As a matter of fact it is just the threshold
As a matter of fact it is just the threshold of the subject, for the odds have been, are, and will remain exactly even that you will be dealt a hand as good as or better than your opponent's! Over a number of deals sufficient to let the probabilities get their teeth into the statistics, say 10,000 or 100,000 deals, the distribution of the cards will be just about exactly even.
It's true in theory; it's true in the practice of many experimenters;
It's true in theory; it's true in the practice of many experimenters; and it's the truth on which casino operators grow rich, since their income is based on the inexorable certainty that the percentages never fail over the long run.