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All comments by Jonathan Weinstein
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In most formats isn't the first stage longer than the second stage, precluding this?
Feb. 24
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True Ira, I just wasn't sure that was realistic! But all aspiring high-level players should do at least some reading, I think.
Feb. 22
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Preparation of these casebooks is a fantastic service to the community. Many thanks to Adam and all the commentators! I am curious as to whether the casebooks are read carefully by all members of the national appeals committee and high-level tournament directors. Ideally they would be read by directors at all levels.
Feb. 21
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Addendum: I would go easier on North if he hadn’t bid 2. Then it would be a straight MI case, with (to me) the correct ruling being changing West’s X to a P and the contract again to 2.
Feb. 20
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Unfair to West, as he is entitled to act on the description of 2 as a transfer. Yes, North’s hedged phrasing was a clue to something funny going on, but he is not obligated to guess that he is getting bad information.
Feb. 20
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There is a general consensus that if North had behaved ethically, -200 or -300 in 2 undoubled would have been likely at the table. Getting to the same result after his unethical actions took significant work by the director and opponents. For this reason, restoring equity is not sufficient, and I agree with the commenters above who say a further penalty of some kind is warranted. This is way beyond some borderline hesitation case, as a good player is supposed to know he absolutely can’t field partner’s 2H here, even though there is a chance he would have guessed to do so behind screens.
The explanation by South is almost irrelevant, by the way, because the failure to alert delivered effectively the same UI. Absolutely no fault to West for his questions.
Feb. 20
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Joe: If West had heard the correct explanations (1NT minors, 2H natural), he would presumably not double.
Feb. 20
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Utter nonsense. The statistical evidence of correlation between bid-card placement and strength was overwhelming. It didn’t match on every single hand, possibly because experts didn’t know their whole system, possibly because they randomized placement when it didn’t matter to prepare a defense. The argument that the experts didn’t know their system is asinine, that actually goes in the other direction, i.e. if strong correlation was found despite this confounding factor, it makes the evidence stronger.
(I was one of a handful of informal consultants asked about the strength of the evidence as prepared by Nick Hammond. I’m speaking mostly for myself, but to my knowledge there was no doubt about the strength of the evidence from any expert consulted.)
Feb. 13
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ok, it appears that it is BridgeComposer which calculates par, using DF as a subroutine. In these cases where par is dealer-dependent, they report multiple values and ignore the actual dealership. See the bottom of http://bridgecomposer.com/Par.htm if curious.
Jan. 23
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It's also easy to construct a deal where South and West both make 7NT, so that par swings from +2220 to -2220 depending on dealership. (This digresses from your original post.)
Jan. 23
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There is also a hand recorded by Pavlicek where all four declarers make 3nt. In these cases, assuming nothing higher is makable, par would depend on who was dealer; dealer would open 3nt (3 in your case) and make the other side save. At least, that's how it should be defined. I don't know if DF is programmed to deal with that, but I would think so.
Jan. 23
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Jonathan M.,
That’s certainly a plausible pattern of learning. There are thousands of pages on learning processes which might get you to equilibrium, without any universal answers.
The second paragraph of Charles Brenner’s comment is a good view on equilibrium. Rephrasing, equilibrium isn’t necessarily what you *should* do; if you have good reason to think your opponent is away from equilibrium in a certain direction then don’t randomize, go ahead and play the best reply. The equilibrium is a useful baseline of what would happen if good players faced this situation a lot, and of course it defends, on average, the tricks you’re entitled to.
Jan. 12
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South actually has *four* strategies when holding KQTx:
A – Start with K from hand, play East for stiff when you see 9.
B – Start with K from hand, play East for J9xx when you see 9.
C – Cross in clubs, small spade from dummy, play East for stiff when you see 9.
D – Cross in clubs, small spade from dummy, play East for J9xx when you see 9.

As you correctly analyzed, South never uses A in any equilibrium. The falsecard is free, so East does it at least often enough to make A worse than B.

When we ignore 8-0 clubs, B and D are completely equivalent. They perform equally well against any defense. Hence the equilibrium you found, where South plays C and D 50-50, is actually part of a continuum of equilibria where South plays C 50% and B/D in any combination totaling 50%. East’s equilibrium strategy is unique (the one you found).

When we *account* for 8-0 clubs, however unlikely, B *dominates* D. That is, it sometimes does better and never worse. Accordingly, South should *never* play D. The now-unique equilibrium is for South to play (50% B, 50% C), and East to play the 9 a *tiny* bit less than 1/3 of the time on a small lead from dummy. Why is that the equilibrium for East? Because it gives South a tiny reward when his club lives: he will pick up a tiny bit more than 3 cases, namely stiff 9 and a bit better than 2 of 3 J9xx cases. This tiny reward compensates for the risk of a ruff. Meanwhile, East knows that when South crosses to dummy, he’ll have the T half the time and will always fall for a falsecard if holding the T. This makes East indifferent to falsecarding.
Jan. 11
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Regarding your paragraph about the 8-0 side suit, page 5: In equilibrium, no one *ever* makes a play which is *inferior* given their current information. The resolution of that particular paradox is that we have simply calculated the equilibrium wrong, when we take the 8-0 into account. The equilibrium is then quite a bit different from the one you gave. It turns out that when we ignore 8-0 splits as in your analysis, the game actually has a continuum of equilibria of which you gave just one; factoring in the 8-0 actually reduces the set of equilibria to a singleton which is *not* close to the one you documented. I’ll write up the details as soon as I can.

In the game-theory literature, we say the correspondence from game to equilibrium is discontinuous; this phenomenon happens to be a focus of my research.
Jan. 11
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Thanks, Kit! I had settled on a line very close to this, also starting with K,A of hearts – then I had the 3-2 case correct, but on the 4-1 case I had resigned myself to going down against 2=4=5=2 because I was taking the second spade ruff after 1 round of clubs, losing one of my club tricks. Your version is a clear improvement.

I find it sort of amazing that a hand with 0 non-trivial card combinations can require such care. My guess is that well less than half of declarers in a Blue Ribbon final would find Kit’s exact plan.
Jan. 11
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See Kit's line, which makes at least 5 and sometimes 6 when trumps 3-2, and still almost certain to make against 4-1.
Jan. 11
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OK, I think it’s not a percentage issue because you can combine essentially all your chances. Heart to Q at trick two. (1) If it wins, K, run T. Cold unless someone has Q9xxx, even then you have good chances in hearts. (2) If heart loses, you get to check for Jx or KJ and then try for 5 diamond tricks when that fails.
Trying diamonds first would lose the chance of Jx with righty when the diamond hook fails.
Jan. 10
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Good article!

Has anyone commented on the play of the very first hand? Looks to me like a close percentage-play issue whether to go for hearts or diamonds first. If you do tackle diamonds for five tricks, either before or after a failed heart play, low to the T gives you the best shot.
Jan. 10
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Yes, that's all true. Just woke up and came straight here wanting to delete that comment but wasn't soon enough :-o.
Dec. 21, 2016
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Ducking Qx doesn’t seem that obscure. If declarer had AJTxx this would be a very well-known position where you need to duck. Ducking Jx is more obscure.
Dec. 20, 2016
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