chess is a draw but in how many moves?

[syzygy]

I think that we can define it by the following game:

Have a rule to decide about drawn games.

Draws with more than X plies are considered to be a win for white
Draws with less than X plies are considered to be a win for black
Draws with exactly X plies are considered to be a draw.

Assuming the theoretical result of chess is a draw It is obvious that there is exactly one X when the theretical result of the new game is also a draw and the Question is what is X

It is possible to ask the same question about what is Y that gives theretical result of a draw when
Draws with more than Y plies are considered to be a win for black
Draws with less than Y plies are considered to be a win for white
Draws with exactly Y plies are consdered to be a draw.

I guess that Y<X because white can force a draw faster than black.

I also expect that Y<X. The second variant, where white has to play for a quicker forced draw (or a regular win), should be the more interesting game.