Longest Possible Chess Game

What is the longest posible chess game? This post will take you to find the answers.

A chess game can end for many reasons. Regardless of whether the game result is a loss-win or a draw. So what keeps the game going? There are factors to consider as follows.

1. There is no checkmate or stalemate.

It is evident that the game ends immediately if there is a checkmate or stalemate on the board. However, both sides can easily come to an agreement to avoid this of ending.

2. No draw by repetition.

Whether it is 3 repetitions or 5 repetitions, according to FIDE rules, both sides can avoid repetition. This is clear because with just one piece on the board and one king on each side, there are more than (64×55)×62 = 218,240 possible positions.

3. Make draws by 50-move rule happen as late as possible.

This is the main factor that determines the longest game. Without the 50-move rule, the game could be INFINITELY long. unless there is giving With the threefold repetition rule, the number of games is limited. This is because the total possible positions on the board are finite. (which has an enormous number I won't mention it yet) The calculations after this will be based on 50-move rule.

The 50-moves count will be reset when a pawn is moved or capture a piece. So we should make the reset happen as slowly as possible, that is every 50 moves.

Notice that the maximum numbers of pawn moves for both side can occur is 2×8×6 = 96 moves. And total of 30 pieces taken, not including the king. It mean resetting the move count will never occur more than 96+30 = 126 times. But wait! how can all 16 pawns be promoted? If no pieces are capture by pawn, a pawn will never change a file if it doesn't capture any other pieces. Cause resetting move by moving the pawns and capturing a piece to happen at the same move sometimes. This is the problem and we will analyze it.

Because each minor pieces and major pieces causes only 1 reset per piece (by being captured). while each pawn can be moved reset up to 6 times before being promoted to a queen. Therefore, according to logic, every pawn shouldn't be capture until they're promoted.

Normally, when pawn capture another piece. they will cause 1 files per player to always be opened, as shown this diagram. Making every pawn to promote there must be 8 pieces captured.

So the maximum possible reset of the turn move in one game is (96+30)-8 = 118 times. And maximum number of moves is 118×50 = 5,900 moves, right?

The answer is NO! The 50 multiplier is calculated assuming that the count of move is reset every 50.0 moves, which are all reset of the turns of same color. While the reality must be a reset move count that happens on both sides. (otherwise, one side have all 32 pieces and the other side have all their piece captured) The longest turns between pawn move or piece captured by different colors before game was decided to be a draw is 49.5 moves (99 turns for both sides).

Resetting the count of 50-move rule in turn of different color will reduce the maximum distance from normally by 0.5 moves. The longest game should be switch the color on moves that make reset the count of 50-moves rule in a row to as little as possible. These are steps of pawns move or/and capture pieces need to happens for both sides.

1. All WHITE pawns will promoted and some must be capture black pieces on the way.
2. In the first steps, neither side was able to push all their pawns continuously until promotion. There is no way to promote pawns if all of black's pawns are on the 7th rank.
3. All BLACK pawns will promoted.
4. BLACK capture all white pieces, leaving only white king left.
5. WHITE capture all black pieces, leaving only black king left. Game drawing with king vs king on the board.

From 5 steps, There are resetting the count of 50-move rule that consecutive occurs in move of different colors at least 3 times, as follows:

Steps 1-2: The first pawn move on the board should occur on move 50.0 (black's 50th turn). When black continues to push their pawns every 50 moves they will stuck with white pawns. However, [1] black is able to create the pawn structure and capture some white piece with the pawn to help all of white pawns have a path to promote. Then black sacrifice their pieces to the white pawn can move away from the blocking of their pawns.

Steps 3-4: [2] After all the white pawns are promoted, black will push their pawn every 50 moves continously until all are promoted. Then take all the white pieces, leaving only the king (to allow resetting count of 50-moves rule will continue to occur on black turns for as long as possible)

Steps 4-5: Now white has only king, while black still has many pieces left on the board. [3] The game continues with black sacrifices all pieces for white to captured. Count of 50 moves-rule will resets occur during white's turn until the game end with the draw by insufficient material (king vs king).

In summary, in the longest chess game count of 50-move rule will be reset 118 times, with 3 times resets being for a different color than the previous 49.5 moves, another 115 times count every 50.0 moves

Therefore, the longest possible chess game controlled by 50-move rule is (3×49.5)+(115×50.0) = 5,898.5 moves

In general case, we can determine the lenght of the longest game using the same calculation above, whatever the "50" moves rule is change to any number (ignoring threefold repetition for huge value of number)

• Let "n" be a positive integer of 2 digits or more, that represents the maximun number of moves without moving a pawn or capture piece before being decided as a draw.
• f(n) represents the length of longest chess game for any value of "n" in domain.

Thus f(n) = (n-0.5)(3)+(n)(115) = 3n-1.5+115n = 118n-1.5

The table shows the relation between some value of n and f(n)

This is idea of playing the longest chess game 5,898.5 moves under 50-move rule.

Black create the pawn structure and accept of white 2 knight sacrifice on d4 and e4 to help all of white pawns coming to promote. From the position below, black pawn moves 20 times, taking 20×50.0 = 1,000.0 moves.

White promote all pawn (here it's promote to a knight) by accept sacrifice of 6 black pieces. There are 8×6 = 48 pawn moves, taking (1×49.5)+(47×50.0) = 2,399.5 moves, so the position below is in move 1,000.0+2,399.5 = 3,399.5

Black promotes all pawns and capture all white pieces except the king. There are 28 pawn moves and capture white pieces 13 times, taking ((1×49.5)+(27×50.0))+(13×50.0) = 2,049.5 moves, so the position below is in move 3,399.5+2,049.5 = 5,449.0

After white has only king left, black sacrifices a piece to the white king every 50 moves until there was only kings left on the board and game was drawn. There are 9 pieces captured, taking (1×49.5)+(8×50.0) = 449.5 moves, so the final position is in move 5,449.0+449.5 = 5,898.5

Finally, the answer of the longest chess game controlled by 50-move rule is 5,898.5 moves

To more easily imagine this length. Suppose that you take 1 second to move each piece, It will take you for (2×5,898.5)÷60 = 197 minutes to complete the longest game.

Hope you enjoyed this post, good luck.