Tuesday, September 30, 2008

And God placed the middlegame before the endgame

Phaedrus added the following comment to my latest post:

"It is completely unclear to me why an "ideal game" should end with an endgame. It might well be possible that the ideal game (played by the super computer that "solves" the game of chess, is already decided in the middlegame. As your assumption of an ideal game is the foundation of this quest, I do not know if you have struck gold here. Yet I am very interested to see where it ends."

There are 3 ways by which a game can be won.
• Winning a piece
• Mating the King
• Promoting a pawn
All combinations that win a piece can be devided in two seperate groups. The first group I have dubbed the duplo-attacks. These work by attacking simultaneously 2 pieces with only 1 move. Notice the similarity with my previous posts where one move served two goals. If the opponent of whom 2 pieces are under attack can only make a single-purpose move, he can only save one piece by making that move.

The question is, can you force that?
Imagine a middlegame position with no pawns. There is no way that you can win a piece by best play because the pieces are simply too volatile. Every attacking move can be countered by either a counter attack or a defensive move. You can only win a piece with a duplo-attack if the pieces are restricted in their movement. Pawns are the agents nec plus ultra to restrict pieces. So the question translates to can you force the restriction of pieces by pawns so that a duplo-attack is unavoidable?

The second group I have called the traps. A trap has as characteristic that you restrict the movement of a piece by moving your pawns forward. This leads to the question can you force the restriction of pieces by pawns so that a trap is unavoidable?

Given the similarity between both questions I think it is justified to say that if one of the questions must be answered with no, it probably means that the answer at the other question must be no too.

I simply cannot belief that the final frontline of the pawns will be far off of occupying about 50% of the board at average. I cannot belief that 1.d4 or 1.e4 give you such forced advantage that you will end up occupying say 75% of the board. A ship with two captains who want to head in opposite directions and where every captain can steer for 5 minutes will end up roughly at the same spot as where they started.

I cannot imagine that owning 50% of the board is enough to trap a piece or to force a duplo-attack. So, overall, winning a piece by force with ideal play from both sides is beyond my imagination.

Which leaves mate as the only method to win before the endgame. I consider mate to be a special instance of a trap. But there is a difference. First the value of the king is infinite, which means that every means is justified as long as it ends up as mate. Second, the king seems somewhat limping, because of old battlewounds, of course. He moves slow. Which makes him an easy target. I have no arguments that an early forced assault must be excluded. On the other hand I have seen no indication at all that such untimely assault is likely.

Because of the application of computers we can be sure that such assault will not take place in the first 12 moves. On the contrary, the longer I let a computer evaluate a position, the closer it gets to a zero advantage, usually. After centuries of chess no indication has emerged that an early forced assault is likely. But I cannot proof that it is impossible.

If it is possible, we are not able to find it though. Which is the same as saying for us humans, with the aid of computers, it is not possible. Yet.

As long as it is not proven otherwise, the ideal endgame will thus end in the endgame.

1. Ideal play from both sies will end in a draw, I'd bet the house on that even though it can't yet be proven

I have an indirect argument, though. The evaluation of a position with ideal play never goes down, but only stays the same (I'm not gonna argue this, but some reflection should show it is true). Hence, the evaluation at the beginning of the game will be the evaluation at the end of the game, if both sides pick the best move.

Assumption: the evaluation at the start of the game is less than one pawn in white's favor (those of you with bad-ass chess engines can experiment with this...I'm stuck with old fashioned Fritz 9, which gives a score of around 0.25 after a tiny 15 minutes of thinking). Of course Fritz 9 evaluation isn't God, as ultimately if my argument is right the evaluation must go to 0.0. But using this as a finite approximation to the true answer, I bet a quantum computer will give the initial evaluation as 0.0.

Since less than one pawn is not enough to win, the game will end in a draw, and the true initial evaluation is 0.0.

2. Dear Temposchlucker,

Seems to me you are chasing the absolute truth here. For this reason I dare to question your line of reasoning.

Without pretending that I have completely thought through your line of reasoning (which very well may be more worthwhile than questioning it), I dare to question some of your statements.

First of all you say a game can be won in three ways. This is not correct. The game can only be won in one way, which is checkmate. Remember we are talking in the absolutes here. though a cases could be made that resigning by your opponent is another way, I don't think that this makes much of a difference, as this is only done because ultimately he does not believe that he can avoid checkmate (however long this will take).

Of course I know that you wanted to state that winning a piece, or promoting a pawn usually equals reaching a winning advantage. But cannot the same be said about winning a pawn, achieving a massive lead in development or creating weaknesses?

Another puzzling statement is that in a middle game position with no pawns (BTW I don't think that we will find a single one in any of the big databases, according to you it is impossible to win a piece by best play by both sides. I don't think that there is a way to prove this statement. It should not be hard to however, to produce positions in which all pieces are on the board, with no pawns left, and in which there is a forced win of a piece.

I would also like to point out that winning a piece or promoting, just not equal winning a game. Sometimes being two pieces ahead is not enough (e.g. King and two nights vs K). Also promotion is sometimes insufficient to win (see for instances endgame studies with stalemate motives). So there seem to be some loose ends to some of your statements.

And returning to the concept of the "ideal game". When I use your definition, of an "ideal game", which is a game without accidents, I do not see a reason why this should lead to an endgame. There is an infamous line in the Zaitsev variation of the Ruy Lopez which leads to a draw by repetition with all pieces and pawns still on the board. Hence an ideal game, that never reaches the endgame.

All in all I get the impression that you want to make clear to us that the endgame dictates the course of the game from the beginning. And though I see some truth in this, I feel that this is only part of the story. I agree that to some degree the endgame features of a position are a factor that has to be reckoned with when evaluating a position or choosing a move. But this is only one of them. There are also other features like king safety and mobility, that determine how the position should be evaluated.

And sometimes an advantage can turn into a disadvantage. In some positions (when there are still many pieces on the board), it is an advantage to have space and advanced pawns. This advantage can turn into a disadvantage however, when pieces are exchanged. After these exchanges you may find yourself overextended (I can reccomend Stean's "simple chess" for an excelent treatise on this subject).

I trust you will believe me if I say that all this ranting is not because I would want to pick on you. It is a sincere attempt discuss your findings with you, and I only do this because I take you very, very seriously!

3. Phaedrus,
First of all you say a game can be won in three ways. This is not correct. The game can only be won in one way, which is checkmate. Remember we are talking in the absolutes here.

My thoughts, or even better, my feelings aren't ripe yet to be formulated in a formal and correct way. This is the incubationtime for idea's. So I'm pragmatic. The idea of "the ideal game" is invented to get rid of distracting mates or wood loss, which only disturbs the mind while thinking about the endgame. I invite you to look through the obvious objections.

Of course I know that you wanted to state that winning a piece, or promoting a pawn usually equals reaching a winning advantage. But cannot the same be said about winning a pawn, achieving a massive lead in development or creating weaknesses?

The point is that some words lack content for me. They are hollow. This is a quest to fill these common expressions with content. "Activity of the king". Only now I know what kind
of goals the king heads for, I can estimate how active a king is. How close he is to achieving his goals. A massive lead in development? King safety? Mobility? What is the content of that. I only have a vague idea. Yet there might be ways to measure that. But that can only be done when I know what I'm talking about.

Another puzzling statement is that in a middle game position with no pawns (BTW I don't think that we will find a single one in any of the big databases, according to you it is impossible to win a piece by best play by both sides. I don't think that there is a way to prove this statement. It should not be hard to however, to produce positions in which all pieces are on the board, with no pawns left, and in which there is a forced win of a piece.

I think it is too early to focus on the exceptions when the main idea isn't clear. I talk about me, not about you. What I did was putting such positions in the computer and let it play all night against itself. At a certain moment I realized that the pieces are just too volatile to be catched.

I am stretching the examples till absurdism. That's the fastest way to see if there is anything in it.

Of course your critisism is justly, and it need to be adressed sooner or later. But I think it is a bit too early now.

4. No matter what we feel the ideal game will come down, the truth be told for us mere humans there may never be an ideal game. Yes we will have games where everything trades down, and neither side will make progress. However it seems in getting to that point there are small miscalculations on both players' part that aren't exploited by the opponent.

We have to navigate our way through the middle game, trying to find the moves that will give us an edge either positionally or materially. We also have to be aware of the fact that our opponent is trying to do the exact same thing. We need to watch out for what the opponent is doing.

Since none of us are a super computer or even Fritz 9, we are most likely going to have something occur before the end game which may shift the balance of power in favor of one player or the other. Lately a number of us have posted positions or full games where we show our missteps.

Sometimes those missteps aren't fatal. BDK showed a combination he missed that would have not only won a pawn, but simplified the game tremendously. He won the game in spite of having to navigate through a more difficult ending with rooks on the board. Having an understanding of how to play that ending probably helped him out tremendously. If he didn't have the knowledge or erred in his thought processes, perhaps the opponent would have been able to hold the draw.

Checkmate is the ultimate way of ending the game. Most of my games end well before that because either the opponent or I feel that the situation is hopeless. Mate might be a few moves away or maybe it's many moves away, but playing on seems hopeless. As humans we may resign because we want to save ourselves for the next game, we feel it's disrespectful to the opponent to play on, we're tired of fighting, or if it's the last round we just want to go home. Computers on the other hand may play all the way out because they don't know to resign.

I played a computer in the 1988 US Open. I was playing a king and pawn ending. I had gained the opposition and was going to win the pawn race. It was an easy win. We had been playing for around 4 hours and the computer operator resigned on behalf of the computer. The computer was evaluating the position as hopeless lost, but since it was not programmed to resign it would play on using all of its' remaining time. The operator was tired and knowing the computer's evaluation of the position decided to end the game at that point instead of having me play the position all the way out to mate.

The beauty of chess is there is no perfection so we need to study and learn this stuff to navigate our way through imperfection.

5. I also found it odd when you made the claim about pieces-only means no duplo attacks. This took up most of the first half of your post, so please forgive my ignorance, but if that wasn't a main idea, then what was the main idea? That with perfect play we will end up with an endgame not a mate in the middlegame?

King activity shouldn't seem all that mysterious. The K needs to be in on the action once its safety is less of a concern as there isn't enough on the board to molest it into mate. It's worth like 4 pawns in attacking strength, so use it! What is unclear about that?

6. "A massive lead in development? ... What is the content of that. I only have a vague idea. Yet there might be ways to measure that."

Come now. You have read a bit of My System if I recall correctly... it's not so difficult to come up with a working definition. A lead in development can be measured by counting tempi--and while Watson rightfully pokes fun at how such methods can be bent to absurdity, in general they're quite useful in evaluating positions.

7. I'm still very curious in where you're heading with this and look forward to your next post. :)

8. Polly,
you are right of course. There is a huge difference between a hypothetical theoretic ideal play and our daily errorprone practical chess reality. What I try to find is a sort of background for my thinking during a game. A kind of framework that helps me to decide in what direction to look if it's directly clear from the immediate tactical or strategical needs of the position.

9. Blue,
I also found it odd when you made the claim about pieces-only means no duplo attacks

"Mother came with the bike and the packed lunch." If you have a two-dimensial view of the world and take the sentence above in a sort of mathematical or literal way you might think that the word AND suggests an equality between BIKE and THE PACKED LUNCH. That is what happens when you are unclear about the exact content of a word. In reality there is a huge difference in this case because the GOAL of my mother was to bring me my lunch while the bike was only a means of transportation. In another context it could have been the other way around, that she brought me my bike and needed to eat in doing so. There is some framework in the background needed that helps you to interpret the sententence. These posts are an attempt to provide such background.

I play with pieces and pawns. In my 2D view of the world I'm inclined to think that there is some equality between the word pieces and the word pawns due to the use of the word AND. My example was an attempt to provide some more content to these words. Stressing the volatility of the pieces and the restricting quality of the pawns. The example took a great part of my post since in the past I have done a lot of research with the computer in order to find out what would happen if there were no pawns.

King activity shouldn't seem all that mysterious. The K needs to be in on the action once its safety is less of a concern as there isn't enough on the board to molest it into mate. It's worth like 4 pawns in attacking strength, so use it! What is unclear about that?

I always learned that during the transition to the endgame the king should walk to the center in order to gain in activity. But when I relate the activity of the king to the goals he is needed for I now have an almost mathematical base to know that in a certain position the king has his optimal activity while standing on a8. That is what happens when the expression "king activity" is given a more exact content.

10. LF,
A lead in development can be measured by counting tempi--and while Watson rightfully pokes fun at how such methods can be bent to absurdity, in general they're quite useful in evaluating positions.

More content of a conception like "lead in development" means for instance that it becomes more clear which tempi should be calculated and which not. And why. Thus adressing the exceptions of general rules with a more precise understanding.

11. LF,
this post was of course only a brief intermezzo in order to address some questions of Phaedrus. These intermezzi are extremely useful for me to adjust the feeling of what is important and what not.

I'm still very curious in where you're heading with this and look forward to your next post. :)

I will take up the original thread soon. I'm quite curious too.

12. This reminds me of the Aasgaard/Watson fight. :)

Aasgaard says the rules are great even though there are exceptions. Watson says right, but my book is focused on the exceptions and the kind of concrete reasoning that leads you to them. The concrete-position focused thinking rather than the abstract rule-based thinking. Of course they are both right.

Rules help tame complexity, and there are exceptions. Yes, a King can be best on a8 in an endgame, but how many endgames, what proportion? Not many.

I think the question of how helpful the rules are depends on someone's skill level. A beginner needs to learn the basic rules, though be told there are exceptions. A GM knows all that, and is much better at seeing the exceptions. But if someone were to suggest the rules were unclear or opaque, I would disagree. They are fairly clear, they just are not universally true. It would be a mistake, for a novice, to not tell them to get their King out there and use him to fight, to focus on the exception by showing him one from the very small number of games in which the King should stay at a8. That should come after showing him 40 games where the King comes out to fight and it pays off or it doesn't and the wimpy King player loses.

13. Blue,
not quite. I didn't intend to define exceptions on a rule, I'm busy to replace a blunt rule without understanding by a more sophisticated rule with understanding. From "in order to activate your king you must walk to the center" to "in order to activate your king you must walk towards the action". With an addendum which defines what action is.

14. Regardless, activating the King is a good thing. As you improve your understanding of King activation will improve, until you die. So perhaps instead of insinuating it isn't a useful thing to say, it would be more accurate to say that you are re-evaluating exactly what it means (and of course we can say that always about every edict).

At this point I am glad.

Tempo is back.

15. Polly: you are right, of course. My argument that ideal play implies draw was theoretical, not practical. I was still not quite clear what Tempo was saying, so I thought I was defending him. Now I don't know if I was defending anyone, but it is a fun computer-type argument, but not one to help anybody's play (well, except the claim that evaluations can only go down or stay the same, which is helpful for move selection as it implies that picking the least bad move is identical to picking the best move).

16. Blue: This is an interesting discussion and exchange of ideas. I wouldn't say it's totally useless in our search for improvement. I think anything that makes us think outside the box, and consider long range goals (gaining wood, promting pawns, mate) helps our development as players. Fortunately we're a civilized bunch, and this type of discussion doesn't turn into a flame war. Though tempo has the proverbial bucket of water (moderation) to put out any flames before they even start.

17. In discussions moderation is never needed. Once or twice a year a troll walks by who starts offending me. Especially my pedantic arrogance, "mister KnowItAll" seems to bother them.

In itself the matter of trolling is quite interesting. The strange need to anonymously offending people in the hope that they react gives us a peek in the nightside of the human brain. Allthough my spamfilter blocks offensive language I often can't resist to have a look at what they write. The secret cause why people always get at war with each other lies within such minds. They must suffer from a strange kind of confirmation bias.