The expected value of the game is positive regardless of Ballmer’s strategy
An old Steve Ballmer interview puzzle about guessing a number between 1 and 100 has prompted debate over whether the game is actually unfavorable for the candidate once the interviewer is allowed to choose numbers adversarially. Commenters explore how mixed strategies and basic game theory show the expected value can still be positive, while also arguing about whether such brainteasers are fair or useful in software interviews compared to job-relevant questions. The thread broadens into questions of risk, expected value versus real-world utility, and how much weight to give “gotcha” puzzles in hiring decisions.
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.