Optimal Turn Order in Russian Roulette

This question presents a two-player Russian roulette game with a single initial randomization of the bullet position, then a deterministic firing sequence as players alternate. The core decision is whether you prefer to act first or second when the cylinder is not re-spun between shots. Candidates need to reason about how the fixed, hidden configuration of the chambers interacts with turn order, and how that affects each player's overall risk. The setting is a classic quant and tech interview puzzle, often used for roles where candidates must be comfortable thinking about uncertainty, strategy, and sequential events under risk.

Solving it leans on conditional probability, careful counting of possible bullet positions, and recognizing that once the cylinder is spun, the randomness does not restart each turn. It tests whether candidates can distinguish dependent from independent trials and avoid treating each shot as identically distributed. Interviewers watch for a clean sample-space construction, correct conditional reasoning from the initial randomization, and an ability to translate the mechanical description of the game into a structured probabilistic model that yields the optimal choice and associated probability.

What it tests

This class of problems is governed by the distinction between dependent and independent trials in sequential probability. When the underlying random mechanism is set once and not refreshed (as with a single spin of the cylinder), the outcomes are determined by the initial configuration, and the sequence of actions simply reveals which pre-set outcome occurs. In contrast, if the random mechanism is refreshed each time (spinning before every shot), each event is independent, and the process becomes a geometric or Markov process where the probability of survival or loss accumulates over rounds. The key is to recognize whether the process is memoryless (independent trials) or not, as this fundamentally alters the probability structure and optimal strategies. This principle holds because the independence or dependence of trials dictates whether past outcomes affect future probabilities, shaping the entire analysis.