The quantifier depth of a first-order formula is the maximal nesting of its quantifiers. A position of the Ehrenfeucht–Fraïssé game on two structures $M$ and $N$ over a relational vocabulary is a pair of tuples of the same length, one in each structure; it is legal when the two tuples satisfy the same equalities and the same atomic relations, that is, when matching them coordinate by coordinate is a partial isomorphism. The duplicator survives $n$ rounds from a position when the position is legal and, if $n > 0$, whichever element the spoiler appends to one of the tuples, the duplicator can append an element to the other so as to survive $n - 1$ rounds from the new position. The structures $M$ and $N$ are $n$-round equivalent when the duplicator survives $n$ rounds from the empty position.