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You actually play 8×8 chessboard in 6 levels for only one move.The whole game you check different 3 tables for both attack and defense, （The table combination is fixed already myself）,and since the logic requires that any two out of three tables under either attack or defense shall meet the logic for position calculation that in attack mode, you make higest valued move and in defense mode you make lowest valued move,there are 2×3=6 tables to check for one move.6 tables for 6 different chessboards.less perspective or tables you check,less information you have for the full complete future status,and when you check them all,you have a very clear idea of what possible future is like,then you can choose to develop your situation in the best way.you can choose to play different style by chcking only attack or defense tables,or checking fewer tables,even checking opposite tables,that decide the style of your play.of course,the highest strength is the one you check them all.But it would be interesting to see what the future would be like if you purposely check less tables and make things worse.For example,when you check too many attack tables where you are supposed to check defense tables as it fits the logic,your chess game would be over defended and thus become a closed game with some hole to be cracked by strong engines.And when you check too many defense tables where you are supposed to check attack tables,you will miss the chance to gain advantage and space thus the game is wide open and quickly turn into end game where you have disgusing pawn shapes or weird king positions,etc.This has something to do with the art of war,the attack and defense balance.
When the position color of ur opponent last moved piece and the your or ur opponent king position either on kingside or queenside considered,There would be altogether 6×2×4=48 tables for each side,and 96 tables for both sides..black and white.It works for Fisher random chess and shuffle chess as well.
It is logic as in our three demensions,any object has 6 perspectives,plus time affair ,96 perspectives deivdes time into 16 partial space. So the whole design is like a time stilled space of 4th demension! I am not guaranteed to ensure the space structure is 100% correct,perhaps just a fuzzy imagine of the 4th demension. but as long as it works for chess,it get the potenial to become developed.
this is the board evulation I made..you can search any move explaniation in the chart:)
there are 8 different situations based on opponents king color and last moved piece color.
any question dear>
How well does the group theory map to chess? I thought you needed invertible elements and associativity to form a group. It seems that with things like check, associativity might go out the window (i.e. certain moves are not legal in certain contexts, so the set isn't closed under move composition). With captures, you have no inverses, so it seems you'd be looking at a semigroup structure at as opposed to a group, although a semigroup still wants associativity. Here I'm interpreting the "moves" as the group elements, with group multiplication like function compositions which would be sequences of moves- am I mis-interpreting? Also, how do the boundary conditions of the board map to the structure? Is there something special about E8 that lets you define operations with those boundary conditions taken into consideration? I'm more into finite structures than continuous groups and topological groups, so maybe I'm missing something really fundamental. Or maybe my interpretation of moves as group elements is wrong. I'd be interested in any more descriptions you could share.
How well does the group theory map to chess?
You can look at my current games with some strong players(one CM , one NM.and one game against houdini2 Pro *64 with PrawnEatsPrawn (2159),and some other games with two other strong players.The final game will be used for E8 chart explaniation.
I thought you needed invertible elements and associativity to form a group.
the group could be defined as the move concept-attack ,indirect attack or defense.
invertible elements are not needed.the move is searched step by step following strict logic.The logic is simple-L mode applies when you need to start attack,so search position with color purple-then blown-then blue.M mode applies for defense moves,so search position with color black-then yellow-then red-then blue.
associativity has something to do with the concept of piece move status-attack-indirect-or defense.
It seems that with things like check, associativity might go out the window (i.e. certain moves are not legal in certain contexts, so the set isn't closed under move composition).
any move is restricted inside of black squares in both L AND M modes.
With captures, you have no inverses, so it seems you'd be looking at a semigroup structure at as opposed to a group, although a semigroup still wants associativity. Here I'm interpreting the "moves" as the group elements, with group multiplication like function compositions which would be sequences of moves- am I mis-interpreting?
the sequences of moves only has something to do with the position to move to,and the potenial position to be checked.for example,two or three piece guarding one position after the move is made.
Also, how do the boundary conditions of the board map to the structure? Is there something special about E8 that lets you define operations with those boundary conditions taken into consideration?
any area outside of black squares are not considered.hard to explanied how I get those 8 maps with figures-I have given the system instructions to get self-improvement function by studying games between engines average elo more than 3200(rybka4 and houdini2).The system absorded all the good value in moves and creat itself own logic.By applying infinite logic combinations,the system gives the best move logic a value-then find out the best logic under any situation-then created the 8 map figures-meaning any move could be explanied.you can take it as the final result calculated for chess board evulation by a weak human intelligence.
a good way to test it is to use it for openings.you can ask me any chess opening explaniation to understand how to use the charts.
I'm more into finite structures than continuous groups and topological groups, so maybe I'm missing something really fundamental. Or maybe my interpretation of moves as group elements is wrong. I'd be interested in any more descriptions you could share.
probability of performing crossover using 8 charts:
1.move logic,piece moving status
5.move value calculation
7.potenial position guarding or protected value
human must consider all those factors to make a good quality move.position value in charts are only a reference to make tactical moves.strategy idears behind moves are far more complciated as all those 7 factors must be considered.
I find one post http://www.chess.com/forum/view/game-showcase/master-vs-master
you can look at master annotion and my charts to find out solutions.
your explanationss seem to involve such high-level mathematics that we do not understand a thing that you are saying.... not to be mean or anything, your ideas are interesting, but we are competely lost in your explanations...
hmm... interesting, I was also thinging about a system like that, where moves are decided using maps. surprisingly, it ALSO as problems with pawns because their moves are so complicated, but it works brilliantly with the pieces and can pick up on tactics, mating sequences, everything...
here's what i've been doing after each opponent's move:
1. "scanning" the piece last moved (looking at each square that the piece could move to) - this identifies direct/indirect threats (looks at the game tactically)
2. making an influence map (i shall use pictures to explain this) - this identifies general game plans, possible attacks, weak squares, etc. (looks at the game positionally/part tactically)
3. picking candidate moves (possible mvoes to fulfill a plan, block an opponents plan, good moves, etc)
4. looking at each candidate separately, calculating some variations, and eliminating those candidates that don't seem to yield good results
5. repeat steps 1-4
In the opening, these things don't work very well, so I rely on opening books, but in the middle/end game, repeating this process 5 times can calculate moves to engine accuracy 80% of the time.
I will make pictures to explain scanning and making an influence map, if you are interested. I don't use e8 or any math really, mainly logic and visualization.
thanks for the nightmares lol
the "best that could be achieved without disadvantaging at least one group." (Allan Schick, in Louis C. Gawthrop, l970, p.32)
I consider the below factors;By applying theory of
PARETO OPTIMALITY,I find the most balanced move consisting all correct concepts stated below.
I use logic and visuslization too.maps are for tactical positions,logic for planning or strategies.
Ditto.Here's a theory to support it.
the "best that could be achieved without disadvantaging at least one group." (Allan Schick, in Louis C. Gawthrop, l970, p.32
For each move,the one which fits all factos would been chosen as canadiate moves.
pieces are supposed to attack or defense at the right moment
main logic thing.different people have different logics.My logic simply is:L mode(upper 4 charts for attack tactical position searching and 4 charts(lower 4) for defense positions searching.more valued piece attack first and less valued piece defense first.
decide to move into the same or the opposite color as your opponent's last moved piece.This is piece coordination.
I have calculated piece values.search under my posts.
figure piece stands on
position figure such piece and other piece are guarding(L mode) or defending(M mode)
Tweaking refers to fine-tuning or adjusting a complex system, usually an electronic device. Tweaks are any small modifications intended to improve a system
see also P versus NP problem http://en.wikipedia.org/wiki/P_versus_NP_problem
The P versus NP problem is a major unsolved problem in computer science. Informally, it asks whether every problem whose solution can be efficiently checked by a computer can also be efficiently solved by a computer. It was introduced in 1971 by Stephen Cook in his seminal paper "The complexity of theorem proving procedures"and is considered by many to be the most important open problem in the field. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US$ 1,000,000 prize for the first correct solution.
In essence, the P = NP problem can be restated as the following question:
Suppose that solutions to a problem can be verified quickly. Then, can the solutions themselves also be computed quickly?
my attempt is to find out computing indictions,those factors I stated above to give the best move=solution.
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