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LetYouDown gave you an excellent terse answer, I will be a little more wordy.

Although this statement is true, it turns out to be surprisingly hard to construct a theory of probability that supports it. This was not accomplished until the 1930's.

Also, this assumes you reshuffle the deck every time, and that your guess about the card is independent of the shuffle. As a counterexample, if you keep dealing from one deck and always guess that the next card will match the rank of the card just dealt, you will be right only 1 time in 17 instead of 1 time in 13.

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Ah thanks! You're always knowledgeable about such things. Any websites to recommend regarding probability theory from its infant stages to now? I'm very interested in probability theory, not really because of gambling but because it seems to govern many aspects of life.