For the chess fans

Hey PZ.. Paul should only live a few miles from me. Want me to stuff him in a box for you and send him your way?

It is my sincere hope that, perhaps one day, distributed computing systems will reach the point where we can actually calculate the Nash Equilibrium for chess. To what end? At the very least, it will force the chess obsessives to do something more constructive with their time ;^)

Interesting comments you have, and I can't make up my mind as to whether or not they're mutually exclusive. I think Paul Davies has a point, that the pursuit of science is based upon the assumption that we can put order to the mess. But the assumption that the mess is orderable can indeed be false. So

I feel like I'm looking at Schrödinger's cat. Only this time... I'm inside his belly.

Well, we know there is for draughts (err, checkers in your tongue). It's likely that with best play white cannot lose. One argument that show this in other games is that if black (playing second) can win against best play, and if no move makes the position worse for white, then white can play a random move, and then play black's winning strategy.

Define "win" as "win or draw", and all you need to do is show that no move can make the position worse for white. I doubt this can be done for chess, but I suspect that there are moves which don't make the position worse.

As to understanding what the best play is, that's a very different question - I guess it boils down to if there's an algorithm that can be used to generate best play, and if the algorithm is a lot smaller than the "look-up table" a computer might use. That's something I'll profess ignorance about.

Grrr, my Hawkwind LPs are in the cellar.

Bob

I don't agree that science depends on this assumption, at leat not if you want to maintain, a la Davies, that it's a completely unexamined assumption that scientists have to take on faith. It's a hypothesis, subject to testing like any other, or, if you prefer, a meta-hypothesis, that tags along with every scientific hypothesis as it's tested.

The only element of faith that enters into science is that some intelligible answer will arise from rigorous methodical investigation: "chaotic" and "beyond current understanding" are, after all, intelligible answers, if perhaps unsatisfying to the inquisitive mind, and I see no evidence that scientists, as a group, disqualify work that leads to such conclusions. (That they may not perform such work in the first place as the problems are widely understood to be intractable is another matter. But one generation's "intractable" is the next's Nobel.)

Can we apply this discussion to chess? Do you believe that chess is ultimately governed by fixed rules and logic, or do you believe it's just a 'random' game where, to paraphrase Myers, things 'just happen that way'?

This comparison is absurd. We know that chess is governed by fixed rule and logic, because we defined it that way. The same goes for mathematics. But that does not apply to the universe. Sheesh. Talking about whether we "understand" the all outcomes of the fixed rules and logic is another matter altogether. Just because something seems "unintelligible" doesn't mean its "random". Of course a move that is required to win is not "random"; it's the least random of all. The author abuses words and logic.

Is chess ultimately a game of order, or a game of chaos?

This is the ultimate silliness and abuse of terminology. We know that the universe is chaotic, but that has nothing to do with whether it is governed by fixed rules and logic. The Mandelbrot set is the ultimate in mathematical chaos, yet is governed by a very simple rule. Sheesh.

Davies's claim that one must have faith to do science because it wouldn't work otherwise is simply a fallacy of affirmation of the consequent. It makes no more sense than to say that one could not propose hypotheses unless one had faith that they are correct.

Not Alaric the Hun? I'm lost on Arioch, too.

Ack! Visigoth. Not Hun. I always get them mixed up. (Not a good idea in dodgy bars.)

Melnibonean Lord of Chaos from Moorcock's Elric of Melnibone. Classic dark fantasy.

@Truth machine, of course chess is a game of rules, but of course that's not what I meant. (I may not be a grandmaster in chess, but I do know the rules... please give me that credit.) What I meant was (and is also obvious from the text): are the ultimate *solutions* to the questions in chess governed by rules, or just by chaotic moves which seem to lack any rhyme or reason? Are there understandable patterns that humans can try to understand to make sense of certain positions or moves?

Well, we know there is for draughts (err, checkers in your tongue).

We know there is what?

In chess, as in checkers, we know that there is either a strategy that always wins for the first player, that there is a strategy that always wins for the second player, or that both players have a strategy that guarantees a draw. The difference between chess and checkers is that, for checkers, the latter of the three has been proven.

It's likely that with best play white cannot lose.

You just make this stuff up as you go along, don't you? It's been proven that, with best play, neither player will lose.

One argument that show this in other games is that if black (playing second) can win against best play, and if no move makes the position worse for white, then white can play a random move, and then play black's winning strategy.

Neither chess nor checkers is that sort of game; sheesh.

What I meant was (and is also obvious from the text): are the ultimate *solutions* to the questions in chess governed by rules, or just by chaotic moves which seem to lack any rhyme or reason?

What is obvious from the text and from what you just said is that you are incoherent, that you are conceptually confused. The solutions to the questions in the universe are governed by the laws of physics -- if there are such laws. And the solutions to the questions in chess are governed by the rules of chess.

Sort of OT, but

I never get this line of thinking. So what? If science is predicated on the 'faith' that the rules of the universe exist and can be determined, then so what? Does anybody else really act in any different way?

So scientists have faith that experience will give us a hint as to what these rules are and how we can predict future events based on them (essentially ignoring the problem of induction). Other than the truly insane, so does every person of faith.

The difference is, people of faith also place faith in a buncha other bullshit as well as induction.

The only element of faith that enters into science is that some intelligible answer will arise from rigorous methodical investigation: "chaotic" and "beyond current understanding" are, after all, intelligible answers, if perhaps unsatisfying to the inquisitive mind, and I see no evidence that scientists, as a group, disqualify work that leads to such conclusions.

If "beyond understanding" is an "intelligible answer", then what would an unintelligible answer be? As far as I can see, all you're saying is that scientists have "faith" that they are communicating with each other in a common language.

There truly is no assumption or faith of any kind required to do science. If you're making some assumption, simply stop making it; that won't prevent you from carrying out the same actions.

@truth machine, of course the solutions are governed by the rules of chess, but what about the rules to win?
You'll never win a game if you apply the rule 'give away as many pieces as you can'. However, you may win some games if you apply the rule 'try to hold on to your pieces', or, a little more sophisticated, 'try to occupy the centre with your pawns or pieces'. Which goes to show: there are also *other* kind of rules than just the rules of how the pieces move. So before you comment on my conceptual confusion, please try to bear this in mind. I'm talking not about the rules of the game (which are totally obvious and indeed not worthy of comment), I'm talking about the rules which makes one win certain positions. We *know* there are such rules to win certain endgames, whereas we can only *suspect* there are such rules to win *all* positions. And it's this suspicion that is what the article is about.

so what?

The idea is that, if scientists can excuse having faith in one thing, they should excuse having faith in another thing. The idea is stupid bullshit.

I don't agree that science depends on this assumption, at leat not if you want to maintain, a la Davies, that it's a completely unexamined assumption that scientists have to take on faith. It's a hypothesis, subject to testing like any other, or, if you prefer, a meta-hypothesis, that tags along with every scientific hypothesis as it's tested.

The point I think Davies is trying to drive at is (and I'll grant you that its a circular logic) that without the faith that there is some higher order, there would be no reason to test anything. You don't bother trying something you know is doomed to fail from the start. (Well at least if you're acting in a rational, efficient mind) If you didn't have the faith that there was some sort of order, all of science would really boil down to some sort of mental masturbation.

Now I'll grant you this. The faith that there is no order, does not mean there is an order it is simply the driving force behind the investigation. If theory pans out that it's chaotic, or otherwise, that's all fine and dandy, but you've got to have that push to keep going.

At least that's what I think Davies is trying to convey.

Truth machine, of course the solutions are governed by the rules of chess, but what about the rules to win?

First, what the hell does this have to do with what Davies and PZ are disputing? You're mixing up very different things. Chess is known to have rules, by definition; the universe's rules are learned by observation.

Second, the "rules to win" are implicit in the rules to play. What's the rule to "win" the game of proving mathematical theorems? It's to obey mathematical logic -- beyond that, it's quite ad hoc. What are the "rules to win" employed by Chinook to play checkers? It's to do deep searches that obey the rules of checkers. How do grandmasters win at chess? It's by doing deep searches, together with an excellent pattern memory. Amateur players may think in such simplistic terms as "put rooks on open files", but such heuristics won't get very far.

However, you may win some games if you apply the rule 'try to hold on to your pieces', or, a little more sophisticated, 'try to occupy the centre with your pawns or pieces'.

You'll only win against very poor players if all you do is apply rules like that.

The point I think Davies is trying to drive at is (and I'll grant you that its a circular logic) that without the faith that there is some higher order, there would be no reason to test anything. You don't bother trying something you know is doomed to fail from the start.

But we don't know that, do we? In fact, we know that, in every case we have ever observed, that isn't what happens. But we didn't start out knowing that, we learned it -- humans moved from imposing superstition on an seemingly incomprehensible world to recognizing patterns in that world.

If you discover some behavior that pays off, say holding your golf club a certain way that gives you more accuracy, it doesn't take "faith" to keep doing that. And since science keeps working, it doesn't take faith to keep doing it.

@Truth machine. So at least you agree with me that there are more kinds of rules in chess than just the ones that tell you how the pieces go, at least that's somehting, even though you seem to think that applying generic rules such as 'put rooks on open files' are only for amateurs. I have bad news for you: it's simply not true, especially not in theoretical endgames, which is something you'd know if you actually played chess. In such endgames, all you have to do is apply the rules and you'll win. Computers have proved this beyond doubt, and so have amateurs who have actually 'learned' this rules. It's just an emperical fact of chess. So no dispute there.
And of course these rules don't always count in all positions, but that is exactly my point: the question is, are such generic rules in principe possible as they are possible in theoretical endgames? That's an open question, and one I tried to explore in my article. There are various possible points of view, one of them is that in the end chess can only be solved by calculation, and another is that humans can actually find generic rules for solving the game of chess. That's all.

Whether or not chess can be "solved" the way checkers has been seems to be incidental to the point. In the endgame used as an example, a computer has ground out a solution to show which side wins if both sides play perfectly. However, as PZ notes in his comment posted, that does not mean we "understand" the endgame.

Since science is about explaining things rather than just describing things, the fact that there is a complete description of a phenomenon is only the beginning of science, not the end. The "why questions" cannot be answered with a description.

so what?

The idea is that, if scientists can excuse having faith in one thing, they should excuse having faith in another thing. The idea is stupid bullshit.

I thought so, but I wasn't sure if there was something meaningful in the idea that I was missing.

We *know* there are such rules to win certain endgames, whereas we can only *suspect* there are such rules to win *all* positions. And it's this suspicion that is what the article is about.

No, the article is about ignorance and confusion. Only someone who knew very little about chess would suspect such a thing, as we already know that numerous endgames are utterly inscrutable by any human being. If this hadn't been clear before, it became very clear in the Garry Kasparov vs. The World match, where each side was using computers to identify queen & pawn endgames with forced wins in over 100 moves. Few of the moves in these endgames were predictable to Kasparov or anyone else; they simply nodes on a path through a possibility space. Nonetheless, chess is governed by fixed rules and is not at all random.

Indeed, fardels bear. The question is not whether chess can or cannot ever be 'solved' like checkers - it's whether humans can ever explain or understand this solution. We don't know this, but we can speculate.

Well, truth machine, you're only emphasizing my point (albeit in an admirably hostile way) that such endgames can be very complex indeed (an even more complex example is the endgame I actually mention in my article, thank you.)
But even the fact that Kasparov doesn't understand the details of these endgames (trust me, he knows a lot more than one might suspect), doesn't mean than nobody ever will, does it? That you personally don't find this speculative question very interesting, is your opinion. I myself think it's a very interesting and even relevant matter, and fortunately for me, so do others like Tim Krabbé and GM John Nunn who, even to your high standards, *does* know slightly more than 'very little' about chess.

I have bad news for you: it's simply not true, especially not in theoretical endgames, which is something you'd know if you actually played chess.

I have played tournament chess; you are clueless and ignorant. I have also spent a lot of time working on chess puzzles, which defy all your "rules".

In such endgames, all you have to do is apply the rules and you'll win. Computers have proved this beyond doubt, and so have amateurs who have actually 'learned' this rules. It's just an emperical fact of chess. So no dispute there.

You are beyond ignorant. As one of the comments to your post says, "Even the table base 5 piece rook endgames are extremely hard to 'understand' (see Dr Nunn's excellent book). We would just have to accept that white mates in 535 moves with perfect play by black." And I mentioned the queen and pawn endgames of the Kasparov match. There is far more in the world of possible endgames than the sort of KBN vs. K endgames that you learned about in Chess Endgames for Beginners.

@Truth Machine
If you discover some behavior that pays off, say holding your golf club a certain way that gives you more accuracy, it doesn't take "faith" to keep doing that. And since science keeps working, it doesn't take faith to keep doing it.

But what you're talking about is Serendipity, not a quest to achieve something (in this case scientific discovery). You're suggesting leveraging a known benefit, not searching for it. If you were looking for a better way to do something, you must believe that there is a better way to do it, otherwise why would you look?

humans moved from imposing superstition on an seemingly incomprehensible world to recognizing patterns in that world.

Wouldn't a series of patterns that makes up the world consist a "Higher Order" (I'm not talking God imposed, I'm talking simply in terms of organization) If the world/universe were a purely random chaotic system everything would fluctuate willy nilly. As is it appears we have at least a semi-ordered system. There appear to be rules which govern the universe (physics). Should we happen to disprove that I'll be the first to jump on board the anarchy bus, but until that day, I'll happily continue looking for order until I can find the counter case. [and that... is where the faith comes in]

But even the fact that Kasparov doesn't understand the details of these endgames (trust me, he knows a lot more than one might suspect), doesn't mean than nobody ever will, does it?

An expected refuge of the stupid and ignorant.

Kasparov does understand the details; he understands that moves early in the sequence work because of circumstances that arise later in the sequence. He understands that, for that reason, you cannot apply only local rules, which is what you are asking for. As I said, we know that your "suspicion" is mistaken.

Truth machine, this is my last reply to you. Dr. John Nunn's book is actually all about *explaining* such seemingly irrational endgames in 'human' terms (perhaps you think he failed, he'd be interested to know), not in just giving long move sequences as the poster suggests.
As to my chess skills, you can see my rating and credentials on the website where I posted my article, as well as links to databases which list my games including a very interesting draw against some dude called Gary Kasparov. And no, normally I don't like boasting, but you had it coming. I suggest next time you check your facts before you call someone ignorant ;-)

But what you're talking about is Serendipity, not a quest to achieve something (in this case scientific discovery). You're suggesting leveraging a known benefit, not searching for it. If you were looking for a better way to do something, you must believe that there is a better way to do it, otherwise why would you look?

All I'm talking about is a behavior that has paid off repeatedly in the past. Doing science is such a behavior. Perhaps it's "serendipity" that the world has remained orderly and lawlike up to this point; it could change at any moment. But it doesn't take any "faith" to continue to do what has worked in the past.

You said I don't play chess, you phypocritical asshole. You are most certainly ignorant about the subject that you are writing about, regardless of your chess skill.

Truth machine, this is my last reply to you. Dr. John Nunn's book is actually all about *explaining* such seemingly irrational endgames in 'human' terms (perhaps you think he failed, he'd be interested to know), not in just giving long move sequences as the poster suggests.

Yes, Nunn develops human-comprehendable strategies where they exist; he's quite good at it. But that says nothing about whether there are cases where such strategies don't exist -- you've employed a blatant fallacy of affirmation of the consequent.

"Yes, Nunn develops human-comprehendable strategies where they exist; he's quite good at it. But that says nothing about whether there are cases where such strategies don't exist."
Indeed. I couldn't agree more. And that was also exactly the point of my article. I knew we'd agree in the end.

"Yes, Nunn develops human-comprehendable strategies where they exist; he's quite good at it. But that says nothing about whether there are cases where such strategies don't exist."

And that was also exactly the point of my article.

What an incredibly stupid thing to say.

Isn't the whole question, um, flawed or something?

There's a teleology in chess - the goal is to win.

The universe HAS NO GOAL.

Truth Machine:
All I'm talking about is a behavior that has paid off repeatedly in the past. Doing science is such a behavior. Perhaps it's "serendipity" that the world has remained orderly and lawlike up to this point; it could change at any moment. But it doesn't take any "faith" to continue to do what has worked in the past.

You put forward a convincing argument. However you've got to believe that the gains you've made in the past via scientific inquiry will continue. Maintaining an endeavour with a known lack of benefit is a nonsensical concept. An expenditure of energy on something that you know can be of 0 gain is either insane (something I wouldn't necessarily put past most physicists) or an idiotic waste.

This does not preclude the use of previous gains. Such knowns have proven themselves useful and hence the faith that they exist vanishes as they have succeeded in moving from imposing superstition on an seemingly incomprehensible world to recognizing patterns in that world. Yet the belief that there is something better yet out there still exists. They day that we stop believing there is something better out there is the day every scientist can sit down and eat a cheese danish together.

As to the the universe/world being serendipitously stuck in a state of balance/order, frankly I can't argue that, I'll leave that one up to the 12 dimensional thinkers.

Vic:

The universe HAS NO GOAL.

... or at least none that we know of...

Now that would be something I would relish disproving.

There's a teleology in chess - the goal is to win.

Whether a given position is a forced win is an empirical question, a question that can be answered in the abstract regardless of any desire to win at chess.

The universe HAS NO GOAL.

The game of chess doesn't have any goal either. But as chess players and as scientists, we have goals.

The game of chess doesn't have any goal either.

To be clear, what I mean is "the game of chess" as a thing in itself, like the universe as a thing in itself. The game is just a set of rules of play; the set of rules is not an agent, it has no desires. No where in the rules of chess will you find any desire to win, or even any preference as to the outcome. The rules don't even express a desire, or require, that games be completed. The rules are simply a description.

However you've got to believe that the gains you've made in the past via scientific inquiry will continue.

If I have to, it's not because of faith.

Maintaining an endeavour with a known lack of benefit is a nonsensical concept.

Making such obviously false claims suggests a lack of intellectual honesty. I buy stocks without knowing that I will benefit; I do all sorts of things without that knowledge. One merely follows what seems like the best available strategy. If you've got a better strategy than science, tell us what it is.

Truth machine, I understand your point about the set of rules not being an agent and having no desires, but in the Laws of Chess there's also this article:
"1.2 The objective of each player is to place the opponent`s king `under attack` in such a way that the opponent has no legal move."
Wouldn't you agree that this objective is also a part of the set of rules that together define the game?

"Maintaining an endeavour with a known lack of benefit is a nonsensical concept."

Making such obviously false claims suggests a lack of intellectual honesty.

Sorry, I misread your statement. But I misread it because it's so ludicrous and I had already answered it -- there is no known lack of benefit from science; how silly.

Truth machine pinned the essence of bad reasoning down at first post. David Hume's 'problem with inductive reasoning' is the only 'faith' required in science and inductive reasoning at this level is a necessary condition for existence, and it is still based upon evidence.

The only analogy between science and chess might be that ones' play is governed not only by the rules of chess, but also by ones' understanding of ones' opponent. In this analogy, we are not uncovering the rules of chess, only the rules that work for this situation (which is how science operates but the 'situational sphere' enlarges with repeated observations). Here is a less-than-perfect game I played many years ago. I am white. My moves were governed by knowledge of my opponent as much as by objectively best moves.
1. e4, c5; 2. Nf3, d6; 3. d4, cd4; 4. Nd4, Nf6; 5. Nc3, a6; 6. Be3, Nc6; 7. Be2, g6; 8. f4, e5; 9. Nxc6, bc6; 10. fe5, ed5; 11. Qd8+, Kd8; 12 0-0-0+, Kc7; 13. R(h)c1, Bg7; 14. Bg5, Ne8; 15 Rxf7+, Kb6; 16. Bd8+ Kc5; Ba5 with unavoidable checkmate in one of two ways (Na4 or b4).

Relevant analysis: On move 6, better is Bg6 or Bc4, my move was dictated on not giving my opponent a simple reflex response. On 8. f4 (castles is better) but I knew my opponent liked to 'counter punch' and I saw the (winning) position at move 13 if he did. Finally, march of science: My opponents' a6 was based on the 'known fact' that there is a white square weakness for black otherwise- except that Fisher (60 memorable games) shows otherwise. On move 4, my opponent played . . Nf6 because we both knew e5 to be bad for black (creates a good square to post a piece on d5 for white)- except that about the time this game transpired, Yvgeny Svesnikov in Russia had just worked out the line such that it is a viable option, my opponent certainly would have picked this aggressive move had he known of it.

Sorry for the long post, Paul Davies is not a real chess player :)

Alaric is Cirala spelled backwards.

Wouldn't you agree that this objective is also a part of the set of rules that together define the game?

What I would agree to is that you are conceptually confused. This defines what winning in chess is, but has nothing to do with the original comment about teleology. And the rule tries to do something it can't; players may have other objectives, as seen for instance in "grandmaster draws", and the rules of chess cannot force players to try to win.

Truth Machine:

"Maintaining an endeavour with a known lack of benefit is a nonsensical concept."

Sorry, I misread your statement. But I misread it because it's so ludicrous and I had already answered it -- there is no known lack of benefit from science; how silly.

That's my point... is that you do have 'faith'(perhaps I should start using a different word due to the incredibly negative connotation that word has amongst the science lovers in the room, myself amongst them).

I buy stocks without knowing that I will benefit; I do all sorts of things without that knowledge. One merely follows what seems like the best available strategy. If you've got a better strategy than science, tell us what it is.

Ok, you're right and my phrasing is inaccurately, yet I hold by the concept I was trying to convey. You engage in those endeavors due to a belief that you will gain something from them. That in some way they'll be beneficial, without having any concrete proof. To me that is the definition of faith.

At the moment, we've got a hunch, we have a strategy that says there must be a better way, there must be more reason, there must be something else we can gain. We have belief, we have faith that, that is the case. So we pursue it with due diligence, looking for an answer.
Whether law or chaos 'wins' in the end is irrelevant. In order to find the solution, as rational humans we have to assume law, and look for proof of chaos.

David Hume's 'problem with inductive reasoning' is the only 'faith' required in science and inductive reasoning at this level is a necessary condition for existence, and it is still based upon evidence.

Contrary to widely held myth, science is not based on induction; we do not count up the number of times we observe something and then declare it as the truth when it passes some threshold. Rather, science is based on inference to the best explanation. Even if we have observed, and can only observed, one instance of an event, the best explanation of that event is the one we go by, and "best" is largely a matter of parsimony. In effect, Ockham refuted Hume.

In this analogy, we are not uncovering the rules of chess, only the rules that work for this situation (which is how science operates but the 'situational sphere' enlarges with repeated observations).

Yes, excellent.

Truth machine, you sure have a way of changing the subject, don't you? This indeed defines what winning is chess it, but it's also part of the offical rules of chess. There's no denying that. So, I may be conceptually confused, but you are factually wrong when you say the rules of chess do not contain any preference as to the outcome of the game. It's very smart of you to switch to teology when you've got your facts wrong (again), but hey, the rules do state such a preference. And yes, players may have other objectives, but it would take a very conceptually confused chess player to forget what the original (and as it seems also official) goal of the game was...

@mothra, I can assure you: 6.Be3 is a perfectly normal move. It's probably even the most popular move on top chess level these days, played by all the best players in the world :-)

That's my point... is that you do have 'faith'(perhaps I should start using a different word due to the incredibly negative connotation that word has amongst the science lovers in the room, myself amongst them).

You can repeat your "point" until you are blue in the face and use whatever word you want, but it won't make it true. And I have no idea what you mean by "that" here; I expressed no faith, I merely pointed out a fact -- that science is not "known to have no benefit", and thus your blather about it being nonsensical is itself nonsensical.

You engage in those endeavors due to a belief that you will gain something from them.

Sigh. What I said is that one follows the best strategy one has; one does not have to "believe" anything, other than that it's the best strategy one has -- but that's a result of analysis, not belief in the sense of religious belief.

That in some way they'll be beneficial, without having any concrete proof. To me that is the definition of faith.

So you're ignorant and too lazy to look in a dictionary. Faith is believing something without reason. Lack of certainty is not lack of reason. I do wish that people would stop making that incredibly stupid mistake.

It's very smart of you to switch to teology when you've got your facts wrong

I did not introduce teleology into the discussion. I'm sorry I've wasted my time on such a stupid and dishonest person (too bad you even lied about your "last response").

. So, I may be conceptually confused, but you are factually wrong when you say the rules of chess do not contain any preference as to the outcome of the game.

This moron either thinks that the rules of chess say who should win, or is incapable of comprehension.

"I did not introduce teleology into the discussion" - no, but when you couldn't agrue with my quotation from the Laws of Chess you cunningly switched to teleology, didn't you?
And I didn't *lie* about my last response, I just changed my mind. How disappointing that you can't seem to make that distinction. Goodbye.

"This moron either thinks that the rules of chess say who should win, or is incapable of comprehension."

This moron just thinks - no, quotes - that the rules of chess say that the goal of the game is to checkmate the opponent. Whether that's a sensible statement is a different matter.

"I did not introduce teleology into the discussion" - no, but when you couldn't agrue with my quotation from the Laws of Chess you cunningly switched to teleology, didn't you?

Fuck you , you stupid asshole; teleology was introduced in #35, I responded to that in #38 and #39, and you responded to me in #41. And the Laws of chess do not express a preference as to the outcome, you fucking moron.

This moron just thinks - no, quotes - that the rules of chess say that the goal of the game is to checkmate the opponent.

Which is not an expression of a preference, cretin.

I wonder if it would help this git if I were to point out that "If Mike Huckabee gets the most votes, he will become president" does not express a preference about the outcome of the election. I doubt it.

"And the Laws of chess do not express a preference as to the outcome, you fucking moron."

I'm sorry, but they do. I don't say it's a good thing (I don't) but they do. Look it up for yourself, if you don't believe my quotation from post #41. You can curse all you want, but it only makes me laugh harder, and it's not gonna change the FIDE Laws of Chess, either.

Truth Machine:

I suspect you either misread or misinterpreted my statement earlier.
Maintaining an endeavour with a known lack of benefit is a nonsensical concept.
I wasn't trying to say that science is a nonsensical endeavour, rather I was trying to convey the point that we have a belief that we can find something better, hence we support a beneficial endeavor.

I'm not sure how you make your jump to a conclusion that I believe that a lack of certainty is a lack of reason, I've expressed no such idea.

I'll cut all the other chaff aside from anything I've said and lay it out clean.

My suggestion is that their is a requirement for a driving force behind science. I would put forth that the quest to find an increasing state of order (regardless of outcome) is that driving force and that is something we must believe in. (or you can believe the counter case I suppose, but any other conclusion and you're simply flailing about.) We have no proof one way or the other (as you've pointed out with your "What if the universe suddenly became chaotic" theory) hence we have Faith one way or the other.

"Which is not an expression of a preference, cretin."

Isn't a goal a preferred outcome? If it isn't, I'm withdrawing what I'm saying.

Truth Machine:
I'm not sure where on earth you came out with #57, but you suddenly stopped making any sense. Up until now you've been fairly constructive.
Explain:

Recently, Canadian researchers created an AI game called Chinook that has solved checkers in the sense that the best that one can hope for when playing Chinook is a draw. The simpler game of tic-tac-toe will also result in a draw if each player makes the "correct" moves. I suspect that for any two player game where players have identical ability, the end game will always be a draw; presumably this will apply to chess as well. There is already an AI that can beat the best human players. What would be interesting to witness is to watch such an AI play itself. I suspect it would end in a draw (i.e., stalemate) on varying locations on the board.

So one could possibly draw the tenative conclusion that for any two player game with identical solution spaces, while Chaos might appear to exist between the initial and end points of the game, the end point will always result in a draw. So deriving a solution for chess (just like the researchers did for the checkers game), might require working backwards from the endpoint, with the primary assumption being that the endpoint involves a draw.

@Sparky, I think he means that a goal for the rules isn't the same as a goal for the players (although I'm probably not formulating this to the high standards of TM) but the fact of the matter is that the goal for the players is part of the rules in chess. Anyway, who cares. Someone who writes so agressively and arrogantly may be right a hundred times, but he's pretty pathetic all the same.

I'm not sure how you make your jump to a conclusion that I believe that a lack of certainty is a lack of reason, I've expressed no such idea.

Sigh. That's not what I said. Faith is lack of reason, but you defined faith as lack of proof, a very different thing. It's not that you believe that a lack of certainty is a lack of reason, it's that you misconstrue what faith is.

We have no proof one way or the other (as you've pointed out with your "What if the universe suddenly became chaotic" theory) hence we have Faith one way or the other.

And there you do it again. Lack of proof is NOT the same as "faith".

It would be nice if we could stop conflating chaos, which is deterministic, with randomness

I'm not sure where on earth you came out with #57, but you suddenly stopped making any sense.

Just because you can't comprehend the obvious doesn't mean that I didn't make sense. Defining what constitutes winning does not express a preference; this is blatantly obvious.

But it dawns on me that perhaps you think it doesn't make sense because you're too self-centered to realize that my comment wasn't directed at you; it has nothing to do with our conversation.

It would be nice if we could stop conflating chaos, which is deterministic, with randomness

It would, wouldn't it? I made this point with my first post, #6.

Anyway, who cares. Someone who writes so agressively and arrogantly may be right a hundred times, but he's pretty pathetic all the same.

Yeah, who care about being right. Talk about pathetic.

Time Machine:

Re: #66; Cool your jets a little, I can follow more than one conversation at a time, and was purely asking for a clarification because you stopped making sense to me if that makes you feel better.

As to the definition of faith... appears to me that someone is "ignorant and too lazy to look in a dictionary".
Look at definition 2b

and with that, I'll bow out with arne.

I suspect that for any two player game where players have identical ability, the end game will always be a draw

This is known not to be true; there are many games where the first player or second player has a forced win. See, e.g., Nim, or Hex (in which a draw isn't even possible).

Look at definition 2b

Yes, one can always dig deeply enough into the dictionary if one is intellectually dishonest enough. Note that it says "firm belief without proof". The point is that faith is unwarranted belief, not merely belief belief without proof; we have all sorts of warranted beliefs in things for which we have no proof.

P.S.

I suspect that for any two player game where players have identical ability, the end game will always be a draw

I don't understand why anyone would suspect this, when the structure of the game can give one player or the other an advantage. For instance, there are all sorts of chess variations where the two players don't have equal material; clearly some of these variations favor one player over the other. Even if one eliminates all such sources of advantage, any game in which players take turns making moves is asymmetric.

@Arne. Yeah, I've played Be3 in other Sicilian games as well and usually survived just long enough to regret it. |[

@70 (truth machine)

Understood. The other qualification I asserted (in addition to player ability) was that the structure of the game involves an identical (or symmetric) solution space. I don't believe who goes first automatically makes the game asymmetric.

By solution space, I mean that when one player makes a move, the structure of the game is such that the number of solutions for one player is reduced. For example, consider a simple game (actually heard as a joke on a show, but very appropriate for my point) called highest number: the winner of the game is the one who says the highest number, and the three rules are you can't say infinity, one person has to go first, and there's only one round to the game. Assuming each player has the same numerical ability, the one who goes first can't possibly win because the game has an asymmetric solution space whereby anything the first person says will be lower than anything the second person says. I assume that the two games you refer to have such an asymmetric solution spaces. This is opposite to say a game where two players have to guess what number a 3rd person is thinking, and the one closest to that number wins. This game has a symmetric solution space even though there's an asymmetry in terms of who goes first, and a game such as this would probably be entirely dependent on player ability; in this instance, perhaps the person with the highest psychic ability.

Tic-tac-toe (9 squares; two players choosing X or O; taking turns) also has a symmetric solution space--but is strongly dependent on player ability; one cannot really lose this game if an X or O is placed on the corners because such moves maximize the solution space for each player.

So, if the game structure itself doesn't have a built-in asymmetric solution space (possibily dependent on who goes first), and, players don't make moves that reduce their available solution spaces.

(Traditional) chess doesn't strike me as having an asymmetric solution space given that each player has the same # of pieces, can make the same moves, and there's the same amount of space between pieces at the start of the game. I don't have enough brain power or mathematical knowledge to determine whether turn taking makes a difference (assuming identical ability).

That's why having an AI chess game play itself would be interesting.

(Traditional) chess doesn't strike me as having an asymmetric solution space given that each player has the same # of pieces, can make the same moves, and there's the same amount of space between pieces at the start of the game. I don't have enough brain power or mathematical knowledge to determine whether turn taking makes a difference (assuming identical ability).

Sigh. Consider a duel in which one person gets to shoot first.

I don't have enough brain power or mathematical knowledge to determine whether turn taking makes a difference (assuming identical ability).

At grandmaster level, white tends to win quite a bit more than black. Black is often content with a draw. Obviously, being white has minimal advantage for beginners. Assuming the trend holds up, one might guess that the advantage of making the opening move is all the greater when two monster AI's are going at it.

I'm with the opinion that to say Faith has anything to do with scientific endeavour is a fallacy; we strive to find answers because as a species with a developed brain we are curious...we do not expect an outcome but we might have a goal, and we use previous knowledge as our markers.

We might have BELIEF in our selves, our skills, and extrapolate possible outcomes from experimentation, but describing desired expectations as Faith is missing the point wildly.

If we were to rely on faith as a tool for development, I don't think anyone would have banged two rocks together, and wondered what to do with the result...which is, of course, 42. Oops, brain lapse into humour mode. /end of obvious post.

Just did a quick survey of games played in the past dozen years or so when both player rated 2700+ (the very top tier of GM's).

Total = 640
Draws = 355 (55.5%)
White wins = 177 (27.7%)
Black wins = 108 (16.9%)

@ truth machine #75

>>Sigh. Consider a duel in which one person gets to shoot first.

Now that's just stupid. Tony specifically differentiated between games that have a symmetrical and asymmetrical solution space. Your example is the ultimate example, I should think, of an asymmetrical solution space: if there is a move the first player can make that immediately wins the game before the second player gets to play, the two sides hardly have symmetrical solution spaces.

One player making the first move does not automatically mean the game has asymmetrical solution spaces. Even though one player gets to go first, Tic-tac-toe has a symmetrical solution space. The question of whether chess has a symmetrical or asymmetrical solution space even though one player gets to go first is not rendered trivial by your duelling example, since there is no play white can make in chess that instantly wins the game before black even gets to make a move. Sheesh.

Perhaps it's a scholastic quibble, but the object of the game rule really is an anomaly. One could easily enough program a computer to detect violations of the other rules, but how does an algorithm figure out the difference between an illegal attempt to throw the game and a mere blunder? Anyhow, what's the punishment for violating the object of the game rule? Automatic loss? That's sort of like inflicting the death penalty for attempted suicide.

Dave S. (@78)

Thanks for bringing some empirical evidence into this discussion. Very interesting.

It does seem to suggest that more than half the time, a traditional chess game with evenly matched players will result in a draw, which supports the general contention that a game with players having identical chess ability and a presumed identical solution space will result in a draw.

The hypothesis does seem to be weakened a little by what appears to be an advantage for White. Can't tell whether it's statistically significant, although I'm guessing it is since the expected percentage for both is around 22% in my estimate (i.e., about 142 expected wins for white and black if there's no advantage for either). It could be that the difference for White going first is psychological, which is entirely in line with research showing the advantage of color (i.e., red) in competitive sports; perhaps the belief that going first creates an advantage results in a psychological advantage that results in the win.

So ultimately, an AI playing itself would likely be the ultimate in testing out the idea because there are no psychological confounds with AI's.

Thanks again for sharing that data.

It would have to be an AI game as 'evenly matched' players (a non-reality based theoretical concept) could not bring 'evenly matched psychologies' to the game. And, there are stylistic differences as well as simple chess savvy. Even in top echelons, a Mikhail Tal would play a very different game than a Tigrin Petrosian. The W-D-L data was interesting. It is worth noting that the goals of white and black are different in the opening stages of the game: white is trying to preserve his '1/2 tempo' edge while black is striving for equality. These are not two sides of a coin.

White also knows what his opening will be, while black is forced to react to it. That advantage would probably be minimal when two AI's are competing.

In fact, black's response to white's first move pretty much decides what the opening will be. If you are playing white, for example, opening by advancing your king's pawn gives black the choice of forcing you to play the Sicilian, the French, the Caro-Kann, the Pirc, the Alekhin, or the Center Counter if he wishes; and each of these opening is quite distinct. To judge from tournament statistics, black is at a considerable overall disadvantage: black chooses what kind of game it will be, however.

A side note. Many years ago I tried to find out which side had the advantage in a chess game in which the moves were randomly chosen. I expected that idiot chess would result in a lot of draws. Instead, trial runs produced a lot of decisive results and black seemed to win more often than white. With no inhibition against moving the king into danger, mating positions occurred frequently and because the white side got to move its pieces into harm's way a little faster than black, white commonly ended up with a serious material deficit.

Now that's just stupid. Tony specifically differentiated between games that have a symmetrical and asymmetrical solution space. Your example is the ultimate example, I should think, of an asymmetrical solution space: if there is a move the first player can make that immediately wins the game before the second player gets to play, the two sides hardly have symmetrical solution spaces.

No, you're stupid. Tony rejected merely having the first move as making the game assymetric; I offered an obvious case where it does. (And, not that it matters, but the first player does not have a move that immediately wins -- shooting an opponent in a duel is not guaranteed to "win", although it certainly gives one much better chances.) Anyone at all familiar with chess knows that the two sides do not have "symmetrical solution spaces" precisely because one player moves first and that constrains the second player's moves.

It does seem to suggest that more than half the time, a traditional chess game with evenly matched players will result in a draw, which supports the general contention that a game with players having identical chess ability and a presumed identical solution space will result in a draw.

No, it does no such thing.

The hypothesis does seem to be weakened a little by what appears to be an advantage for White.

A little? It's weakened a lot. The draws are irrelevant to your hypothesis; what matters is whether the non-draws are split between the two players.

It could be that the difference for White going first is psychological, which is entirely in line with research showing the advantage of color (i.e., red) in competitive sports; perhaps the belief that going first creates an advantage results in a psychological advantage that results in the win.

Is this a joke? It could be that space aliens manipulated the results. But anyone who is familiar with chess, even merely by reading books for beginners, knows that the first player has an advantage of a half tempo, which is the obvious and most plausible explanation for the first player winning more often,

If you are playing white, for example, opening by advancing your king's pawn gives black the choice of forcing you to play the Sicilian, the French, the Caro-Kann, the Pirc, the Alekhin, or the Center Counter if he wishes; and each of these opening is quite distinct.

But in all cases Black's goal is to equalize, while White's goal is to maintain his advantage. Also, 1. d4 gives Black a lot fewer options.

In any case "symmetric solution spaces" when talking about Chess is just ignorant. (Which is not to say that White necessarily has a forced win; personally, I consider that unlikely.)

precisely because one player moves first and that constrains the second player's moves.

Sorry, that wasn't precise at all. White's advantage is that it controls space first, by attacking squares or occupying them (which prevents opponent pieces from moving through them, and prevents opponent pawns from moving onto them), and by making threats first. Beginners sometimes try to copy their opponent's moves symmetrically, but that can't be maintained indefinitely for a couple of reasons: if Q's or R's face off on a file, White capturing the opposing piece can't be echoed; and check (or mate) can't be echoed. The latter is a critical point: if White checkmates, Black can't obtain a draw by checkmating in turn; this shows how the advantage of going first is real -- and it's the same sort of reality, though of lesser degree, than going first in a duel (although in a duel, someone who receives a fatal shot may be able to get off a fatal shot in return before dying).

One player making the first move does not automatically mean the game has asymmetrical solution spaces. Even though one player gets to go first, Tic-tac-toe has a symmetrical solution space.

That's absolutely retarded. Have you ever played the game? Have you noticed that there's only one center square? There's no symmetric response to a move in the center. And, most importantly, whoever gets 3 in a row first wins. With best play the second player can draw, but there's nothing "symmetric" about it; if the first player takes a corner, only a center response avoids losing. OTOH, the first player has to want to lose in order to do so. Sheesh.

I was wondering if people who went second in chess would play for a draw from the very beginning?

I was also wondering if playing for a draw was an easier goal than playing for a win?

Could this skew the win loss ratio?

Sorry if this was already covered.

Well, first I read that Bobby Fischer has died and then I come to this thread. Obviously the universe has the goal of making me think about chess this morning. ;^)

Actually, I haven't read the entire thread, first because the chess theory quickly got to a level far over my head, and next because at some point the "my chess dick is bigger than yours" back-and-forth stopped being fun... but I did want to make one comment on this goal of chess/goal of the universe thing.

On the one hand, truth machine has a valid point (despite being consistently intemperate and obnoxious throughout the discussion): The game of chess, in and of itself, does not have the "goal" of winning. Players have the goal of winning, but the game itself simply is, and has no inherently preferred outcome. In a similar way, the universe simply is, and (as far as we know) has no inherent goals or preferred outcomes.

On the other hand, though, because it is a game, chess inherently, implicitly (and apparently explicitly as well, though I have to take others' comments about the Laws of Chess on faith) embraces the players' goal of winning. Competition leading to a winner is a definitional attribute of those things we call "games" (and yes, I know there are other senses of the word, but you know what I mean). While the game itself can be said not to have "winning" as a goal, nor to care which player wins, it is a created thing[1], and implicit in its existence is its creators' goal that somebody win. If two people sat down at a chess board and moved the pieces around with some goal other than winning -- say, for instance, they were collaborating with the mutual goal of generating aesthetically pleasing arrangements -- we wouldn't call that a game of chess. It's the players' purpose of winning that defines the game.

Here's where the analogy with the universe breaks down: We have no evidence that the universe is a created thing, or that it has rules designed by its creator for the purpose generating winners and losers. That, of course, is the claim of religionists (without being a comparative religion scholar, I'd guess it's the implicit claim of every religion that has a creation myth... which is to say, I suspect, all of 'em), but we have no evidence that claim is true, and considerable evidence that it is not.

So, to sum up...

Chess: artificial construct designed for people to win or lose; universe: not so much.

We now return you to your regularly scheduled penis-measuring contest. ;^)

[1] Yes, I can see that there might be an evolutionary model of games, given that many modern games are clearly derived from earlier games, and variations may well have thrived or become extinct along the way based on their fitness in the social "environment" of game playing. I can also imagine a whole taxonomy of games, in which checkers and chess and other grid-based board/patterned piece move games share some common ancestor but are on a different branch from, for instance, card games. All that said, though, I stand by my assertion that games are created things, because for each modern game, some person or group at some point consciously codified the rules.

The notion that winning or losing is crucial to the definition of game playing is a bit ethnocentric. We in the West are the heirs of the Greeks, for whom the whole point of life was to excel and outstrip the others; and, obviously, other civilizations have also been obsessed with competition. There are, however, cultures in which games and sports are played until a tie results and in which victory is bad form.

Jim (@92): Yah, I'm aware that "game" signifies different things in different instances, including cultural and historical instances. Hence my comment about "and yes, I know there are other senses of the word." Perhaps I should've been more precise... but, you know, we humans encompass a great deal of cultural diversity, and we speak and write in natural languages rather than in artificial languages carefully designed for a strict one-to-one correspondence between symbols and the things signified. Given our gloriously messy cultural/linguistic state of being, one has to allow for a certain amount of "but you know what I mean" if anything resembling conversation is to take place.

In other words, lighten up, dude. (I guess it's my own fault for daring to comment on a chess thread.)

OK, let me "revise and extend": Competition leading to a winner is a definitional attribute of those things we call "games," at least in the sense we mean that word when we apply it to chess and other similar activities, while understanding that the word-symbol "game" is also applicable to other sorts of activities, both current and historical, for which competition leading to a winner is not a defnitional attribute.

Satisfied? In any case, I'm not convinced that the chorus line of angels dancing on the head of this particular pin materially affects the point I was trying to make: Chess is a designed thing that has as an aspect of its design the expectation that players try to win; the universe is not a designed thing at all.

Shorter me (@93) to Jim (@92): Please lay off calling me a bigot (which is what "ethnocentric" is polite, polysyllabic code for) just because I used a common word in its common usage. Thanks in advance.

So far from calling you a bigot, I'm unaware I was addressing you at all. I was making a point that seemed relevant to the ongoing discussion and extended my comment above about the peculiar status of the "object of the game" rule in chess, which apparently refers to chess as a social activity or ritual rather than chess as a logical structure. The other rules of chess indeed define the conditions under which you can say that one side has won, lost, or drew; but asserting that there is something desirable or obligatory about trying to win seems extraneous. People have there own reasons for throwing chess games, after all, including innocent reasons such as losing on purpose in order to encourage a child. For that matter, grandmasters in tournaments often draw games by mutual consent in order to conserve energy, a practice that disappoints the spectators but is not treated as a violation of the rules, even though it apparently does violate the object of the game rule.

Sorry, Jim, if I overreacted; your "ethnocentric" remark seemed like a direct response to my comments about players' goals of winning being a definitional aspect of "game," but if you say not, I take you at your word.

The other rules of chess indeed define the conditions under which you can say that one side has won, lost, or drew; but asserting that there is something desirable or obligatory about trying to win seems extraneous. People have there own reasons for throwing chess games, after all, including innocent reasons such as losing on purpose in order to encourage a child.

I don't know about "desirable" or "obligatory"; I would say that playing to win is inherent in the design of chess (or any game that's competitive, for that matter). To be sure, there are reasons a player might play for a draw in or even throw a particular game... but that doesn't alter the fundamental underlying expectation that playing to win is the point of the game.

By comparison, there may be reasons why a football team (hmmm... should say "American football," in view of the international readership here) might not make winning a particular game its top priority (e.g., a team already qualified for the playoffs might rest its best players) or might even choose to forfeit (e.g., in the case of a natural disaster, financial crisis, or the death of a coach or key player)... but that wouldn't change the fact that, generically speaking, the point of a football game is to win. If two teams took the field and neither had any intention of trying to win, you'd call that something other than "a game"... like "practice" or "a scrimmage."

That's the distinction I was trying to make earlier: Games (of the competitive sort we're discussing) are designed systems that are entirely predicated on the concept of winning and losing, regardless of the fact that there may be reasons why a particular player doesn't try to win in a particular case; the universe, OTOH, is not designed (as long as you don't live in Texas, Florida, or Kansas, I suppose), and doesn't seem (to me, anyway) to be predicated on the same sort of win/lose intention.

BTW, the fact that chess has a specific rule requiring players to play to win was a surprise to me: I would've thought that would literally go without saying, in any competitive game.

@89 (truth machine)

Re: That's absolutely retarded. Have you ever played the game? Have you noticed that there's only one center square? There's no symmetric response to a move in the center. And, most importantly, whoever gets 3 in a row first wins. With best play the second player can draw, but there's nothing "symmetric" about it; if the first player takes a corner, only a center response avoids losing. OTOH, the first player has to want to lose in order to do so. Sheesh.

** "...one cannot really lose this game if an X or O is placed on the corners because such moves maximize the solution space for each player."

I'm not sure what part of that sentence was hard to follow.

If any move is to any of the central squares, I guarantee you will lose the game because since you will LITERALLY reduce your solution space.

For this to be clear, imagine a telephone keypad (numbered 1-9). As each player makes a move, draw an imaginary line that connects where each player places their piece (i.e., X or O) on this numbered grid. It should become immediately clear that placing your pieces on the corners maximizes the amount of space that is covered.

I'd encourage you take some kind of anger management course. There's no need for this kind of juvenile name calling; mind you, we are talking about tic-tac-toe, so perhaps it's understandable.

@86 (truth machine)

It does given the parameters of the analysis. (It's important to pay attention to the qualifications that are inherent to most logical arguments. If you do not critique the qualifications, you are not actually engaged in logical argumentation, and instead are engaged in reasoning that primarily concerns various types of logical fallacies. Thus far, your general comments seem to fall into the fallacious arguments such as arguments against the person, appeals to pride and snobbery, straw man, inappropriate analogies, and put downs.

Re: A little? It's weakened a lot. The draws are irrelevant to your hypothesis; what matters is whether the non-draws are split between the two players.

**Draws are necessary to support one qualification that identical (or at least similar) player ability is needed to observe a draw; very dissimilar ability would predict a win for the advanced player regardless of whether such a player goes first or second. The non-draw data is relevant for the second qualification that a draw also depends on chess having a symmetric solution space. Thus far, the non-draw data appears to negate the notion of a symmetric solution space (but not the prediction of a draw--the data indicates this event happens most of the time).

So now one is left to figure out how there can be more draws (55.5%) than non-draws (related to similar player ability), but yet not an even distribution for white and black (with a slight advantage for white). And as a side-note, if White clearly had an advantage (for players of equivalent ability as determined by ranking), the data should really be showing a 55.5% win for White--meaning that there should be more non-draws than draws in favor of white.

One way to reconcile the paradox is to suggest that there's a psychological variable involved that has something to do with white, and doesn't really have to do with the fact that the game has an asymmetric solution space (i.e., the asymmetry perhaps exists in the mind of the player).

Re: Is this a joke? It could be that space aliens manipulated the results. But anyone who is familiar with chess, even merely by reading books for beginners, knows that the first player has an advantage of a half tempo, which is the obvious and most plausible explanation for the first player winning more often.

**No. This is a documented phenomenon in psychology--in competitive sports, any team or individual wearing red tends to win more often than predicted by chance. There is no reason to believe why this so called 1/2 tempo advantage could not be a psychological phenomenon, similar to a placebo effect whereby the belief that one has a 1/2 tempo advantage makes it easier for white to engage in the mental calculations necessary to win the game rather than worrying about being 1/2 step behind. And it's a fact that anxiety does interfere with cognitive performance. Furthermore, as I indicated, the current data indicates that the advantage is only about 5% for white given that random chance predicts a 22% win for both colors (using a chi square analysis). That's not really a large affect in statistical terms, and so it's most likely a psychological phenomenon.

Again, AI intelligence playing against itself will help deal with this riddle.

Bill, in #91, said:

Chess: artificial construct designed for people to win or lose; universe: not so much.

Thank you - that's exactly what I was getting at with my first comment (#35).

I was wondering if people who went second in chess would play for a draw from the very beginning?

It depends on such things as the strength of your opponent and the consequences of the outcome; if you only need a draw to win the tournament, it would be silly to take a riskier line to play for a win.

I was also wondering if playing for a draw was an easier goal than playing for a win?

Yes, of course.

** "...one cannot really lose this game if an X or O is placed on the corners because such moves maximize the solution space for each player."

I'm not sure what part of that sentence was hard to follow.

If any move is to any of the central squares, I guarantee you will lose the game because since you will LITERALLY reduce your solution space.

Tony. you're an extremely stupid person. Aside from the fact that your comments aren't relevant to the point, they aren't correct.

**No. This is a documented phenomenon in psychology--in competitive sports, any team or individual wearing red tends to win more often than predicted by chance. There is no reason to believe why this so called 1/2 tempo advantage could not be a psychological phenomenon, similar to a placebo effect whereby the belief that one has a 1/2 tempo advantage makes it easier for white to engage in the mental calculations necessary to win the game rather than worrying about being 1/2 step behind.

Moron.