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Mechanically speaking, at the start of the game, the action rolls will largely be determined by chance, since the only control over the result the player has comes from the two numbers the player selected as their starting knowledge. But, by having two numbers at their disposal, it allows the players to always have their roll fall within a certain area. Re-rolls are gained if the player is able to have their action roll fall within the same area as the determined mean. With a little luck and strategy, the player will be able to stockpile re-rolls to narrow the range of their rolls and increase the chance that a given action roll will result in the correct result. Also, if an action roll does hit the determined mean by chance, the player will still benefit from this result, it just won’t count towards “mastery” of a virtuous act.
In regard to the basis on Nicomachean Ethics, the notion of starting out with little knowledge is supposed to represent the notion that life experience is necessary to become virtuous. Because things in the real world are messy, one needs to be able to determine the relevant factors in a given scenario and act as the situation calls for. So, starting out, the young character does not have as much life experience to draw on when accessing a given situation, but over time they gain an understanding of the world and are more able to act virtuously. Of course, just living longer and experiencing more things does not necessarily mean one will be more virtuous, but as a conceit for the game, we have to assume that the characters are striving to become virtuous.
For a quicker, or perhaps more balanced game, the Determiner of the Mean could decide on granting the players extra starting knowledge at the beginning, or at certain milestones to keep the game moving.