Across the world, the acceptance criterion for concrete made with non-potable water (SA) is stipulated for mean strength with reference to similar concrete made with potable water (SP). The basis for the strength design of concrete is the characteristic strength. The effect of the acceptance criteria on the characteristic strength of SA and SP was examined using statistical simulations, for the first time. It was found that, compared with a two-sample set, using a three-sample set would improve the characteristic strength of SA. A higher allowable ratio between the means of SA and SP and a lower deviation of individual samples from the mean would improve the characteristic strength of SA. The effect of the coefficient of variation (CoV) of the original population on the characteristic strength of SA varied. On the one hand, a higher CoV reduced the characteristic strength of SP, thereby increasing the probability of SA strength being higher than SP strength. On the other, a higher CoV of SP meant a wider spread of the samples and that could increase the CoV of SA, thereby reducing the characteristic strength of SA. Probabilistic charts were developed for the characteristic strengths of SA and SP for different combinations of the aforementioned variables, with guidance for practical application.