A game of Chess always comes to an end.There is no known way by which a chess game can end other than by checkmate,stalemate,draw or resignation.Obviously,the outcome of the longest possible game of chess has to be a draw.So,how long can a game of chess last?It turns out that in the longest game,the White can claim a draw after Black’s 5948th move.This involves the usage of a formula :

N=(Pawn Moves + Captures – Duplicates + Drawing Interval Grace Period) *(Drawing Interval), or 16*6 +30 -8 +1) * 50 = 5950.

Now,we have to subtract 2 from the above result because sequences of Captures/Pawn Moves must have at least 4 alternations between the two players.Thus,we get the number 5948.Now,let us calculate the total absolute number of chess games possible.We make some assumptions here:

• All the pieces are considered equal.
• A piece can acquire any position on the chess board,even though its not actually allowed.
• There are 16 white pieces and the same number of black pieces.
• The chessboard is a standard 8X8.

The assumptions allow us to get an accurate estimation of the maximum number of games possible.Simple usage of Permutations and Combinations would tell us that there are 64!/32! ways to arrange all the pieces on a chessboard,where ! represents factorial of a number.The number we get upon calculation is quite large.

64!/32!=4.82*10^53

Now,the maximum number of chess games equals (4.82*10^53)*5498.This equals 1.0516*10^270993,which is a mammoth number,but not mammoth enough as we would find later.There’s a mathematical term for huge numbers.Numbers of the order of 10^100 are called googols.There is a still bigger number,googolplex,which is 10^googol.Sure,the absolute maximum number of chess games is much bigger than the total number of atoms in the universe we have studied till date and is also bigger than a googol,but it’s still very small when compared to a googolplex.So,chess is not infinite,if we talk in strict mathematical terms.Hence,the quote by Mr. Vladmir Kramnik, “Chess is an infinitely complex game, which one can play in infinitely numerous and varied ways” is factually incorrect.Consider this:A billion is a shrimpy number when compared to what we have calculated.Still,if a person were to count till billion at the rate of one number per second,he/she will take 32 years.So,we can imagine how big our number is.Thus,the best evaluation of Mr. Kramnik’s quote would be that chess is not an infinite game,though it sure appears so and it wouldn’t be outrightly wrong to deem it an infinite game.

There are variants of the traditional game of chess.If we think outside the traditional game,there are various other ways of playing it,like Blindfold,Rapid etc.Also,we have recognized variants,such as an Infinite chess board,which doesn’t have to be infinite for play purposes,though ideally it is an infinite chessboard,with the motion of White pieces only constrained in the left and bottom directions.The Black pieces can be placed relatively,considering in an ideal infinite chessboard,the coordinates of the ideal positions of black pieces would be infinitely large numbers.Even the so called game of ‘Infinite Chess’ is not infinitely complex,though ideally it should be so.It should be possible to make infinite number of moves but Infinity is only a concept,it is something far from the reality.Thus,infinite chess represents an idea of potential infinity,rather than absolute infinity.We must appreciate the fact that there is only one way of making chess an infinite game,and that is by extending the chessboard to infinity.

-Mayank Kashyap