Russian Roulette Survival Odds

This question presents a Russian roulette style scenario with a revolver, multiple chambers, and a specific pattern in how bullets are arranged. The candidate must decide between two possible actions before a second trigger pull, using only the information that the first pull produced a blank. The heart of the problem is comparing which choice gives a higher chance of survival once you have seen the first outcome, and recognizing that the spatial arrangement of bullets (for example, adjacency) constrains what could be true about the cylinder's state. Variants of this style sometimes appear in quantitative trading and tech interviews to probe instinctive reasoning about randomness and information.

The problem leans heavily on conditional probability, Bayes-style updating, and careful enumeration of compatible states after an observation. It tests whether the candidate can move beyond a naive "nothing has changed" intuition and instead condition correctly on the first click. An interviewer is watching for a clear sample-space construction, logical elimination of impossible configurations, and an ability to compare revised probabilities without handwaving. Clean explanation, not just a final choice, matters.

What it tests

This problem class is governed by conditional probability and information updating: after an event with known outcome (like an empty chamber firing), the set of possible states is reduced, and probabilities must be recalculated based on this new information. The key is that the initial randomization (spinning the barrel) creates a uniform prior, but once you observe an outcome, the posterior distribution over possible states is no longer uniform. The structure of the system (such as bullets being adjacent) further constrains which states are possible after the observation, often eliminating some arrangements entirely. The principle is that every observed outcome provides information that should be used to update the likelihood of subsequent events, and the optimal decision uses this updated distribution, not the original one. This is why the probability after the first click is not simply the same as the initial chance, but must be recalculated given the new constraints.