Originally posted by thire
How long is the longest possible chessgame?
Please have in mind that a 3fold repetion ends the game, as well as the 50-moves rule.
hint: it is a finite number: all possible chesspositions are finite and every position can just occur 2 times...
We must avoid a draw by the 50 move rule, therefore we must have a piece capture, or a pawn move by either side, on move 50
The general plan is that each side hops their knights around without hitting the same position for 49 1/2 moves, them someone moves a pawn etc. We must also try to rarely capture pieces with pawns (some pawn piece capture's are necessary to get the pawns past each other to queen), and we must never capture pawns because once they queen they give us a whole piece more to do 50 moves with.
Considering only white. his pawns can each make 7 moves, queening on the seventh move, and 4 of those pawn moves must be captures to get his pawns past blacks. He has 15 black pieces to capture so he has 11 captures which aren't also pawn moves. That gives him 8*7+11 = 67 "50 move rule reset" moves. We also want to avoind switching resetting between black and white too much - because each switch costs us half a move.
so the general plan is
A) after 50 moves, Black moves a pawn to free his bishop, queen and two knights. we are on move 50
B) sort out white's pawns - white captures black's bishop, queen and knights with pawns to get his pawns into a configuration where black's pawns can pass, now we are on move 249 1/2
C) black makes 7 piece captures and his 55 remaining pawn moves, 4 piece captures are also pawn moves so that's 58*50 - 1/2 = 2899 1/2 more moves - putting us on move 3149
D) white makes his remaining 11 captures and 52 pawn moves leaving black with a king only - putting us on move 6298 1/2
E) black captures white's remaining 8 pieces, with his king putting us on move 6698
F) The players shuffle their kings around for 50 more moves, ending with a draw by the 50 move rule on move 6748
I'm pretty sure I've missed some things there, and that number is either a bit too big or a bit too small, any improvments on that folks?
EDIT: Doh - there is a huge mistake there - pawns can only do 6 moves without queening!