In this paper we propose The Play Grid, a model for systemizing different play types. The approach is psychological by nature and the actual Play Grid is based, therefore, on two pairs of fundamental and widely acknowledged distinguishing characteristics of the ego, namely: extraversion vs. introversion and agency vs. communion. The former pair concerns a person's orientation towards either inner or outer reality, while the latter has to do with orientation towards autonomy vs. being a part of something. When placing these pairs of characteristics on different axes and combining them, we arrive at the Play Grid. Thus, the model has four quadrants, each of them describing one of four play types: the Assembler, the Director, the Explorer, and the Improviser. It is our hope that the Play Grid can be a useful design tool for making entertainment products for children.