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Probability and Statistics · Easy

Cash or Reroll

Supported standard problem · Match confidence: high

Jane Street · Topic guidanceSusquehanna (SIG) · Topic guidance
About this question’s source match

A freely accessible catalogue statement confirms the stated mathematical structure and parameters; wording and worked explanation are original. The public statement has been read and its stated parameters matched; solution calculations have been independently verified.

A fair eight-sided die has labels 1 through 8. Observe an initial roll. You may keep it as your cash payout or discard it and roll once more, when you must accept the second face. What policy maximizes expected payout and what is the fair entry value?

Assumptions and constraints

  • Use the random mechanism explicitly specified in the prompt.
  • Give exact expressions where possible and justify each requested result.

Examples

first roll 4
→ reroll

Fresh expected 4.5 exceeds 4.

Company preparation relevance

These links connect this exercise to companies’ public examples or stated interview topics. They do not establish that a company asked this exact Learnr question.

  • Jane Street

    Official topic guidance

    Topic overlap: expected-value decisions “Cash or Reroll”, additive waiting expectations “Collecting Stickers”, and dependence in “Variance of Two Variables” connect to the guide’s expectation, linearity and independence sections.

    Probability & Markets — official guide ↗
    Evidence scope and uncertainty

    General probability preparation; numerical tasks and structures beyond those topics are Learnr choices.

    These are Learnr-authored exercises selected for topic overlap. The company does not name these catalogue titles or verify that these exact questions were asked.

  • Susquehanna (SIG)

    Official topic guidance

    Topic overlap: payoff decisions “Cash or Reroll”, stake-growth reasoning “Kelly Betting #1” and conditional probability “Liver Disease” practice probability, odds, expectancy and decision-making under uncertainty discussed on the firm’s trading-careers page.

    Susquehanna — Trading careers ↗
    Evidence scope and uncertainty

    Trading education and candidate puzzle culture. This page supports preparation relevance, not exact interview-question provenance.

    These are Learnr-authored exercises selected for topic overlap. The company does not name these catalogue titles or verify that these exact questions were asked.

References

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Catalogue metadata captured 2026-10-12. Metadata source.