Monochrome Blocks

What this expected-value interview question tests

This is a medium-difficulty probability question that asks you to compute the expected number of monochrome blocks (runs of consecutive same-colored cards) in a shuffled deck. It's the kind of problem quant interviewers use to assess whether you can combine linearity of expectation with careful case analysis.

The question rewards a structured approach: define what counts as a block, identify the transitions that matter, and use indicator random variables to avoid summing over all possible permutations. Most candidates find that breaking the problem into manageable pieces—thinking about when a new block starts—is far more practical than enumerating outcomes.

• Linearity of expectation over indicator variables
• Symmetry and conditional probability in shuffled sequences
• Run-length analysis in random arrangements