Every snake makes one move per tick and gets the same apple sequence. The fewer moves a method needs, the sooner it fills its board.
Every finished game is recorded on this device: from Watch, Race, benchmarks and the marathon.
A Hamilton loop is a closed route that visits every cell exactly once. If the snake's body lies along such a loop as one unbroken piece, the snake can always just follow the loop: the cell ahead is either empty or the tail that is about to move away. It can never crash, and it reaches every apple within one lap.
Before every move the AI checks that such a loop still exists after the move. That is a calculation, not a guess.