joshs

I know all 4 members of the team pretty well and have partnered two of them. 2 of them are a partnership in DC, (Hailong and JJ) and have played together for about 8 years (The only time I played with Hailong, which was 6 years ago when I lived in DC, we had a 65% game in a very tough field. He is a fine player.) but don't play in nationals very often. Jiang Gu from new jersey has at least 1 national championship (with Nik Demirov) and a number of top 20 finishes over the last few years. He is an excellent player (but really slow!). The 4'th member of the team is from georgia (former soviet union) and lives now in San Diego, but used to live in DC.

Give East x AQx Axxxxx Kxx. Over 3S its pretty clear that 3N is not right unless opener has significant extras (you have no tricks) or if opener's spades are running, in which case 4S is probably as good a spot. The problem is you have no idea which is the correct major (partner can have 4 small hearts after all). So personally I would have assumed that 4H was something like the hand I gave above, and asking partner to pick a major. Opposite that actual West hand 3N is the best contract, but 3N will get raised to 4N, and that may well go down. For those who claim that 4H is a slam try, its a slam try in what? While I think its playable to have both 4C and 4H be slam tries for spades, I don't see why a moysian can't be the right game contract on this misfitting sounding auction, so I would never have suspected that 4H was anything other than a suggestion of a final contract.... (If it might be natural, it is natural...) Having said all that, of course 4H on the actual hand was rediculous, as was bidding to 6H. If you interpret 4H as natural and showing 3 card support, it has to be a minimum hand since with extras you would never choose to play in a moysian (as the short hand). (Or did you think that 4H was a natural 4N bid with a strong 3 card heart suit? And what are you suppossed to do with the minimum, just concede -100 in 3N instead of trying to go plus?) After all opener can have AJxxxx Jxxx K Ax and all his calls would have been perfectly normal, and 3N hoping to run diamonds is you best chance for game. So given what I expect for 4H I would have passed 4H in a sec..... (Note: with 6421 and Hx of diamonds, opener will usually bid 3D and not 3S unless the spades are super strong.)

While I am the first person to preach the ODR gospel there are at least two other issues in determing ODR here: Having intermediate honors in partner's suit and primary honors outside has a greater ODR than the other way around. Just as I commented that when you overcall on a 4 card suit your side tricks should be fast (Aces and Kings) the same applies to raises when you are short a trump, you should have good trumps and prime side cards. You should not raise on a short trump holding when holding quacks on the side. There are too many ways that can be wrong. Second, Anyone who thinks that with KQxxxx x xxx Axx that its clear they should compete to 3 over 3 after the auction (1H)-1S-(P)-2S-(3H) has either missed a bridge lesson or their partner's 2S bid is much stronger than mine is. From a Law analysis point of view, you think your side has 9 trumps and the opps have 8 or 9, probably 9. First lets suppose its 9 and 9 and estimate tricks. Partner did not cue bid, so probably will only supply 2 cover cards, possibly a 3'rd, and occasionally only 1. So your side can typically take about 8 tricks, and the opps can take about 10. Your best available score here is defending 3H. You don't want to push them to 4H. If there are only 17 total tricks then bidding 3 over 3 might work out ok at mps (when you can take 8 tricks) but still doesn't gain all that much at imps, unless the opps make a later mistake. Now even supposing that partner has the right cards and shape for you to be able to make 3S, such as Axx xxxx xx Kxx (an example of the purity adjustment to the law). Whenever spades are 3-1 in the opps hand they will make 4H (they have 6H tricks and at least 4 diamond tricks). Bidding 3S is total brinkmanship. I think to bid 3/3 when partner hasn't cuebid you need extra offense and at least some extra defense (e.g. high cards) beyond what the simple overcall showed. Now the 4/4 issue is totally different (and you might well get this one wrong). But how often have you seen the auction 1H-1S-P-2S 4H Anyway, thats my two bits.

In fact I think it's a negative correlation. If you give me the number of spades in my hand and RHO's hand, I can compute the probability distribution of partner's number of spades. The number of cards in other suits is not relevant. So the only way my number of clubs effects partner's number of spades, is that it effects RHO's number of spades. The more clubs I have, the more likely RHO is balanced and has some spades. So more clubs for me implies more spades for RHO and less spades for partner. Note that this is only true because of the restriction that RHO has a 1♣ opening. I agree with Elianna that the value in holding clubs when overcalling a four-card suit is that it increases the odds that partner has a useful ruffing value to go with his three trumps, not that it in any way makes partner more likely to have three trumps. Its not just that partner will have shortage. Its that partner will have well placed shortage (shortage that can't be overruffed). If you have 4C and 4S, AND RHO opens 1C, and partner raises there is an increased likelyhood that partner's shortage is Clubs (which probably can't be over ruffed). Furthermore, you had a doubelton in a red suit. Unless partner has 5 or more in that suit, its very unlikely that your LHO can over ruff you. This makes playing a 4-3 fit very effective. So when this is the situation, the opps almost have to lead trumps, and that surrenders the tempo to you, and means that they can't force you.

Ok, LHO opens 1H Partner overcalls 1S 3'rd hand passes And you have Qx xxx Axxx KJxx Sadly you can not make a responsive x of partners bid. You also have a 10 count with a good fitting honor, but you lack a 5 card suit to bid and lack anything that resembles a stopper for NT. I think a 2S bid would be nearly unananimous in a bidding panel here (you have some extra values to make up for the lack of a 3rd trump).

A few comments on 4 card overcalls. In general the following factors are relevent: a. Strength of the suit b. Overall Strength (since a 5'th card is worth at least 1 trick, and often 2 tricks, you need that much values to make up for it. c. Length in the opps suit. 4 card overcalls are most effective holding 4 cards in RHO suit (often can ruff that suit in summy if you catch a fit) d. Nature of side cards. Playing in a 4-3 fit you often do not have much time to develop side tricks, so your side cards should be mostly ace's and kings. Side Quacks are a negative feature. e. Holding in RHO's suit Holding Axxx or xxxx is ideal. Holding Quacks in RHO's suit are dreadful since they (usually) have defensive values and (usually) not offensive values. f. Colors. In general, you always want to bid more (especially at mps) at W/W and be most conservative at R/R. When the opps are vul, just passively passing can get you 100 or 200 defending their contract. But keep in mind, just because you make a mistake and bid 1 to many (say competing to 2 over 2 when you should have defended) doesn't mean that the opps might not occasionally bail you out and give you a bigger score. Busy bidding at low levels works more often than it should on a double dummy basis.

Playing 2/1, I would sadly never mention clubs. 1S-2H-3D(extras. yes maybe my void in partners suit should slow me down, but I do have a 5-5 15 count)-3H-3N-4H Without the heart T I might pass 3N and take my chances, but its generally better to be in a suit on a misfit, if there is a suit thats good enough. Note: I generally play that in a GFing auction after partner has bid NT you can bid the 4'th suit naturally, but this only applies at a lower level. At the 4 level, the best use for a bid of the 4'th suit is a good bid of a different suit. Which suit is it a good bid for? Well look first at if you can set all the suits as trumps below game. If there is only 1 suit you can't set below game, thats the suit this 4'th suit bid shows. If there is more than 1 such suit (or if you can agree all the suits below game) than this is a good raise of the most recently bid of those suits. E.G. 1S-2D-2H-3D-3S-4C=Slam try in Spades (spades bid more recently than hearts, can bid 4D naturally below game so thats eliminated) 1S-2H-3D-4C=Slam try in Diamonds (Can bid all suits below game, so next look at what is most recently bid. Note: I consider this sequence the most contraversal, since you can legitamtely set all the suits below game, so the question is if there is a better use for this). 1S-2H-2S-3H-4m=Cue bid for hearts. yes these are only the 3'rd suits but in general, we don't introduce suits at the 4 level when we could have introduced them earlier and didn't. 1S-2H-3C-3H-4D=Slam Try in Hearts (As 3S and 4C are forcing, and 4H is not forcing, this must be for hearts). Is this basically the rules that everyone here plays? If not what are the differences? Note: There are other auctions where only 2 suits are in play, where you can't set either suit below game. For instance if you play 1N-3S, as both majors GFing, then most play 4C=Good 4H bid, 4D=Good 4S, 4H=bad 4H bid, and 4S=bad 4S bid. There are other auctions, such as 2N-3C-3M where you can't possible want to play in the other major unless partner can bid it (if you had only 5 of that one but not 4 of the other you would have transfered not bid stayman) but you might have a 5+ card minor you were intered in playing in. Hence 4 of either minor is natural, and the idle bid of the other major is the only strong raise. Once again note, there is no cue-bidding before you agree a suit... Principle: When there is only one idle bid available, you should use it to show "extras" and interest in going higher, and not use it as a cue bid or a specific help suit. (For instance in the auction, 1S-(2D)-2S-(3D), 3H is the only game try available, so it shouldn't promise hearts. there is a similar principle at the 4 level when trying for slam and at the 6 level when trying for a grand. When there is two or more suits to choose from, then they become semi-natural (below 3N) or cue-bids when trying for slam.

I remember an australian pair sat down against me in the reisinger playing about 8 different pre-empts like thats (including the 6S or 4S and 5+ minor pre-empt) with a small sheet of inadequite defenses and we had no time to go over them and come up with reasonable defenses, even though there are completely unsound.... This kind of stuff is one of the reasons the acbl decided they had to approve defenses in the first place. Perosnally, I think in a pairs movement, there should be a limit to the number of your pre-alerts (at least for not totally routine stuff like multi or x-fer responses to stuff which partnerships really should be expected to be pre-pared for these days, hence probably should not even require a prealert in a national event). You just don't have enough time to even figure out wha the methods are (and make the appropriate negative inferences) let alone discuss defenses....

There are a couple of interesting points of bidding theory here. Lets Consider 1S-2C-2H-? First what is 3S? This depends a little bit if you are also playing strong jump shifts. If you are not playing SJS, this shows the hand that used to be shown with a SJS and then support. Good minor (usually 5+ cards, but on rare occasion can be an excellent 4 card suit) 4S spades, and slam interest. If you are playing SJS's this should be only 3 card support (but good trumps) and definitely a strong 5 card minor and real slam interest. Its possible to play this as 3 or 4 card support and slammish although I think distringuishing 3 trumps and 4 trumps is a good thing. Next what is 3D? In classic 2/1, since we are in a game force bidding is natural. So 3D showed 3+D and a hand that doesn't want to bid 2N or 3N. The problem here is that people were bidding this with a. Qx Axx xxx AKxxx b. x Axx KJxx AKxxx c. x x KJxxx AKxxxx It was impossible to sort out what to do next, since opener had no idea if responder had a suit, a flexible hand with no stopper, or a freak. Consequently its no longer mainstream to bid 3D on hand b (just bid 2N or 3N, 3N shows extra values and is typically played as 15-17, but its usually a balanced hand, so what to do with 15-17's with a stiff is far from universal). Opener assumes hand a, but bids cheaply. If opener bids 3N, responder can bid the 4'th suit a second time, and this time it shows a 5 card suit. Of course it still might be right to pass 3N. If opener bids 3H or 3S over 3D, opener bids 3N next. But there are three other important hands: responder can be 2335 with Axx or Qxx or Jxx of D. Here you have doubt about NT and are doubtful if NT is right from your side but do not want to rule out the contract. Its nice to be able to bid 3d and then 3N to mean "I would like to play 3N if you have some help in diamonds, but run like the wind with a stiff, or with a weak doubleton and someplace else thats playable". Of course if you want to bid that way on this hand, you can' bid that way on hand c above. So the the other style is that, strange as it may as it may be, the practicle thing is to rebid 2N on both B and C. If partner is 5431, partner will often pattern out over 2N (everything is always natural after a NT bid) and you can find your 5-3 diamond fit that way. Also, partner will sometimes make a 3'rd round bid in your 2/1 suit on Hx. Finally there is the false preference issue. take a hand like Qx Axx Axx Axxxx. This hand really doesn't want to play NT, and especially not from your side, so there is a strong case to be made for overloading the 2S bid. Partner will often be able to bid a natural 2N showing wasted diamond values over 2S and you can raise. If partner bids 3C, 3H or 3S next you probably don't belong in NT. Remember, after a 2 level suit agreement in 2/1, the next bid is natural, not a cue bid, so opener would almost always make the exact same bid if 2S promised 3 cards as if it can be made on Hx and a flexible hand. The main difficulty is in some auctions you can not tell partner that you only had 2 card support, so it occasionally hurts slam bidding (for instance if partner bids 3S next, you have no way of slowing partner down, but your cards are pretty slamish here). Anyway, this is an alternate way to play but not mainstream at all. Note: If the 4'th suit is available at the 2 level its vastly superior to use that as the punt bid and have the bid of partner's suit guarantee 3. But when the 4'th suit is at the 3 level, saving space allows opener to show pattern or bid 2N with a moderate holding. (you are always much safer to bid 2N in a forcing auction on Qx since it doesn't end the auction then to guess to bid 3N on Qx later). So if you bid 3D with the Kx Axx Axx Axxxx hand partner will have to guess what to do with AQxxx Kxx Qx Kx or similar hands (if partner has Kx of spades and no D card you belong in spades, if partner has Axx of diamonds you have to get to 3N from your side). Over 2S partner can bid 2N as long as it doesn't promise really strong diamonds. Also if 2S can be made on a strong doubleton, when you bid 3D partner will know to bid 3N on very moderate holdings unless he has extra shape or a super strong major. Anyway, like I said there is a slam bidding disadvantage of bidding 2S on doubleton's since opener can have a pretty strong hand, but requires a 3'rd trump for a good small or grand slam.

I'm not so sure about that. All I said was that the optimum will occur somewhere in the interior but it must be at a local optimum or somewhere on the boundary but not necessarily at a local optimum since the local or global optimum might occur beyond the boundary. In mathematics there are often ways to check for local optima so we would normally find those points and then check the boundary. In terms of a bidding system it might be relatively hard to determine the local optima especially if we wanted a great deal of precision (excuse the pun). However my main contention was simply that if we consider that the global optimum might be outside the contraints then it will be natural and wise to check the boundaries. This will be made much harder if the boundaries are fuzzy or not well defined in some other way. Sorry Wayne I was using your name in vain. I just reread your original post. It wasn't you who made the claim about convexity at all (somehow it snuck into the discussion). Of course what you said was 100% correct.

jajaja My point of contention here is on the statement "isn't even really in the set up for the problem." That is so picky. First off, a continuous function on a compact set is compact. That's the theorem to which you are referring. This only guarantees the existence of a max. Of course a maximum may still exist if the set is not compact. So the setup you refer to is one in your mind. Second, if you are so concerned about the compactness, we can always make x >=1/2 and x<=1. And to your point about boundary + interior is everywhere, of course we mean that there are only going to be a few critical points to check. Anyway, I'm sure you'll agree with me that there's not much point in worry about convexity or concavity as there's no reason to believe that that's what our function will look like. Come on Matt. I took your example seriously, and changed it ever so slightly (by putting another boundary condition on in addition) to make it conform to the spirit of the problem we were talking about. The content of your example had nothing so every with the fact that the set was unbounded at one end, so I didn't nitpick about that at all. Without the compactness we are not guaranteed a max or a min at all. If we want to prove something definitive about the locations of max's or mins, you need to know if there has to be maxs or mins in the first place. Yes there might be a max or min for a particular function, but a theorem is a statement that given some conditions some conclusions are ALWAYS not just sometimes true. Here is your argument in a nutshell: Wayne made (or tried to make) a statement that If susch an such a condition is true, then such and such is true for the maximum of the function. And you said, but wait, take this example where that condition does not hold, then the same fact was still true for an example. I orginally thought that your confusion was merely about statements about maxima vs statements about extrema. But now its looking like you seem to think that: A implies B has some logical bearing on if 1. Not A implies B or 2. Not A implies not B Of course there no such logical relationship. Of course we all agree, that for the problem we were interested in (the existance and location of the optimal system) that even if there existed a function from the space of systems to the real line such that a higher number means a better system (where better means will beat the other system over the long hawl). that we all doubt that that function is convex or concave. I was just trying to correct the statements of the theorems, lest someone here finds another example in there life where they truely have a convex or concave function.... Note: Most of modern economics is built on the assumptions that there exists a utility function from the set of baskets of goods to the real line that satisfies a. If someone prefers A to B, U[A] > U b. Transitivity holds (People are rational, which is doubtful) c. The Utility function is convex, that is people always prefer a mix of goods than one or the other (on a technical note this only applies to goods that have positive utility, so you would not choose to purchase something that makes you unhappy or has no value whatsoever). So the set up in the theorems discussed here are pretty common.

Maybe I am not sure who your question is directed at. Convexity means if you take 0.7Acol + 0.3Moscito then its better than either one, and that in fact for any two systems aSystem1+(1-a)system2 is always better than either one. Concavity means that these combos are always worse. By always I mean always. Without this being true, the math conclusions (theorems)about the locations of maxima (for convex) or minima (for concave) do not hold. That doesn't mean that they might not be true anyway in a particular case, but its not a logical/mathematical necessity based on the information given.

Right. So explain how your discussion of linear, concave, and convex meshes with the example I gave of a concave function who's solution is on the boundary, namely: f(x) = 1-x^2, x>=1/2 P.S. I have done a lot of work with constrained optimization, not to mention for multivariate functions (where your notions of concavity and convexity are going to be too strict). P.S.S. Wayne's original point was that one should not only check the interior, but also the boundary. I still do not see why that would be untrue, unless you are going to put further restrictions on your function. One can simply imagine the "interior" solution lying outside of the feasible set. I am still missing something: Convex Function: Maximum is On Boundary, No comment on where the minimum is. it might be on the boundary or in the interior. Concave Function: minimum is on the boundary, No comment on where the maximum is, it might be on the boundary or the interior. In fact, your problem which was maximize 1-x^2 with x>=1/2 isn't even really in the set up for the problem (not a bounded, or more generally compact constraint space) but yes its maximum is at its boundary. The theorems cited Said absolute nothing about the maximum of a concave function or a minimum of a convex function. Change your constraints to x>=-1 and x<=173 and now the maximum is in the interior. On the other hand, pick ANY convex function with those contraints and the maximum will be at -1 or at 173. Wayne wasn't remembering the math theorems very well. The interior plus the boundary is everywhere.... :P

Lagrangian is fine and dandy if you have a simple function with an equality constraint. Once you have inequality constraints (such as hcp >7) or mixed constraints, you are talking about Kuhn-Tucker conditions. Again, I don't see what convexity has to do with the problem. You can still hit boundaries with concave functions. You of course can use Bolzano-Weierstrauss to show a maximum exists if it's continuous. We don't have continuity of course, but I don't think it's too big a step to approximate with continuity. We have a pretty good range once we start adding texture into the hands, such as comparing a suit of AK432 with AK984 or with AKT98. The Lagranian multiplier tells you how "strongly" the constraint influenced your answer (and will equal 0 if the optimal answer was not on the boundary at all). That is, if you take a normal to your surface at the point of the maximum, the lagrangian multiplier tells how much the objecive function improves as you cross the boundary. If it is high, its likely (although not certain) that the true optimum was a decent ways away from the constraint surface. Basically this is a first derivative. Theorem A: For a linear program (maximize a linear function on a space with linear constraints), the Maximum always occurs on the boundary, and in fact will always occur on the corners. Note: A non-zero linear function never has a zero derivative anywhere so has no local maxima or minima. Theorem B: if we replace your linear functions with convex functions, the same is true. Proof: Suppose there was a local extrema of the function. That is the gradient of the function was 0 there. This is in fact a local minima and not a local maxima. Why, because convexity implies that the hessian (the matrix of second derivatives) was positive definite everywhere, and that plus a 0 gradient is the criteria for a local min. Theorem C: If you don't want the maximum but instead want a minimum you can replace the word convex with concave. Proof: See above proof. For a concave function the hessian is negative definite everywhere, hence every local extrema is a local max. For a convex problem, its minimum might well be in the interior, and for a concave problem its maximum might also occur in the interior. The issue isn't about existance of maximums (continuity and compactness answer that question) its about if the maximum has to be on the boundary. I hope that helps.

I was about to comment on convexity and lagranian multipliers but Adam beat me to it.... I strongly doubt that this is a convex problem. Now if this is a continuous function real valued function on a compact set.... This also is an interesting game theoretic problem where transitivity almost certainly does not hold. You can easily imagine a rock paper scicors situation with regard to systems (where we include defensive methods and competative methods in a system). Like many of the people here I will mention that boundary type system regulations do have a serious negative effect on the effectiveness of methods. when you play a 15-17 NT you can upgrade KTx Ax AQJxx T9x and you can downgrade KJx KQ Qxxx KJxx. My claim is being able to upgrade and downgrade improves the results you get with the method. When you play 10-12 NT you can't upgrade ATx xx KQT9x T9x which is better than 80% the hands you do open a 10-12 NT. This hurts the effectiveness of the 10-12 NT in constructive auctions. Because of this, ranges like 11-13 or 10+ to 13- are probably more effective than 10-12.

You can find my canape club system on dan neill's system page. Basic Structure: 1C: Strong 1D: Balanced out of 1N range, D, Minors, or any 4441 1M: 4M and longer minor OR 5+M and other major OR 6+M 1N: Balanced 2C: 6+C, no 4 card major 2D: Multi when allowed, Flannary when not (since thats a problem hand in the system) 2M: 5M, 4+m My usual ranges are 10-15ish 1/2 white and 11-15ish 1/2 red and about 2 points Heavier in 3/4 (so 1C is 16+ and then 18+). You may modify ranges to taste. I do recomend if you open very light in 1/2 that your 3/4 seat bids are sounder, or you play a different system in 3/4. It makes no sense to have a 1C opening in 3/4 seat be a puppet to 1D since responder rarely has enough for a positive.... The 1M and 2M openings create a lot of action, especially the 2M bids. Over the 1M bids, 2 of a lower suit is Constructive to INV but not forcing. 1N is forcing, asks for hand type (you bid your long suit, or the other major to show both majors). 1N then a new suit is game forcing, and then there is a natural gameforcing auction. The response to 1N was not forcing, and you can bid 1N on any balanced hand looking for the best place to play, even without values if you think that will improve the contract (or make life difficult for the opps). There are a few ART raises and asking bids also, see the notes.... 5332 hands with a major but out of the range for 1N are usually opened 1D, but can be opened 1M (rebid=2M) or 2M depending on honor structure. Flannary hands, when not playing flannary you have to open 1H and rebid 2H over 1N. The Flannary hand is the biggest problem hand in the system since you sometimes have to rebid Jxxxx type suits. A funny hand from sunday's swiss: Alex: ATxx - Ax KQJTxxx Me: KQJxx xx KTxx xx Auction: Alex in 1'st seat both white. 1S(If only 4, then 5+ in a minor)-P-3D(limit raise)-4H 5C(natural)-5H-P-P 6C(natural)-x-P-6H P-P-6S-P P-x-All Pass One opponent xed 6C on Axxx, trying to chase us from the cold 6C into 6S which could be beat. I held my ground. The other opponent ran for cover. I had no idea who was making what, but I knew partner was something like 4027 so bid 6S. The player with a club void forgot to lighter x, and the other opponent went crazy and decided to not lead the CA and a club which beats 6S.

My opinion is: a. Competing to the 2 level does not show extras, it merely shows 4 trumps although I don't mind the style where you might pass with 4 trumps if your x was hopeless. The problem with not competing to 2S on an auction like 1H-x-P-1S-2H-? when you hold 4 trumps is that partner may elect to bid a minor next and then you have to play at the 3 level instead of the 2 level. If you know partner will rebid his 4 small spades on his 6 count, then you can pass on a min, but thats not the way most people bid. b. competing at the 3 level does show extras, and is INV to game. Of course you have to take some pressure off partner so can bid these Invites sightly lighter in comp than you would normally if you have a good fit, but it still should not be junk. c. Here partner has shown an INV hand, so you really don't need all that much extra to bid 3S. d. So the question is do you have any extras? You certainly don't have in high card points but the 4513 shape is promising, especially with the HK probably well placed. So having said that I think its close between pass and 3S. I would have passed, but thats because I don't x very agressively opposite a passed hand and I expect a passed hand to bid agressively when I do make noise.

I will be in Nashville seeing lots of live music. Maybe I will decide to play a few hands of bridge also....

What Adam should have also said is that his partner looked pretty sleepy, so probably would not have understand what is going on anyway....

I think x is equivalent to a x of a precision 1D bid, or of a could be short 1C bid, values and the majors (ambiguous as to minors) or a big hand. Of course, there is some risk that partner might think you have diamonds, but wait, you have that also! :)

OK, so you are 1. clearly saying that Penrose in NOT qualified, since he is not a computer scientist. Its very interesting that you are praising his argument, and then saying other people with similiar background do not have the background to make an argument about the subject. 2. Further, you are saying that someone who studies computers is capable of making a statement that compares computers and brains, but someone who studies brains is not qualified. Facenating. 3. What supposition? You are making a supposistion that humans can do things that turning machines can't. I have never seen any proof of this statement. Hence your argument is based on a premise without any foundation. Why exactly can't a turing machine prove godel's theorem? Or some other interesting statement starting from the same axioms. As a mathematician, with some expertise into what constitutes proofs, I would dispute that a sequence of statements that are not translatable into something tha can be described in a formal language, and proven sequentially, was a proof to begin with. So almost by definition, a proof is a sequence of statements that a computer can devlop. So the main question is "does the brain have to use something from outside the formal system, to realize what the correct sequence of steps was?" Further, is that extra thing the brain is using from outside the formal system its self just part of a slightly largely formal system (and hence can be part of a turing machine) or does the key ingrediant come magically from someplace other than the formal physics rules that govern the neurons in the brain.

Actually what you should say is that Penrose claims that Humans have performed mental tasks that a Turing machine could never complete. You should probably also note that very few scientists accept Penrose's claim... "Scientists" shouldn't really get a vote in this matter. A climatologist would be quite unqualified to voice an opinion. Same for physicists and biologists. They can say they don't believe it all they want. They can say they don't see how it could possibly work. What they need to do is show the flaw in his argument based on computer science. I've yet to see a convincing refutation. Ooh, I am going to have a field day with this. Penrose is a Mathematical Physisist. He important work is in Differential Geometry and the Structure of Space Time. He is most famous for his work on Black Holes. Now while some people's brains do in fact remind me of Black Holes, I have to remark that he has no special expertese in Cognitive Science, although one of his students did change fields and do work on AI and on a bridge playign program (GIB). I in fact, did my thesis research in a similar area to much of Penrose's work (his work on twister's and on minkowski space)- I certainly don't think that that qualifies me as an expert on the brain (any more than it qualifies him). In fact most people I have read who do work in the field of Cognetive science (For instance Richard Hofstader, Daniel Dennet, etc.) don't agree with Penrose at all. I personally think penrose's argument is poppycock. Why can't a turing machine prove Godel's theorem? That penrose asserts that there are things that a computer can't do, doesn't make it true. Where you don't see a conclusive refutation, I don't even see a claim. As far as I am concered this is like my claiming that God is a Blue guy from a planet orbiting Riga, and saying we should accept God is Blue and from Riga unless you can prove otherwise. Anyway Godel's Theorem a very formal theorem that can be stated and proven in a very formal system. It just happens to have meta system conclusions. We proved it in a finite number of steps in my theory of computation class, probably a monkey could get this one right eventually with a little luck... Anyway, what the heck is this argument Todd? WHo exactly are you claiming is qualified to make an argument about conciousness.

I think pass is clearly forcing. Game forcing auctions imply forcing passes. A freely bid game implies a game forcing auction. While 3N might be a tactical bid, and a subtle advanced save over some 3 level contract of there's, the presumption without some understanding to the contrary (which should be alerted) was that 3N bids are allways based on a belief that 3N will make. I don't think the x of 4C changes anything, except that it clarify's responder's hand type (not that there was that much doubt as to the hand type before--there was too much bidding, and opener showed no inclination to defend). As to what bids mean now: x is penalty, pass is forcing (so takeoutish). Yes its possible to invert these in the direct seat if you have specific agreements about pass/double inversion in high level forcing auctions. Now that I look further in the thread, well I guess there was doubt about opener's hand type, since the 3N was a missbid, and xx was clear....

Hand 1: If 2N is lehbensohl you are kind of stuck, and I would have to bid 2N planning on passing 3C. It might be better to play 2N as scrambling over a passed hand x. Hand 2: After 1S-2D-2S-3C opener migh punt with 3H, since he does have doubt about strain, but with 1.5 stopper in the 4'th suit and a misfit for responder's 2/1 I like 3N. I think 6N was a bit misguided. 12+19 and a misfit is only 31 which isn't enough for 6N, so you need partner to have extras. If you want to force to slam, certainly you should bid 5N (pick a slam)m which will let you find 6C. But I think the correct bid over 3N is 4H which is a natural slam try, showing the rest of your pattern. 4H is like a 4N bid (although it could have some extra values) . Over 4H opener is only worth a 5C bid. 5C is more encoraging than 4N since it shows a fit, but it denies any extra values. On the other hand, responder will like the 5C bid since opener will have to be 5314 or rarely 6214 with strong hearts and weak spades. Since responder only has the DJ wasted, but otherwise his hand fits well, he will probably gamble 6C over a 5C bid. Hence my suggested auction: 1S-2D 2S-3C 3N-4H (forcing to 4N) 5C(Not forcing)-6C(I like partner's shape!) Hand 3: After 1C-1H 1S 2D (ART GF) (Note: most play 1S as non-forcing these days, but I sort of like the old KS style of this being forcing unless responder made his first bid on a 4 count) At theis point, 2N is a mistake. yes you have a diamond stopper, but you don't want to declare NT, and you have a perfectly good natural bid of 3D. 3D shows something like 4045, or 4144 (if you open that 1C in your partnership), or possibly 4135. In any case, after bidding 2D responder has two different slam tries available next, 3S and 4S. Most play 4S as a mild slam try with 4S and strong hearts. Partner can bid over this on suitable hands. Since 4S uses up so much space it should probably be a very specific hand such as a strong 5 card heart suit, 4 spades to a top honor, and no control in the 4'th suit. Perhaps it should have no control in either minor, I have no strong opinions. Anyway, in your sequence: 1C 1H 1S 2D 2N (3D is a better bid) 3S (4S is the other option) Now 3N is rediculous. You really do not want to play 3N with a heart void. You definitely should cue bid 4D but I have trouble seeing these two hands get past 4S on any sensible auction. Maybe they will get to 5S if both players are enthusiastic.

My Various Long Lasting Partnerships: A. Standard American with Ben Shapo. This partnership lasted for 5 years in DC, but Ben had various kids, and eventually moved, and pretty much stopped playing bridge. Besides, he was paying attention to kids and career, so wasn't really getting better at bridge.... B. 2/1 GF with Kevin Avery. A hybrid between some washington standard methods and lots of my toolkit including natural and GFing 2N bids over all 1 level openings, and lots of 2'nd round in the auction relays. Kevin also mostly dissapeared from bridge persuing career and stuff. C. 2/1 GF KS style with Bob Kerchner. This partnerships agreements was largely built around Robson and Segal's book. Bob took a few years off from bridge but is getting to play again some now that he has retired. D. Standard American with Ken Katzner. Ken died about 7 years ago and I miss him. E. Washington Standard with about 20 semi-regular partners from DC (Leo Lasota, Ellen Klossen, Ellen Chirnovsky, Susan DePorte, Mita Banerjee, and many others). These are people who I have played in sectionals and regionals with or even in national events with, but none of them I played with all that much, but there was a pretty common system among us all. F. 2/1 GF with Marc Umeno. Ok perhaps this system resembled Bocchi and Duboin's system more than standard 2/1. We started with a natural 2N and soon added transfer walsh methods (1999?). We then added a 2C ART Gfing relay over 1M and other x-fer 2/1's, but we have gone back to straight 2/1 over 1M since we don't play often enough and Marc was having trouble remembering the methods. This was by far my most complicated system. G. TOSR with Dan Neill (Transfer openings, strong club with symmetric relay) H. Strong Club with Symmetric Relay with John Pendergrass. We started as 4 card majorites but switched to 5 after a few years. Over the non-strong club we play a hybrid of Meckwell, Berk-Cohen, and my old 2/1 methods. I play similar methods with Josh Donn and Adam Meyerson. I. Strong Club, Baby Meckwell Style (Like Hampson Greco, and now Cheek and Grue) with Clem Jackson. J. Strong Club, Canape. I originally designed this system for Ben and to give Dan and I something to play in events where we could not play TOSR (which is most of them). I have mostly played this with Chris Monsour and Alex Kolesnik over the years, but have yet to try it in a national event. This years Spingold with Alex will be interesting... I have had other semi-regular partners over the years (Marshall Miles, Alan Kliest) were I did various other non-standard things... I have always had a secret love for magic diamond. :P