Insofar as I seem to have a blind spot for gving up a trick unless anticipating a squeeze, I would play on spades:

Unblock the KQ of Diamonds, take AK and lead another Spade. On a good day, they break and I take 3 tricks in each suit. If not, I fall back on clubs and now have to hope for redemption with a 3/3 there.

1. Is that line substantially inferior to yours?

2. Are the odds for success in my approach additive, i.e 33%+33%?

I was going to ask a somewhat similar question. Playing spades A then K then small would allow a defender that started with four (suit split 4-2) to cash both remaining spades before declarer can test if the diamond jack fell (Jxx) or the clubs split 3-3.

The line I was going to ask about was to cash the diamond KQ and then duck a spade instead of a club. That line does allow success if spades are 3-3, if clubs are 3-3, or if the diamond jack is Jxx (or shorter).

The chance of a 3-3 break in one suit seems identical to the chance of specifically 4-2 in another suit, so the column line would initially appear to have the same chance of overall success.

However, the club duck line allows the defenders to easily continue with a second club and eliminate squeeze chances, since declarer will be unable to cash hearts while still having an entry to the diamond ten.

Ducking the spade, instead, allows declarer to reach the following position with the lead in dummy, unless a club is returned:

S – x

H –

D – 10

C – x

S –

H –

D –

C KQx

This appears to win additionally when the defender with long clubs also has either long spades or the diamond jack.

A club return seems less obvious with a spade duck but, with a club return, declarer can still reach the following position with the lead on the Board:

S – x

H – x

D – 10

C –

S –

H – A

D –

C – KQx

This appears to win additionally when the defender with long clubs also has both long spades and the diamond jack.

I may have missed something, however, and I cannot quantify what improvements the squeeze chances actually add (so they may be essentially zero).

Jim-

Your approach is better then mine. Why I do not see these obvious first round “ducks” remains a mystery. I simply don’t see the obvious!!!!

However, if the odds of either black suit breaking 3/3 are 66%, is that as good as playing first on clubs.? Have no idea what the change of odds on a second 3/3 are when the first breaks 4/2 or worse. Surely they are worse but…how much?

Thanks…

Bruce

My math is far from perfect and our host is the bridge expert, not I.

For example, I goofed in my post but cannot apparently edit it. A 3-3 split is about 36%, a 4-2 split is about 48%, as of 64 possible distributions, those splits number 20 and 30, respectively.

Thus, adding a 4-2 suit chance in clubs looks superior to adding a 3-3 chance in spades.

Here, though, ducking a spade at Trick 2 (before clarifying the hand for the defense by cashing two high diamonds) adds squeeze chances that a club duck does not, and this is far tougher for me to quantify.

In general, though, probabilities do not add directly; note that two (or even three of four) 50% finesses do not make a 100% chance of success.

Hi Bruce and Jim2,

We now need to consult the mathematical tables in bridge to determine what the exact percentages are said to be.

First, Jim2 is correct in that ducking the first spade is necessary and once you, Bruce, start thinking in those terms, it will be like learning to ride a bicycle, never forgotten again.

When 6 cards are out against you, such as spades and clubs it is: 35.53 of a 3-3 break and 48.45 of specifically a 4-2 break and therefore after rounding off it is 36% on a 3-3 and therefore 84% on no worse than a 4-2.

Of the remaining 16% it would be close to even money, but slightly less on the Jack dropping either singleton, doubleton, or tripleton which chance should then be added to the 84% making the combined odds of the column line approximately 91%. The alternate line of giving up both a club and a spade early would be considerably less (36% + 36% +48% (diamond jack falling) making that line around 79%. To that, one we need to consider squeeze chances but as Jim2 mentions will be busted up by the spade winner leading clubs eliminating the communications back and forth for a squeeze to develop. All in all the column line appears clearly superior.

Thank you, sir!

I certainly accept your analysis but I must confess that, when I read the column, I ducked a spade at Trick 2. However, the competition level that I would face would be far less likely (I suspect) to find the club shift at Trick 3 than those at the level you play.

On the human side, I so very rarely ever execute a squeeze, that I would gladly trade a few probability percentage points just to have a chance to do one!

While we are nit-picking.

If DJ drops on first or second diamond honor, declarer should change plans. Cash all major-suit winners, cross to ca, discard spade and a club on diamond winners.

Always making 6; overtrick if clubs 3-3 or long clubs with 4+ spades.

Hi Steven,

You are not nit picking, you are speaking cold reality.

In real life and being at the table with excellent players,

sometimes these players outthink themseles and after brilliantly finding the solution, then get careless in the execution and immediately cancel out by committing a blunder.

Not unlike an exceptional football athlete making a sensational catch only to fumble away the ball upon getting tackled. All of us need to be judged on successful completion, not interim brilliance.