Chess Online

Play online chess!

From	Message
poeticdragon 27-May-21, 02:18	Mathematics of chess OK- I admit that I only joined this group after seeing this years old post ( gameknot.com ) on your forum while searching for solutions to an entirely different mathematical problem. If you don't want to link to it the question posed is essentially: what is the longest possible chess game in theory? Somebody quite rightly stated that three move repetition and 50-move rules have to be invoked, but that seems like a cop-out answer even if it is correct. For those who want to know the answer- it's 8848.5 moves if we assume that any draw conditions immediately end the game. That's not the part of the question that got me though. The part that *really* got me thinking was having to show mathematical proof for the answer. Now, in these modern times we're living in this can be done quite efficiently by computers, but the questions that I now want the answer to is: are there any mathematical formulas that can be used to work this out without a computer or even how many possible board set-ups there can be after, for instance, 20 moves? Any help with this topic is hugely appreciated, and contributors helping me figure out this conundrum earn my undying respect. Even a good starting point for helping me solve this will earn you, at the very least, my sincere gratitude. Thank you in advance to anybody willing to help me move on from this devilish problem
mo-oneandmore 27-May-21, 05:22	I don't believe mathematics or physics has much to do with chess, but both disciplines seem inclined to play the game. Here's Einstein vs Oppenheimer --- Einstein apparently won handily. www.youtube.com
5imon 27-May-21, 15:29	poeticdragon The formula is 118*75-(3*0.5) = 8848.5 It turns out there is a more recent rule whereby the game is a draw if there are 75 moves without a pawn move or capture. (rule 9.6b handbook.fide.com), so the cop out answer is no good. Each pawn can move forward 6 times, and 30 pieces can be captured to leave just two kings. However, 8 pawns will have to capture in order to move past each other, so there are 118 possible delay moves. 6*16 + 30 - 8. 118*75 because we want to delay each of these moves as close to the drawing limit as possible, so that the pawn move or capture is the 75th. However, because the pawn moves need to be shared between white and black, there must be 3 plies lost in order to pass control from one to the other. This bit is the trickiest to work out. There's a worked example here. handbook.fide.com
archduke_piccolo 27-May-21, 17:04	Mathematics of chess ... Here's on I have posted elsewhere, that goes towards determining just hw much you know about the endgame King and Rook versus lone King. Imagine a chessboard with 1 finite corner at a1, but which stretched to an infinite number of squares in front of the White player, and an equally infinite number of squares to his right. Let us define the squares by the notation (x,y). The White King stands at (1,1) [a1] and the White Rook at (2,1) [b1]. The Black King stands somewhere in the blue - let us say at (x,y). Is it possible, disregarding all drawing move limits, for White to checkmate the Black King? If 'yes', how is it to be done? If 'no', why not?
archduke_piccolo 04-Jul-21, 05:01	Well over a month... ... and still no response. I'm surprised and a little disappointed, too. The answer is, of course, yes: given White knows the location of the Black King and the moves Black makes, White CAN force checkmate in those circumstances.
teardrop34 07-Jul-21, 21:22	This club has been sadly inactive as of late, and I have not even seen this thread. Though work has me quite busy so it probably wouldn't have done me much good.
5imon 15-Jul-21, 12:49	Ion I'll bite. I don't understand how white can checkmate in your example. If the black king stands at (x,y) then white can only checkmate by forcing the king to the side of the board and in your example that means the right hand or bottom side since the others are infinite. So a sensible starting move for white might be to play R x,y+1 to stop the black king heading to infinitely up the y axis. Can't black now head off to infinity on the X axis with K x+1,y? The white king would need to be further out on the x axis to stop the black king moving that way and forcing the white rook to move out whenever it tries to block on that axis.
archduke_piccolo 15-Jul-21, 15:18	It has all to do... ... with the geometry of the chessboard, in which, to the kings, a diagonal is equal in length to an orthogonal. 5imon's first move is correct: restrict the Black king along an orthogonal e.g. 1.R(2,1)-(x+1,1) to cut off a file OR 1.R(2,1)-(2,y+1) to cut off a rank. But isn't the rook capable of cutting off both? Yes it can. But there remains one little escape route: the square upon which stands the rook. So now the question reduces to 'has White the means (time, space and material) to stop up this escape route?' The only material is the King. Can the king reach that critical point betimes, given Black's head start? Supposing then that you can corral the king in some (x+k, y+m) rectangle, can mate then be forced? When I first encountered this puzzle, that was my first question. I answered it to my satisfaction almost at once: the task is quite simple, if tedious (King and Rook checkmates of a lone king takes several moves e.g. White takes 14 moves to checkmate). I'll leave it here for the nonce, and come back with the definitive answer another time.
5imon 16-Jul-21, 00:17	Yes, you're right! The diagonal move makes all the difference if the white rook switches between cutting off the ranks and the files. I hadn't thought of that. Once the black king is contained the rest is easy.

GameKnot: play chess online, chess teams, chess clubs, monthly chess tournaments, Internet chess league, online chess puzzles, free online chess games database and more.