The expected value of the game is positive regardless of Ballmer’s strategy

Interview question and tech hiring

• Many see this as emblematic of flawed tech interviews: puzzles detached from job skills, rewarding confident bluffing over careful reasoning.
• Others argue it’s a good prompt to probe thinking, communication, and how candidates handle ambiguity, not about getting the “right” answer.
• Disagreement over whether an interviewee should say “you’re wrong”; some advocate direct challenge, others a diplomatic “yes, and…” approach.
• Concerns raised that the question, as reportedly used, had a single “correct” answer in the interviewer’s mind, making disagreement risky.

Mathematical depth and expectations

• Several note the problem is “basic” game theory in formal terms, but still too hard to solve rigorously in interview time.
• Some claim the only honest answer in-interview is “I don’t know, but here’s how I’d approach it,” while others think partial structure (binary search, adversarial framing) is already strong performance.
• There’s confusion from some readers about why this doesn’t yield a better-than-binary-search algorithm for normal CS use; others explain the difference between random vs adversarial inputs.

Expected value vs risk / utility

• Large subthread on why positive expected value isn’t sufficient when you get one shot, or when stakes affect survival/ruin.
• References to Kelly criterion, risk of ruin, St. Petersburg paradox, and ergodicity: EV assumes many trials, while life and bankruptcy are often single-path processes.
• Counter-arguments: here the stake is just $1; tail-risk reasoning seems overblown unless the stake is implicitly life‑changing.

Adversarial vs cheating interpretations

• Some interpret “adversarial” as still committing to one integer at the start; under that model, mixed strategies can guarantee positive EV.
• Others note that a truly adversarial opponent could change the target after each guess to maximize remaining options, making winning impossible—equated to “cheating” by some.
• Discussion of commitment schemes (e.g., pre-committing via a hash) as a way to enforce a fixed number, though this is not part of the original puzzle.

Strategy and game-theory discussion

• Comments mention Nash equilibria, mixed strategies, and linear programming formulations.
• Some explore variants, such as adjusting the search to counter skewed or adversarial distributions, and numerical attempts to approximate optimal strategies.
• Debate on whether the original puzzle is really about search complexity, probability, or human psychology of betting.

Broader reflections

• Thread digresses into evaluations of the question as a “quant-style” brainteaser vs practical engineering filter.
• Meta‑discussion on whether a person’s wealth is evidence of correctness or skill, with pushback against both “rich ⇒ smart” and “rich ⇒ just lucky” extremes.