The paper has three basic objectives: (1) to discuss and analyze the subtleties of ranking wines in blind tastings, (2) to analyze the degree of agreement or disagreement among the tasters (judges) and (3) to shed some light on the problem of identifying the wines and to determine when the identifications of the judges might be called statistically significant. The first issue utilizes the rank sums or the related measure, “votes against,” and discusses the appropriateness of a statistical test introduced by Kramer. The second introduces Kendall’s W coefficient of concordance and discusses some other, related measures. The third derives the finite sample distribution of the number of correct identifications under the null hypothesis of random identifications, from which critical values can be obtained, both for the case in which each wine has to be identified exactly and the case in which there is a small number of different types of wine that have to be identified.