The squares of a \(3 \times 3\) board are randomly coloured black or white. Let \(W\) be the number of white squares and \(B\) the number of black squares. The expected value of \(\vert B - W \vert\) can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b\)?

**Details and assumptions**

The board is blank at the start.

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