Once his self-image has been shattered, Dent can do one of two things: he can act in good faith, and acknowledge his own nature--or he can continue to act in bad faith. Unfortunately, it's his nature to deceive himself--and he does so by essentially reversing his previous worldview. Like so many losers, he refuses to acknowledge that he lost because his opponents were too strong and skillful for him. He refuses to acknowledge that there was any justice in his defeat. It was all just luck--chance. If he can't be in complete control of events, then he refuses to exercise any control at all: he'll just leave everything up to a coin flip.
The italics are added. The Joker's superiority is a script cheat, of course. Apparently there are people who get off on the Joker's sheer coolness, physically impossible or not, and live in a fantasy world where people are losers because they, themselves, are losers. This is why the absurdity of the Joker's escapades is bad faith writing. It can't really be passed off as simple entertainment. In truth, many people lose a rigged game. The Joker rigged the game with Maggie Gyllenhaal and rigged the game with the ferries. Dent replacing his rigged coin with a real coin means there's no way to hold the interpretation above.
Everybody who heard Gordon's admission that all the cops called him Two-Face the whole time knows that there is in fact no change
in Dent at all. Which means (if something like Dark Knight could actually be said to have meaning at all,) that there was no point to the Joker/Dent confrontation. It merely seemed to about something. Which is pretty much the summary of the whole damn movie.