Result: Example results taken from the bottom of Notebook 4 from the Repo:
The player who makes the first check loses the game more often than they win, and this is consistent upon stratifying against elo and time control. The difference in the probabilities is approximately 5%.
If the first check is not checkmate, then the player who made the first check ends up losing 56% of the time.
The player playing black makes the first check more often than the player playing white.
About 12% of the time, the first check is checkmate.
The player with lower elo makes the first check about 50% of the time, but this probability increases as the gap between the players' elo increases.