A well-shuffled, standard 52-card deck is dealt out into \(26\) piles of \(2\) cards per pile. The expected number of piles that consist of pairs is \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. Find \(a + b\).

**Clarification:** By "consists of pairs" I mean that a pile consists of two cards of the same denomination, i.e., a pair of Jacks, a pair of \(6\)'s, etc..

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