 The theory behind back-and-forth games uses very few assumptions about the logic in question. As a result, these games are one of the few model-theoretic techniques that apply as well to finite structures as they do to infinite ones, and this makes them one of the cornerstones of theoretical computer science. One can use them to measure the expressive strength of formal languages, for example database query languages. A typical result might say, for example, that a certain language can’t distinguish between ‘even’ and ‘odd’; we would prove this by finding, for each level \(n\) of complexity of formulas of the language, a pair of finite structures for which Duplicator has a winning strategy in the back-and-forth game of level \(n\), but one of the structures has an even number of elements and the other has an odd number. Semanticists of natural languages have found back-and-forth games useful for comparing the expressive powers of  generalised quantifiers.  (See for example Peters and Westerståhl 2006 Section IV.)