Game not letting player 1 win straight away

[nilamo]

I'm not going to rewrite it for you, but it looks like gameRun already tracks whether or not someone won.  So you could just do something like:

while True:
    gameRun = True
    while gameRun:
        # player 1
        gameRun = checkX()
        if gameRun:
            # player 2
            gameRun = checkY()
    keep_playing = input("Want to play again? [Y/n] ")
    if keep_playing.lower() != "y":
        break