An assessment is made of the efficiency of four UK high street bookmakers?betting odds for the 2004 European football (soccer) championships, based on an analysis of match results data from 15 previous international tournaments. Pre-tournament probabilities for the outright winners of Euro 2004 are generated using Monte Carlo simulations. There is no evidence that the bookmakers underestimated the win probability of the pre-tournament outsiders and ultimate winners, Greece. However, the odds quoted for bets on the host nation team, Portugal, appear to understate the importance of home advantage. The bookmakers?odds for fixed-odds betting on the outcomes of individual matches appear to satisfy the criteria for betting market efficiency, although this finding is based on a very small sample.