The banker's offer is usually a lot lower than the expected value of the reward. For example, let's say there's $0.01 and $1,000,000 left on the board. The expected value is (1,000,000+.01)/(number of prizes left) = 1,000,000.01/2 = about $500K. Imagine it this way - if you made the choice a thousand times, about half the time you'd pick the 0.01 and half you'd pick $1,000,000. The average of your prizes would be about $500K.
The banker usually offers about $300K given that circumstance. The reason is that we attach "bonus value" to certainty.
I think the banker has an algorithm that computes the expectation and subtracts some fraction of that due to the value of certainty.
I don't think that "knowing what's in the suitcase" drives his offers, because given a case where the banker knows the player is holding a $0.01 suitcase, he'd never offer the player more than $0.01 to leave the game. The banker would be inclined to keep offering him lowballs because he'd know what the outcome will be when the player kept declining the low offers and winding up with his own suitcase.