Consider the problem of constructing random variables such that they collide with each other as much as possible. That is, if formula_48 and formula_49, we would like to construct formula_6 and formula_51 to maximize formula_52 in isolation, the highest formula_53 we can achieve is given by formula_54 where formula_55 is the Total Variation distance. However, suppose were weren't just concerned with maximizing that particular pair, suppose we would like to maximize the collision probability of any arbitrary pair. One could construct an infinite number of random variables one for each distribution formula_56, and seek to maximize formula_57 for all pairs formula_58. In a fairly strong sense described below, the Probability Jaccard Index is an optimal way to align these random variables.