Rawls asks you to choose the rules of a society from behind a veil of ignorance: you do not yet know who you will be in it — rich or poor, gifted or not. Stripped of that knowledge, self-interest becomes impartiality.
Behind the veil, Rawls argues, you reason by maximin: choose the arrangement whose worst position is as good as possible, because that worst position might be yours. This is the difference principle — inequalities are just only insofar as they raise the floor.
The catch is that equality is not free. Incentives matter: a perfectly flat distribution can shrink the total output, so some inequality may lift even the worst-off higher than dead-level equality would. The floor is maximised at an interior point, not at zero inequality and not at winner-take-all.
Pull the lever and live a random life. Ten births into a spiky society, versus a floor-raised one, turn the principle from a slogan into a felt gamble: would you really bet on being born lucky?
Something in the simulation stopped unexpectedly — the lesson continues without it. You can move on; nothing you did was wrong.