you nearly 40%, rhm is probably right that my estimate was too pessimistic. Especially if West will sometimes give away the contract by leading from ♣Jxx/Txx when another lead would have defeated us.

[HighLow21]

Excellent analyses guys -- thanks for the insight.

 

Rainer, where can I get a software package that does DD analysis as you described? If there are several, which do you recommend?

[rhm]

Excellent analyses guys -- thanks for the insight.

 

Rainer, where can I get a software package that does DD analysis as you described? If there are several, which do you recommend?

I use Dealmaster PRO.

It is easy to use

 

Rainer Herrmann

[rhm]

deleted

[HighLow21]

I use Dealmaster PRO.

It is easy to use

 

Rainer Herrmann

OK thanks