They will take a chance on something other than maximizing the minimum only if they believe that more than the minimum possible would be necessary to their conception of the good. Only then will it be rational to take a chance on more than maximin. But they do not know what their conception of the good is, and so do not know whether it would be worth the risk to try for something other than maximin. So they do not prefer anything other than maximin. Rawls takes it that utilitarianism is the main opponent.
Utilitarian principles say to maximize overall well-being.
But there may be overall well-being in a society that has slavery. That is, a few people suffering may be of so much benefit to everyone else that there is a net gain in well being for the society as a whole. But it is possible that one will be a suffering slave in that society. And, given we don't know how possible, any possibility is unacceptable. So utilitarianism has an unacceptable outcome.