Expected colour runs in a shuffled deck

A run is a maximal stretch of consecutive cards of the same colour; for instance BBRRBBB contains three runs.

(a) For a well-shuffled standard deck ($26$ red, $26$ black), find the expected number of runs.

(b) Describe a program that, for a deck of $X$ cards divided equally among $Y$ colours and shuffled at random, returns the mean number of runs.

(a) $27$. (b) $X-X/Y+1$, computed in $O(1)$. Runs equal $1$ plus the number of adjacent pairs whose colours differ. A given adjacent pair differs with probability $1-\tfrac{X/Y-1}{X-1}$, and linearity over the $X-1$ pairs gives $X-\tfrac XY+1$; for $52$ cards and $2$ colours this is $27$. A Monte Carlo shuffle can be used to check it.