The Bet Narrator:
Third Person (Limited Omniscient)
One of the things that makes this story so strange and hard to interpret is that even though there are only two characters, one of them is totally inaccessible to the reader. We spend the whole story in the head of the banker. We hear his memory of the party (which, incidentally—can we trust that he's remembering all of that accurately?), his stress about paying up on the bet, and his thoughts about just killing the lawyer already:
"To-morrow at twelve o'clock he will regain his freedom. By our agreement I ought to pay him two millions. If I do pay him, it is all over with me: I shall be utterly ruined. […] Why didn't the man die? He is only forty now. He will take my last penny from me, he will marry, will enjoy life, will gamble on the Exchange; while I shall look at him with envy like a beggar, […] No, it is too much! The one means of being saved from bankruptcy and disgrace is the death of that man!" (2.2-3)
But the lawyer? He's so isolated in his little jail cell of solitary confinement that even the narrator doesn't have any insight into what's going on in his mind.
Why the bias? Well, for one thing, if we were in the lawyer's head, we would probably have to stick with him for all fifteen years of his confinement, which would make for a much longer story.
But more importantly, it also leaves it up to us readers to decide the meaning behind the lawyer's transformation. We're in the banker's shoes, and probably just as befuddled. But hey, at least we're not two million rubles in the red anymore.