Monday, July 27, 2009

Card combinations you're surprised not to know

Or at least, I was surprised not to know.

Consider the following combinations:

A: AQ983 in hand opposite 542
B: AJ82 in hand opposite K543

and assume you are maximizing average tricks, with no entry restrictions.

Alan Applebaum was asking a bunch of people on Friday, just before the LM pairs started, about A. Almost everyone (including some top players) played low to the 8, then if that lost planned to hook the Q the second time. This is actually wrong, because it only gains when lho has JT doubleton and loses when he has stiff “jen,” compared to hooking the 9 the second round – it’s a restricted choice position, but one that seems to have gone unnoticed by almost everyone.

Then later that day at the table, position B came up, which happens to be a very close cousin. Our opponent cashed the K, and when the T appeared on the left hooked the J, commenting that she wasn’t sure that was right. Actually it’s right to hook the 8 (or cover righty’s 9 cheaply) on the second round, for similar reasons. You win against stiff T ( or 9), lose to doubleton T9; by restricted choice the stiff “tine” is more likely. At the table, only the third-best approach of going up ace worked; lefty had QT tight. I bet many good players would briefly consider going up ace, then hook the J because they know going up is too susceptible to falsecarding…but wouldn’t even consider the best option of hooking the 8! All I can tell from the recap sheet is that about 25% of the field dropped the Q; no idea how many hooked the J versus the 8.

By the way, there was another consideration on this hand: About 25%** of the field got to the optimal 6nt while the rest, as did my opponents, bid to 6h with this as the trump suit and no other losers anywhere. I’m ignoring the very few who went minus in a grand. Those in the inferior 6H would be justified in taking an anti-field approach in the play, which rates to gain about 70% of the mps when right but lose only about 30% when wrong. I can’t say for sure if the J or 8 is anti-field, but I do know the A is! Disappointingly, a glance at the recap seems to show no correlation between the contract and the number of tricks taken -- those who went +1020 should be a bit ashamed, as 990 was already a good score!

** Update, 7/30: I actually counted frequencies of the scores, see comments.


Memphis MOJO said...

I think if 990 was going to be a good score, then you should make the standard safety play of low to the Ace, then back to the king.

This protects against what can be protected against, and, in this case, b-i-n-g-o.

I didn't see your name in the Spingold team listings.

Jonathan Weinstein said...

It's not that 990 per se is automatically a good score, but taking whatever the "normal" number of tricks in 6nt is should be a good score, you beat 6h by 10 points. (There were 35 points, no one is missing slam.) So just try to play however you think others will play, probably to finesse.

I came home for the work week, will be back in DC for the final Swiss.

Memphis MOJO said...

Ok, I see.

Well, GL in the Swiss.

Anonymous said...

Hey Jon,

I recognize the hand -- it was the very first board Dan & I played in DC. I have two questions:

1. Do you recommend that the guy with 9xx of trumps (that was me) play them in random order against mediocre declarer?

2. Should declarers in 6H randomize their play? Say declarers in 6NT know what all 6H players would do. Might they try to lock points from 6H tables by doing the same at the expense of fractional points from other 6NT tables.

Looking forward to your insights.


Victor said...

There's a slight extra argument for the jack on the second round on the actual hand. If you score three tricks without losing one, there's some chance of a squeeze. At my table the lead was a diamond from what looked like length, and in fact diamonds were 5-2. (though weak opponents may well leave only one diamond guard anyway).

Jonathan Weinstein said...

Hi Alex,

1. You made this interesting by specifying mediocre opponents. I'll first answer an easier question: how to defend against good opponents who know you are good. If both defenders play spots (including T and 9) uniformly at random when they have an option, except righty always plays low spots from QTxx and Q9xx, they hold declarer to the minimum. Namely, he succeeds against (3-2 Q onside)-(T9 tight offside)+(T or 9 stiff offside). There is some slack in all the inequalities, so it's not important if the randomization is really exactly uniform, or if you sometimes play T from QTxx.

Against mediocre opponents, or good ones who don't think you are, I guess I would play the 9 second round from 9xx more often than random, because I don't think they expect this. Psychologically, instead of them thinking "Did lefty falsecard? Maybe he wouldn't falsecard..." they'll be thinking "One of them falsecarded for sure, but which..." and I would hope they are more likely to take the normal finesse.

2. You make a good point; in theory there is yet another "guessing game" as to what the other tables will do. If all the 6H declarers were playing for the drop, it would be correct by a significant margin to mimic them in 6NT. Of course, if they thought 6NT declarers would think that way...etc., etc. But many 6H declarers probably don't even think about trying to play against the field. Much more practical than game theory is a survey of what actually happened, and in the name of science I actually counted:

The hand was played 169 times. Scores were:
1020: 7%
990: 24%
980: 44%
Other: 6%

106 tables played 6H, and 29% made an overtrick; of 53 tables in 6NT, 23% made an overtrick. The difference in strategy between 6H and 6NT is not statistically significant (p=.37 for chi-square test) so the field has disappointed us yet again.

Practical conclusions: Given these proportions of the 4 contract-strategy pairs, it appears a 6H declarer should stick with the theoretically best play against opponents who falsecard appropriately, but it's close. 6NT declarers should definitely make the "normal" play, it's not close. Of course, the fact that we don't know who hooked the 8 versus the J makes it all a bit murky!

Becker said...

I got a chuckle out of the "other" category--Kenny and I landed there when our auction went south at the six one will be able to guess our final contract, but suffice it to say it was't pretty! Good luck in the Swiss Weinstein!

Becker said...

I just remembered another story from this hand--Peter Bertheau led a trump against 6 hearts and put his head in his hand when his partner played the queen and declarer the king. The declarer missed this piece of table feel and duly finessed into the then-stiff ten on the way back.