A pure strategy is like instructions written in a notebook that an overprotective father gives his child before the child goes to middle school in a big city. They should describe clearly and precisely what to do in each every situation the child might encounter. Many will not occur, because of chance or because the other persons don't make the decisions that lead to them, or because the child makes decisions that prevent them from occurring. The child can avoid some situations but not others. The strategy prepares the child for every possible situation.

Continuing the metaphor, we can think of a mixed strategy as a set of notebooks to shuffle before leaving for school, choosing one to follow according to a probability distribution. In one play (one day at school), the child would take only one notebook to school, but which one would be unpredictable. A single random choice suffices for behavior in all situations to look random.

Behavioral strategies differ from mixed strategies. Instructions are written in a notebook and cover every situation. Instead of giving definite instructions, the notebook lists all options and assigns probabilities to them. As with mixed strategies, the other players do not know what strategies the child will play. The child would uses a random device, like a pair of dice, to determine what option to choose. As with mixed strategies, the behavior of the child is unpredictable, but unlike mixed strategies the child consults the random device repeatedly.