True or false? Chess will never be solved! why?

Actually that was the c pawn.

Oh, my bad.

Puzzle

How many legal chess positions are there having 3 chessmen on the board, assuming that it is white to move?

Sounds simple enough? I don't know the answer myself, but I guess that even in this trivial looking case ( just two kings plus a piece or a pawn ) it is not that easy to come up with an exact answer.

However it is very easy to come up with an upper bound:

64! / 61! * 10 = 2 499 840

How many of these almost two and a half million combinatorially possible chess positions are legal?

False, because chess with 6 pieces are already solved(6 men tablebases) and it's only a matter of time before 32 men tablebases.

Easy to solve 2 piece chess, 2 bare kings is a draw. 4 piece chess is a draw if you place the pawns in front of each other and no king can outmaneuver the other. It becomes unsolvable at a certain point though.

whoplaysssech wrote:

whoplaysssech wrote:

Theoreticaly white should be able to win every game if they make their best move possible and black should be able to draw every game for the same reason.

Please tell me this was meant as a joke.

boom

I have like answered this before, if not here then somewhere else. Chess will never be solved because humanity will reach extinction long before we become capable of solving the game.

Okay. As I've said before, there is a # out there - and it is way way out there everyone....but there is a # of possible chess moves - and as physical infinity is not conscionable, neither is this. Is it Avagardo's # cubed (6.023 x 10^23)^3 ? We don't know where it is, but science tells us it's there....Take it from Dr Zhivago....It's "somewhere my love".

My question is: Do we have to find this # b4 we can solve this great mystery ? Either way, does Rex Sinquefield have the desire (he's got the $ !) to hire a team of computer sorcerer's to look n2 the needs to find it ? I would hope so, but I'm not counting my heartbeats.

That is incorrect, because as tablebases are generated backwards (from mate), they include illegal positions. Shredder, for example, accepts this one:

This being said, I don't think it would be so hard to find the legal 6-men. 6 pieces does not leave a lot of room for fancy retros.

Only one thing is for certain: there are 3612 legal positions with only two kings on the board ( assuming white's turn ).

I have started a thread in the Puzzle section to see whether anyone can tell how many 3 men positions are legal when it is white to move. No one could tell. I'm currently struggling with the two kings and a white rook situation.

Telling how many legal positions there are is comparable in difficulty to solving chess...

When you want to find out legal positions with two kings it is useful to think about the board like this:

First put the black king on the board.

There are three different situations marked as red, green and yellow.

If you put the black king on a red square, there are 4 forbidden squares for the white king.

If you put it on a green square, there are 6 forbidden squares for the white king.

If you put it on a yellow square, there are 9 forbidden squares for the white king.

From this it follows that there are 4 * 60 + 24 * 58 + 36 * 55 = 240 + 1392 + 1980 = 3612 positions.

I'm currently studying the case of two kings and a white rook, white to move.

It turns out that the same coloring is useful in this case as well.

You have to distinguish two situtations:

a) the two kings are on the same file or rank

b) the two kings are on separate files and ranks

You have to be careful, because if the rook is on the same file or rank as the black king, then black king may be in check and the position is illegal. The only way a position can be legal in this case is when the white king shields the check with its own body. In case b) this is impossible, so in case b) all positions where the white rook is on the same file or rank as the black king, are illegal.

Case a) is truly elaborate, because you have to separate cases in which the check is shielded from the cases where the check makes the position illegal.

You can discount symmetrical positions.

This is the spreadsheet I have currently. It is very beta now, so it may be utter nonsense.

Nevertheless I'm currently counting 223 994 combinatorially possible positions ( with legal kings, irrespective of checks ) out of which 175 488 seem legal ( 78 % ).

Just happened to drop in on this discussion. I haven't read all the posts (obviously!) but it struck me that maybe the reason chess has not been "solved" yet is because nobody seems prepared to consider that chess is actually a win for Black. Obviously a proper scientific approach would have to consider this third possibility. It is my belief that White is in Zugzwang in the opening position. In other words, any move that White makes at move 1 will play right into Black's hands and Black wins. If you don't believe me, take a look at this game.

http://www.chess.com/photos/view_album/Josechu/chess-match and

http://www.chess.com/photos/view_album/Josechu/chess-match---day-2

As long as people are only prepared to analyse chess as a win for White or a draw, they will never find the true path, so chess will never be solved. If anybody ever spends some (super-computer) time analysing the third alternative, they will soon find the correct answer.

Everyone is entitled to his or her opinions, no matter how wrong those opinions are.

SmyslovFan. Did you look at the game? If you do you'll understand where I'm coming from. If you won't then you're just proving my point: a refusal to consider that which appears illogical leads to a failure of comprehension when it turns out that what appeared illogical is actually feasible. Thinking the unthinkable is a necessary step along the path to enlightenment. Try it. You might enjoy it!