Positronium in the triplet state decays by the emission of three photons and it has been proposed that their simultaneous detection can be used for medical imaging. The three-photon yield has been observed to be enhanced in low O(2) levels in some fluids but has never been measured in biologically relevant liquids. In this study, the delayed three-photon decay yield, at both high and low O(2) levels, has been extracted by fitting the time dependence of the two-photon yield to a set of coupled differential equations. The differential equations, in a simple yet seemingly satisfactory fashion, account for the e(+) capture to form positronium, its decay and the interconversion of the two spin configurations. Our results indicate that the delayed three-photon fraction is 0.25% in water (or blood-like) samples and exhibits no (or exceedingly small) dependence on the dissolved oxygen content. If one assumes that the direct component contributes a fraction expected by annihilation on free electrons (1/372), then the total three-photon fraction is 0.52% in the samples of biological relevance.