Let's suppose we have some sort of game (for instance tic-tac-toe) with a limited amount of moves. I want to simulate that game, and with that I will use a random number generator (RNG) to calculate the moves.
In the case of tic-tac-toe, there are at most $9!$ moves (if we forget about the games that end before the last move). If I were to run that number of simulations, there is no guarantee that I've ran all possible scenarios due to the inherent randomness of the process. The only way I would have ran all scenarios is if the RNG would magically pop out a straight sequence of moves.
Assuming my reasoning to be correct, I ask if there is some way to determine a threshold or a probability of cases run that would allow me to set a representative number of simulations?
Storing the moves and looking at what was made is not, for this purpose, an option.