As a boy, Harvey Dent had an unhappy childhood. He was beaten regularly by his father, who made the choice by flipping a lucky coin. The coin became a reoccurring theme in Dent's life, which he used to make crucial decisions. The abuse he suffered made him unable to make any choices of his own.

On the surface the symbolism is pretty obvious. Dent flips the coin to decide any questions that need answering, leaving his actions up to fate rather than making any conscious choice himself. It's an easy short-hand way to reflect what's going on in his mind, both before and after he goes nuts.

He subsequently goes insane and adopts the "Two-Face" persona, becoming a criminal obsessed with the number two, the concept of duality, and the conflict between good and evil. Two-Face obsessively makes all important decisions by flipping a two-headed coin.

In the movie " The Dark Knight" Dent goes insane and becomes Two-Face, who chooses to do either good or evil depending upon the results of flipping a coin. He makes all important decisions by flipping a two-headed coin, one side of which is scratched.