OPTIMAL STRATEGY OF CHESS
Ludwig Plutonium
jgr...@frodo.d.umn.edu (john greene) writes:
> Why does your method of successive moves tell you that P-K4 is
> the best first move? If White is allowed to move repeatedly, then
> White can capture the black king in 4 moves. This can be done in
> more ways than I care to count. Many of these involve P-K4. However,
> P-K3 works as well. Here are several more that do not involve
> moving the king pawn at all: N-QB3, N-K4, N-B6, NxK
> P-QB3, Q-N3, QxBP, QxK
> P-KN3, B-R3, BxP, BxK
Thanks for the info on prime existence N,2N.
The successive moves is only a technique. To be effectively used, for
the OS of White, it must consider all of White's pieces against Black.
Each move by White must have maximum advantage. Think of it this way.
It is generally conceived that at the start of chess, a knight is worth
3, taking a pawn as worth 1. But these values shift as each move is
made. Now one can assign numerical values to pieces and to positions,
considering the first move to N-QB3 vice P-K4.
Here I could go on for five pages, but have more important irons in
the fire,..
In answer to your question. Successive moves must consider the whole
entire army of White's pieces not just one piece such as your knight
running down there and Black being a total novice not seeing that a
solo knight is about to capture his king. Successive moves is only a
technique. It is a pretty technique which I am sure will uncover the OS
of chess from the opening through the middle game. The endgame is
standard knowledge.
Successive moves needs a computer set-up because, re-analysis on
every move by every opponent.
Ludwig Plutonium
d...@cwi.nl (Dik T. Winter) writes:
> In article <2ko59s$p...@dartvax.dartmouth.edu> Ludwig.P...@dartmouth.edu (Ludwig Plutonium) writes:
> > Successive moves is simply this. White analyzes what successive
> > moves, without Black making any move, will capture Black's king. This
> > is a technique which works. This technique says that pawn to king 4 is
> > the best first move for White.
>
> Wrong Ludwig. This says that Knight to c3 is best (followed by d5, f6, e8).
> Back to Aljechin.
> --
No. I am correct Dik. The Successive Moves (SUM) Technique works
beautifully in fetching-out the OS of chess. A computer would make it
easier, but it is not necessary. You must realize Dik, that the OS of
chess is a very difficult problem, and not easy like finding the OS of
tic-tac-toe. As Karl Heuer found that the total number of positions of
king-capture-queening-only is exactly
301713997230054847933486967990950152652695930240. My point is that
unlike tic-tac-toe, chess has this huge field to sort through to find
the OS. The OS of tic-tac-toe is easy to discover and widely known by
earnest players of the game.
SUM must be used with the consideration of all of Whites pieces as
one. White must make the first move. Is there a very best first move
and can it be discovered for chess? In tic-tac-toe the OS has you take
the center square. What is the first move in chess?
Considering the centuries of chessmasters who have played the game,
certain patterns have emerged. The following are felt about the opening
and middle game, but not assured, (1) control of the four center
squares (2) develop the minor pieces (queen out early is a target) (3)
castling. As I say, these are felt and not assured. The probability of
(1),(2),and (3) being in the OS of chess are very high.
Logic entails that if there is a weakness in Black's position before
the first move, that this weakness would be utilized in the OS.
I propose SUM can discover any inherent weakness in Black's position.
But, for SUM to work with maximum effectiveness, all of White's pieces
must be considered as one force. So then Dik, your knight to c3
followed by d5, f6, e8, may win against a player who is playing for the
first time, but would lose against anyone of comparable abilities. Dik,
you have not applied SUM to Whites whole force. SUM does say that
knight to c3 is a better move than knight to f3 in the opening. Just
here in the choice of which knight to move out first is given by SUM.
Knight at c3 has a quicker highway to king capture, but we must
consider the analysis in whole. Knight at f3 opens castling quicker.
But, I feel that SUM will find out at what move(?) 10th move(?) is
castling maximally effective. You can begin to see why a computer would
be so tremendously helpful.
SUM says that Black (also White) has a point-of-weakness in the
opening before there is a move. Before the first move by White, an
analysis through SUM indicates that Black's king bishop pawn which is
square f7, is the weakest square, the point of weakness for Black. SUM
shows that White with two knights, one bishop and it's queen can put
maximum pressure on Black via f7 corridor. Fool's (mate) king capture
is one of those combinations.
Thus SUM indicates that pawn to e4 is the very best first move for
White and is the first move in the OS of chess. I claim e4 is the first
move of OS because of SUM and the control of center squares. Knight to
c3 is not a good first move by White because in the application of SUM,
you must consider the WHOLE of White's force. SUM says that f7 is the
weakest point of Black because so many pieces of White's army can
attack through that corridor in a hurry. Whereas, Dik, your solo knight
to c3 is a solo act.
SUM is a technique, not a guaranteed procedure. If SUM was anything
more than a technique then that over-SUM and the OS of chess would have
been discovered centuries before.
I believe the OS of chess when played by both White and Black, the
result is a tie. Assuming a tie, then this is a guarantee-- if someone
believes they have discovered the OS of chess for White (and if true),
then White playing the OS will never lose a game of chess forevermore.
No matter who White's opponent is, human or computer.
The recent Scientific American article on chess, as computing power
increases, computers replace human grandmasters, is a case of bad
reporting, because it gives the general public the impression that
computers will be the grandmasters of chess forevermore, and from there
on out the computers will dominate chess playing. It is bad reporting
because the article fails to give the understanding of the OS of chess
as per VonNeumann's math game theory. It is my opinion that the author
of the article did it for the express reason to leave the impression
that computers are almighty and indispensable, and subsequently causing
a run-up in computer sales. It is my impression that computers are
merely tools, and will only be a better means to an end. Scientific
American should have run an article on the OS of chess. Because it is
my opinion that it will be a Human who discovers the OS of chess, not a
computer. And it will be a Human who uses the computer to check and
verify that the OS of chess was indeed, discovered. I predict it will
be SUM that more than anything else, helped to discover the OS of
chess.
THE OPTIMAL STRATEGY (OS) OF CHESS IS A PART OF THE 13th PLUTONIUM
PROBLEM. The Plutonium Problems are the successor of the Hilbert
Problems. ATOM
Dik T. Winter
> The OS of tic-tac-toe is easy to discover and widely known by
> earnest players of the game.
The earnest player will not play it. There is no OS for the first player.
> In tic-tac-toe the OS has you take
> the center square.
Why? Because there are 4 answers that give a forced win (and 4 answers that
can lead to a forced draw)? When you start at a corner square there are 7
answers giving a forced win (with only one that can lead to a forced draw).
And with a middle edge start there are also 4 answers with a forced win.
A center square start is the most disadvantageous you can do as your opponent
has only two essentially different answers to consider. The other starts
give the opponent much more opportunity to give the wrong answer (as long
as he does not know the game reasonably well of course). You better start
studying tic-tac-toe before you tackle the much more difficult game of chess.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924098
home: bovenover 215, 1025 jn amsterdam, nederland; e-mail: d...@cwi.nl
Ludwig Plutonium
d...@cwi.nl (Dik T. Winter) writes:
> Why? Because there are 4 answers that give a forced win (and 4 answers that
> can lead to a forced draw)? When you start at a corner square there are 7
> answers giving a forced win (with only one that can lead to a forced draw).
> And with a middle edge start there are also 4 answers with a forced win.
> A center square start is the most disadvantageous you can do as your opponent
> has only two essentially different answers to consider. The other starts
> give the opponent much more opportunity to give the wrong answer (as long
> as he does not know the game reasonably well of course). You better start
> studying tic-tac-toe before you tackle the much more difficult game of chess.
I count 4 possible two-in-a-row two ways for X starting from center,
and the same number of 4 for X starting in the corner. However when X
starts in the corner, then the O player can go on the offensive on O's
second move. Whereas starting from center, X is always on the
offensive.
HERE IS THE OS FOR X IN TIC-TAC-TOE
Put X in the center. Only two possibilities for O: (1) If O goes in a
middle-edge, put X in a corner next to the O. This gives X
two-in-a-row. If O fails to block on the next move, make
three-in-a-row. If O blocks, put X in the empty corner such that X has
two-in-a-row two ways. No matter what O does on the next move, X makes
three-in-a-row.(2) If the first move of O is a corner, put X in one of
the middle-edges next to O. This gives X two-in-a-row. If O fails to
block make three-in-a-row. If O blocks, put X in the corner that is
next to the second O and on the same side of the grid as the first O.
This gives X two-in-a-row. If O fails to block, X makes
three-in-a-row. If O blocks, put X in the empty square next to the
third O. This gives X two-in-a-row. If O fails to block X makes
three-in-a-row. If O blocks, X fills in the last square for a draw.
Dik T. Winter
> I count 4 possible two-in-a-row two ways for X starting from center,
> and the same number of 4 for X starting in the corner. However when X
> starts in the corner, then the O player can go on the offensive on O's
> second move.
You are counting wrong. When X starts in corner the only response that does
not give X a win is O in the center. Number from 1 to 9.
X: 1, O: 2, X: 5, O: 9, X: 7, wins
X: 1, O: 3, X: 9, O: 5, X: 7, wins
X: 1, O: 6, X: 7, O: 4, X: 5, wins
X: 1, O: 9, X: 3, O: 2, X: 7, wins
similar for O in 4, 7, 8 and 9. Second move O is forced.
That I have to teach in sci.math somebody the basics of tic-tac-toe...
Wei
> I count 4 possible two-in-a-row two ways for X starting from center,
>and the same number of 4 for X starting in the corner. However when X
>starts in the corner, then the O player can go on the offensive on O's
>second move. Whereas starting from center, X is always on the
>offensive.
Is there anything in game theory says being "on the offensive"
in tic-tac-toe means anything? What does it mean when you have an "OS"
for tic-tac-toe, the best outcome is a draw after all, how can one drawing
opening be better than another? And the previous poster (Mr. Winter)
did point out that putting in the corner gives O a better chance of
screwing up (more losing moves possible).
James Alan Riechel
> [text deleted]
> In answer to your question. Successive moves must consider the whole
>entire army of White's pieces not just one piece such as your knight
>running down there and Black being a total novice not seeing that a
>solo knight is about to capture his king. Successive moves is only a
>technique. It is a pretty technique which I am sure will uncover the OS
>of chess from the opening through the middle game. The endgame is
>standard knowledge.
> Successive moves needs a computer set-up because, re-analysis on
>every move by every opponent.
> [text deleted]
Just how many example positions would you like in which your strategy
leads to a loss for the player-to-move rather than a win or a draw?
---------------------------- -James Riechel (jrie...@cc.gatech.edu)
| *k: ::: ::: ::: |
| ::: ::: ::: ::: |
| *p ::: ::: :::*p ::: |
| ::: ::: ::: *p: |
| ::: ::: ::: P ::: |
| ::: ::: ::: P ::: P |
| ::: ::: ::: P :K: |
| ::: ::: ::: ::: | White to play and draw!
----------------------------
James Alan Riechel
People that have studied chess tell us that in a typical game each player
has an average of 30 moves to choose between at each move and that
a typical game lasts 40 moves (usually ending in resignation). The "game
tree" associated with a typical game of chess, then, consists of
30^80 nodes. This is why chess has been so difficult to *solve*.
Many people have and still are studying chess, especially chess masters
and people in artificial intelligence. One approach that people have taken
involves trying to reduce the number of choices at each turn. The
intuition here is that n^80 is better than 30^80 for n < 30. These
people have found, however, that it is impossible to not "throw out the
baby with the bathwater."
That is, there is no metric or heuristic function that always correctly
classifies a move as either being worthy or not worthy of consideration.
Therefore, when a (possibly winning) move is incorrectly classified,
"the baby gets thrown out with the bathwater." And there is the other
side of the coin, a (possibly losing) move is deemed worthy of
consideration.
(Why is this so? Essentially, this is the case in chess because chess
as a problem cannot be divided into not-interfering sub-goals. For
example, the goal of attacking your opponent and winning material can
interfer with your goal of protecting your king from being checkmated.
There are, of course, more than just two interacting sub-goals in
chess --- witness, even, the complexity of the evaluation functions of
commercial chess programs. In the language of AI, chess is non-monotonic.)
But even supposing that a metric exists that is guaranteed to
classify one-half of the possible moves as being "not worthy of
consideration," we've only reduced the game tree from 30^80 nodes to
15^80 nodes. We are no closer to *solving* chess as the game tree is
still too large.
Apparently, you are claiming that the "SUM algorithm" provides an
optimal strategy in chess. This is just your intuition and one would
expect proof to follow. If you really don't want to do that much
thinking, I can tell you now that it'll be much easier for you to prove
yourself incorrect rather than correct.
Ludwig Plutonium
jrie...@gaia.gatech.edu (James Alan Riechel) writes:
> Just how many example positions would you like in which your strategy
> leads to a loss for the player-to-move rather than a win or a draw?
>
> ---------------------------- -James Riechel (jrie...@cc.gatech.edu)
> | *k: ::: ::: ::: |
> | ::: ::: ::: ::: |
> | *p ::: ::: :::*p ::: |
> | ::: ::: ::: *p: |
> | ::: ::: ::: P ::: |
> | ::: ::: ::: P ::: P |
> | ::: ::: ::: P :K: |
> | ::: ::: ::: ::: | White to play and draw!
> ----------------------------
I wish I could picture the 5f6 on the screen with the orbitals and
electron dot cloud. If I could have, I would have flooded the
newsgroups with it.
James, this is an endgame. My SUM is merely a help, a handle in
hopefully digging out the OS of chess. SUM does not reduce chess
analysis to deduction. SUM is a tool in analyzing points of weakness,
avenues of attack, which moves are superior. SUM is not useful in the
endgame. SUM, hopefully will uncover the OS for the opening and
middlegame. Once the endgame is reached that is standard analysis and
it is well known.
Ludwig Plutonium
> The "game
> tree" associated with a typical game of chess, then, consists of
> 30^80 nodes. This is why chess has been so difficult to *solve*.
I think the total possible number of games of chess are less than 3 x
10^47. But my definition of a chess game is different from yours. I see
my definition as well-defined and your definition as ill-defined, but
so be it. It is not worth hassling-over.
James Alan Riechel
>jrie...@gaia.gatech.edu (James Alan Riechel) writes:
>> [text deleted]
>>
>> ---------------------------- -James Riechel (jrie...@cc.gatech.edu)
>> | *k: ::: ::: ::: |
>> | ::: ::: ::: ::: |
>> | *p ::: ::: :::*p ::: |
>> | ::: ::: ::: *p: |
>> | ::: ::: ::: P ::: |
>> | ::: ::: ::: P ::: P |
>> | ::: ::: ::: P :K: |
>> | ::: ::: ::: ::: | White to play and draw!
>> ----------------------------
> I wish I could picture the 5f6 on the screen with the orbitals and
>electron dot cloud. If I could have, I would have flooded the
>newsgroups with it.
> James, this is an endgame. My SUM is merely a help, a handle in
>hopefully digging out the OS of chess. SUM does not reduce chess
>analysis to deduction. SUM is a tool in analyzing points of weakness,
>avenues of attack, which moves are superior. SUM is not useful in the
>endgame. SUM, hopefully will uncover the OS for the opening and
>middlegame. Once the endgame is reached that is standard analysis and
>it is well known.
Ludwig,
The above chess position is known as a .signature file. It is
not intended to be an example of a position that "your" "SUM algorithm"
cannot handle.
Comprendo?
James Alan Riechel
Ludwig,
It is true that many of the 30^80 nodes in a "typical game" are not
unique, but at least I tell you how I arrive at my number. In that sense
my "definition" of a "typical game of chess" is well-defined, whereas yours
is not. Just how do you come up with the number 3 x 10^47?
But whether the complexity of chess is better "described" by this
number or by that number is beside the point. You did not address anything
of importance from my post. Therefore, I conclude that you either did
not understand it, or you're really not interested in learning. Instead,
you seem to be playing some silly game. (I don't know, you might even be
a bona fide nut case.)
"Pet ideas" are great, but they should really be abandoned if:
(a) it turns out somebody's already done it and you have nothing new or
interesting to offer; or (b) the pet idea withers under the weight of
empirical evidence. Both (a) and (b) apply to your "SUM algorithm."