An Impossible Chess Question

The Impossible Question

The impossible question in chess is: If both white and black play absolutely flawlessly (completely without mistakes), how will the match end?

Theoretical Explanation

If both white and black play absolutely flawlessly, theoratically the match will be draw.
Because when white wants a checkmate, black will defend it with the best move. If black wants a checkmate, white will defend again.
So the match will not finish with any winnings, because all threats will be repelled by the opponent. If we count that these two players never repeated three moves and never shook hands, the match will end in a draw in the position of black king against white king. This causes the draw because if they don't shook hands, they must exchange every piece and it will be draw.

Why can't we solve this question mathematically?

I think you are saying "We can solve it with Stockfish" now. But no. We can't solve it with Stockfish because Stockfish is a machine, it uses machine learning and learn from the older games. And the older games didn't play with 100% accuracy. So we can't solve it with that.

What can we do to solve it?

If you want to solve it, you must write the 10^43 location probability and 10^120 move sequences. This numbers are very big numbers, so it takes very long time to write them.

We are not completely perfect.

Thanks for reading.

@Kaan_Burak