  In asynchronous games, Melli{\`e}s proved that innocent strategies are
positional: their behaviour only depends on the position, not the temporal
order used to reach it. This insightful result shaped our understanding of the
link between dynamic (i.e. game) and static (i.e. relational) semantics. In
this paper, we investigate the positionality of innocent strategies in the
traditional setting of Hyland-Ong-Nickau-Coquand pointer games. We show that
though innocent strategies are not positional, total finite innocent strategies
still enjoy a key consequence of positionality, namely positional injectivity:
they are entirely determined by their positions. Unfortunately, this does not
hold in general: we show a counterexample if finiteness and totality are
lifted. For finite partial strategies we leave the problem open; we show
however the partial result that two strategies with the same positions must
have the same P-views of maximal length.
