Actually, the whole thing about 1000 chimpanzees eventually typing a Shakespearian play given unlimited time is not statistically correct, it is a myth. 

Chimpanzees could never beat Carlsen, but they might stand a chance of drawing, given his recent draw %.

I stand corrected. Wikipedia gives the monkeys, ignoring punctuation and spacing, and Hamlet at 130K letters, typing like crazy, roughly the life of the universe and they still wouldn't get it right.

Assuming legal moves (of course) for a rough order of magnitude calculation, assuming no pieces exchanged (just a rough calc) we have 2 x Rook x 16 squares, 2 x N x 8 squares, 2 x B x 16, 1 x Q x 32, 1 x K x8, and 8 x P x 1 (ignoring pawns can move two on first move). Obviously that is an upper limit as pieces are exchanged and not all pieces can be moved to all their possible extent each turn due to the board position.

Given the idea of even 100 moves for a game, if I've added correctly, that would give us 128 to the 100'th power.

Wikipedia gives the monkeys to type Hamlet more like 3 to the 184K power.

So I was a little bit off....

Someone actually put typewriters in a room full of chimps. The most they got was the letter S repeated numerous times. They also got typewriters filled with excrement. 

Some may say that's an improvement over what some humans have written, especially in chess forums.

Sergey is beating Carlsen right now!

By 1/5 of a pawn...

Don't forget the typewriter that was thrown through the window that let the chimps escape.

Chimps are not dim. They knew what the important thing to do with the typewriter was.