Two players take part in a task where they each attain a score that, for ease of explanation, is between 0 and 100.

Say these players had each done this task multiple times and I know the mean and standard deviation of the distribution of scores of each player.

Is it possible, given just these 2 means and standard deviations, to work out the probability Player 1 would beat Player 2 in any given iteration of 'the task'?

Can this be done analytically with some sort of formula, or would it require more complex simulations?

Thanks