Alice's 2-Pt Lead Win Chance

This quant interview question is about a biased random walk between two absorbing boundaries, framed in an intuitive sports setting. It appears in quant interviews to see whether a candidate can translate a narrative description into a clean probabilistic model. On MyQuantPartner, this fits into the core "events and state processes" part of quant prep, where many finance problems reduce to hitting one boundary before another.

It trains comfort with discrete-time stochastic processes, conditional probability, and reasoning on state transitions. You practice encoding states, understanding independence, and working with stopping conditions. It also reinforces intuition for how small biases in win probability compound over many steps.

This matters for quant interviews because pricing, risk, and algorithmic trading often reduce to boundary-hitting questions. Interviewers want to see if you can recognize that structure quickly and reason about absorption probabilities under asymmetry.

What it tests

This problem class is governed by the theory of absorbing Markov chains, specifically the non-symmetric Gambler's Ruin process. The key structure is that the process is a random walk with fixed absorbing barriers, where each step has a constant but possibly unequal probability of moving toward either barrier. The probability of absorption at a particular barrier depends not on the path taken but on the ratio of the step probabilities and the distance to each barrier. This arises because, over many possible sequences, the memoryless property of independent trials ensures that only the relative likelihood of moving toward each barrier and the number of steps required matter. The formula for absorption probability emerges from solving the recurrence relation for the probability of reaching one barrier before the other, reflecting the exponential bias introduced by unequal step probabilities.