PeterH:
Sounds like you plan to use a timer interrupt to indicate 'end of game' and force the Arduino to reboot to start a new game. Both those approaches seem like bad choices to me. The polling solution you "don't want" is the way I'd do it.
Please show how you can accomplish what the OP wanted (!) , not what most replies wanted, in ONE line of code as can be done using WDT.
Personally I have a small issue with "gurus" here repeatedly coming up with stupid suggestions like " read blink without delay " and not paying attention to OP requirements.
Cheers