The Lucky Trader

What this expected-value interview question tests

This is a medium-difficulty probability question commonly used in trading interviews to assess how candidates approach linearity of expectation and reasoning about dependent events. The problem asks you to find the expected number of "records" (cards that exceed all previously revealed cards) across a sequence of random shuffles.

Rather than enumerate all possible orderings and their probabilities—which is computationally heavy—strong solutions decompose the problem into simpler indicator random variables and exploit linearity of expectation. This tests whether you can recognize structure in a seemingly complex counting problem and simplify it into independent, calculable pieces.

• Indicator random variables and their expectations
• Linearity of expectation over dependent events
• Symmetry and uniform probability in permutations
• Record-breaking processes in random sequences