[jvage]

Scoring: MP

---

This was the last hand of this weekends County pairs final. Unfortunately very few average players participate in this event, so the field is small (7,5 tables) and strong (about half the players are "BBO stars"). I was East and of course didn't know it at the time, but before this board we were exactly tied for the lead with another pair sitting N/S, and all 7 tables declared 6NT from South.

This is definitely not a hard-luck story, but how would you guess we scored when declarer (a BBO star) misguessed clubs after I had ducked the first round, resulting in 1 down?

Bonus question: I recently read a Bridge World article about "Mixed strategies". During declarers planning at trick 1 I considered winning the first club (it is not too difficult to see the point of the hand from the East position). Declarer knew I was good enough to play small without hesitation from my actual holding, so he might then play me for AJ doubleton. Is this a position where mixed strategies are relevant, and would it be correct to win the first club? Of course you have to plan this in advance, if you start thinking when a club has been played you have ruined your chances whatever you do.

John

[FrancesHinden]

Missing 7 clubs, it's about 7:5 that you have AJ doubleton rather than singleton ace. Missing 6 clubs it's about 16:12. You might not know from the auction how many clubs declarer has.

If you take the ace on the first round only from AJ doubleton and singleton Ace, declarer will be very slightly better than 50% to get the suit right after you take the ace. I believe that if you take the ace very slightly more often than that, it won't change your expected number of tricks, but it will in theory increase the standard deviation.

In practice, I believe declarer's optimal strategy is always to finesse, because there's always a chance that you would have taken the ace from Axx or Ax due to not paying sufficient attention to the play, or various other uncertainties. For example, if south's hand had been

K8x
AQ52
KQJxx
x

ducking the club leads to a very embarrassing overtrick after you are squeezed in the blacks.

[jvage]

I forgot to add the important info that South opened 1NT (15-17 almost standard around here). At our table North just jumped directly to 6NT. Frances's layout is therefore close to impossible (I know this South would never open 1NT with a small singleton).

[inquiry]

If you win the club ACE, he will cash all his red cards and you will have to find three discards. If you throw three spades, well, he will not have to guess in clubs. If you throw the club 9, well, you will not have a singleton club nor AJ doublton. He is also very likely to cash two spades before the last red card. With your holding Spade QJ, the club duck seems clear even if you are a fan of mixed strategy.

To guess how you did, since you said all pairs bid 6NT, I would think that most would make since the correct play seems to be small club to the king, and if that wins, small back to the Ten. Since this was MP with a 6 as a top, I would guess you got a 5.5 (2 went down, 5 made) or 5 (three made, 4 went down).

[FrancesHinden]

Declarer isn't going to cash two spades before playing the second round of clubs. That boringly goes off when someone has the CA and a spade to cash as their last two cards.

But back to the original point.
Now we know the auction was 1NT - 6NT, I'll restate my suggested hand for declarer as

Kx
AQxx
KQxxx
Jx

to give another reason to take the CA on the first round (club menace now in hand).

In fact, even if you can't construct a hand where it costs to duck the ace, there are still defenders - even BBO star defenders - who would take the ace on the first round because they are worried about the overtrick, and clearly don't have time to think the hand through fully. So I think it's always right to finesse from declarer's point of view even if you take the ace.

[inquiry]

FrancesHinden, on Jan 29 2007, 11:40 AM, said:

Declarer isn't going to cash two spades before playing the second round of clubs. That boringly goes off when someone has the CA and a spade to cash as their last two cards.

Well i did say IF YOU took the ace of clubs.. .so they wuld not have the club ACE left to take after cashing two spades

[hrothgar]

jvage, on Jan 29 2007, 04:31 PM, said:

Bonus question: I recently read a Bridge World article about "Mixed strategies".

Silly question: Could you provide me with a pointer to the article in question?

I submitted an article with a similar to the BW a couple years back, but it didn't get picked up. I'd be interested in seeing what they did publish.

[cherdano]

The article was by Jeff Rubens on randomization in card combinations.

[hrothgar]

cherdano, on Jan 29 2007, 08:36 PM, said:

The article was by Jeff Rubens on randomization in card combinations.

Did Jeff actually use the expression mixed strategies?

[jvage]

The article was in the november or december issue last year by Rubens, and yes, I think he used the expression "Mixed strategies" (I am currently at work, can confirm tomorrow).

The funny part of the hand was how 6NT-1 scored in what I believed was a strong field. Like those who have answered I would have expected the majority to make. In real life we recieved -2 for 1 down, when 5 declarers went 1 down and 2 went 2 down

The reason this was no hard-luck story was that one of those going 2 off was the pair with whom we were tied for first

I don't know how the play went at all tables, but at that table declarer had reduced to this position:
AT
-
-
QT

K8x
-
-
7

East had discarded to ♠QJ and ♣ A9 (so declarer had 3 spadetricks and his contract, one would have expected a clubdiscard more from this holding), and when declarer misguessed the defense took 3 clubtricks!

Inquiery spotted an important reason not to win the first clubround (I can't claim I had seen this when I ducked). A good declarer planning to play me for AJ doubleton would take his red-suits winners before deciding. If I discard spades the suit is running, if I discard a small club he would surely finesse.