I have calculated the longest possible chess game

Chess games cannot go forever, they must end sometime, since there is the 50 move rule that means that once every 50 moves, one player must move either a pawn or capture a piece.

With this in mind, I was able to calculate the longest possible chess game like so:

If a pawn moves 1 square each time, it takes them 6 moves to promote. Since there are 16 pawns in total, that would be 16 * 6 which is 96, BUT in order for the pawns not to cross over, a total of 8 captures must be made, so assuming that the pawn captures a piece, we can subtract 8 pieces lost in that process. Since every pawn move and piece capture occurs once every 50 moves (in the longest possible combination), we will subtract 8 from the piece capture/pawn moving moves. So let us calculate the pawn moves that have an effect on the 50-move rule firstly:

16 * 6 = 96 (to promote every piece).

Since there are 30 possible "capturable" pieces on the board, minus the 8 pieces that were captured for the pawns to promote, that leaves 22 moves that lay an effect on the game.

96 + 22 = 118 moves that lay an effect on the game.

Since every move that lays an effect on the game only needs to be played once every 50 moves, we can multiply that number by 50.

118 * 50 = 5900 moves.

After 5900 moves, there will be nothing left on the board except two kings, so the longest possible chess game that follows the 50-move rule can last 5900 moves.

Please correct me if I made any mistakes with my calculations.

Asuming of course that somebody actually claims the draw....

Well... games CAN go on forever.  It's not mandatory that the game end after 50 moves without a pawn having moved or a piece captured.  Yes, at that point either player can CLAIM a draw, but if neither player claims it, the game goes on.  This is true in skittles games and over-the-board tournament chess as well.

However, let's rephrase the question:  What's the maximum number of moves a game of chess might last before one side is able to CLAIM a draw?

This site:

http://www.chess-poster.com/english/notes_and_facts/did_you_know.htm

lists the answer as 5,949.   But it doesn't back it up.

I think that once the two kings are left on the board, in theory they can also shuffle around for 50 moves before a draw is claimed.  That might explain the difference between your answer and the above site's answer.

Ahhh I see what I did wrong! I assumed that the first move must be a pawn push, but in reality, you can wait 50 moves before the first pawn push. Thank you for that!

I see two minor problems with these calculations. The 1st problem is that if you are going to use the 50 moves rule as a constraint for the number of moves possible in a game, you have to be very strict about enforcing it. That is to say that, after 50 moves by each side without a capture or pawn advancement, White would be obligated to immediately claim a draw rather than extend the game with another pawn move/capture. The 2nd problem is that BOTH sides must at some point make all of their available pawn moves + captures, which means that in some cases you will only get 49.5 moves per capture/pawn move, instead of the ideal 50 full moves.

For instance, let's say Black makes the 1st pawn move. This will be something like 50...d6 , after 50 reversible moves (all of them knight moves, of course) by White and 49 by Black, giving you the full 50 moves. But if instead White makes the 1st pawn move, that gives you 50.d3 (and not 51.d3, since after Black makes a 50th consecutive reversible move White will be obligated, under our restrictions, to claim a draw immediately) , after 49 reversible moves by White and 49 by Black (for a total of only 49.5 moves).

Now, after 50...d6 in the above example, it will be White's move. So, after 49 reversible moves by each side, it will again be White's move. If White does not advance a pawn (or capture a piece), Black will once more have the task of doing this (perhaps with 100...b6), and while 50 complete moves are achieved it is clear that Black cannot continue like this indefinitely. Soon White will have to advance one of his own pawns, and when he does it will come after only 49 reversible moves by each side (as opposed to 50 + 49). When this happens, however, it will now be Black who starts the next 50-move "bracket", giving White the opportunity to advance another pawn, this time after 50 Black moves (and 49 White moves) for the ideal total of 50 full moves for the segment.  

As you can see, the basic pattern is that one side should continue to make ALL pawn moves + captures for as many consecutive segments as possible, but each time Black and White are forced to "switch shifts" there will have to be a segment of only 49.5 moves.

I've already determined that the minimum number of "switches" required to simplify down to K vs. K is 4, so just knock 2 moves off your number and it should be right (5,898 moves is what I got when I calculated this myself more than 2 years ago ). Note that the 5,949 moves given in post #3 is based on an extra 49-move K vs. K endgame, which I would have to disagree with since a draw by insufficient material could be claimed by either player immediately after the final capture was made.

Actually, the longest possible chess game is 50*117 + 25 = 5875 moves long, because of the twenty-five move rule. When it's down to kings plus a queen or rook, only 25 moves can remain.

I wonder if the 2 fastest chess players in the world cooperating could play 6000 moves in a bullet game.

Deranged, I agree with your count of 118 for the maximum possible number of captures and pawn moves in one game.

I just would add one detail: When calculating 118*50, you have assumed that there will be always 49.5 moves played before the next pawn move or capture occurs. However, this would mean that black does all the pawn moves and captures, which cannot be the case.

So we need to look for the minimum number of times in which the capturing or pawn-moving action has to change sides, on each of these changes there will be only exactly 49 moves (= 98 half moves) played before the next capture or pawn move occurs.

I count this the following way:

First, black makes some pawn moves, freeing his pieces, allowing them to move to squares on which the white pawns will be able to capture them (e.g.creating white doubled pawns on the b, d, f and h-files). (During this, the white knights hop around capturing nothing.)

First change of sides.

Then white makes some pawn moves, freeing his pieces so that black will be able to capture them and make doubled pawns on, say, the a, c, e and g files. And white makes the 4 pawn captures which create the necessary doubled pawns.

Second change of sides.

Then black makes some pawn moves, including the captures that double his pawns, so that all of white's pawns will be able to pass through to promotion. And black makes all the pawn moves till promotion. However, he cannot yet make all the captures, because the white pawns still need to make all of their moves before being captured.

Third change of sides.

White makes all the remaining pawn moves and all his remaining captures.

Fourth change of sides.

Black's king makes all the remaining captures for black.

So because of the 4 times a change of sides in making the captures and pawn moves is necessary, the end result will be lower by 4 half moves, which is 2 moves less.

So the longest possible game in that sense would be

(118 * 50 - 2) moves = 5898 moves,

ending after the black king captures white's last piece on black's 5898th move.

The source indicated by MrEdCollins (giving the number of 5949 moves) must have forgotten not only that bare kings are an immediate draw, bust must also have forgotten to include the implications of the side changes required.

(I agree, of course, that all this assumes a strictly enforced 50 move environment, such as an arbiter who would be allowed and required to interfere and declare a draw as soon as 50 entire moves were played out without any pawn move or capture, and players who cooperate to draw out the game for as many moves as possible "against" this arbiter.)

---------

edit: I came to these results before reading cobra91's solution, so of course I agree with his results. Maybe my having written this up a second time in slightly different words contributes to an even better understanding for some, so I think I am leaving this in, even if it is basically just all what cobra91 has already written before me.

There is a 25 move rule? I never heard of that. So if I have a king and queen vs a king and rook, I have just 25 moves to capture the rook?

If it was 960 chess , is it possible to calculate maximum moves , of every possible arrangement of back row ?

Yes, froghollow, it is. It is the same maximum number of moves than for a chess game with the normal starting position, for the same reasons as given by cobra91 and myself above.

The result given above does not depend on the ordering of the pieces behind the pawns.

 I believe the 'extra' 49 moves problem has already been addressed by the OP - it comes not from the bare kings, but from the initial position, in which the two sides dance around with the knights.

That does not matter, because that does not keep the knights from hopping around without capturing anything.

If a pawn/pawns make it to touchdown ,8th line- would the maximum number of moves increase ? i have a feeling that in that case , the original multiplications might increase : taking into account the transformation of the pawn/ pawns .  also could en passant have a bearing on maximum possible moves .

Yes, timesetting  0 min + 1 second increment

@frrixz There is no 25 move rule. At least not in the FIDE-regulations.  Is it perhaps the USCF or a specific tournament which has this rule?

nice.  Now post the game please. 

Also:  by moving only the knights for 50 turns.  would this be a legal way for grandmasters to draw without trying to reach complicated positions?

You sure have put a lot of thought into a thread you consider a useless waste of time.

technically the game can go on for too long, night moving back and forth until 49th move then pawn push. each side can move the pawn 3 times.

3x8=24

49x24=1176

1200 moves so far.

capture would equal almost (estimate) 200 moves.

im getting kinda board with the math dho

Your figure is in good alignment with previously calculated values.  Of particular interest is this Blog:

http://blog.chess.com/kurtgodden/the-longest-possible-chess-game

I'd also indepently performed the calculations from the ground up and posted the analysis in the discussion of a follow up Blog post by kurtgodden (that's since been removed for some reason) and came very close to the same figure cited in the initial blog (within a handful of moves if I recall).