Shadows (2002)

Shadows, A roleplaying game for all ages, was specifically designed to be played by children.

The children play themselves, and they also have a shadow, which is some kind of monster or invisible person who always wants to get the child in trouble. The adventure begins with the children being startled awake in the middle of the night. As the children go about their adventure, the GM asks them to make Shadow Rolls. They roll their Good die and their Shadow die to determine what happens next. If the Shadow die wins, then the will of that player's shadow is accomplished, bringing complications into the life of the character.

You can download the rules for free at the official Shadows website.