Hard · Expected Value & Decision Theory · Numerical · ~15 min · #56

Add One or Invert

Real interview · Jane Street

You start with 100 pounds. A fair coin is flipped 10 times. On heads, your amount increases by 1. On tails, your amount $x$ is replaced by $1/x$ (so 100 becomes 0.01, and 0.5 becomes 2).

Estimate the expected amount after 10 flips, to within 1%.

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Worked solution

Give the problem an honest attempt first, then reveal the full explanation.

Reported in interviews

Jane StreetGlassdoor interview question

Candidate-reported and unverified; the firm may phrase it differently or no longer ask it. The wording here is our own paraphrase, and the solution was written and checked independently of any answers posted at the source.

Concepts

Path decompositionFibonacci countingExpectation dominated by rare paths

Relevant for

Quant TraderQuant Researcher