Rolling till I die?

What this expected-value interview question tests

This is a medium-difficulty probability question that combines Markov chains, expected value, and recursive reasoning. It's the kind of problem quant trading desks use to see whether you can model a multi-stage stochastic process and set up the right equations without getting lost in the algebra.

The core challenge is recognizing that the payout depends on both the sequence of rolls and the stopping rule (consecutive identical numbers). You'll need to track states, compute transition probabilities, and use linearity of expectation or recursive decomposition to find the overall expected payout. Interviewers value clean problem setup and correct identification of symmetries over brute-force enumeration.

• Markov chains and state transitions
• Recursive expectation equations
• Linearity of expectation across independent stages
• Symmetry and problem reduction