Friend's Coin Toss Win Prob

This coin game question is about competing patterns in a random sequence, a classic theme in quant interviews. Instead of just counting simple outcomes, you must track how partial progress toward each pattern evolves over time. It sits at the intersection of probability, sequences, and state-based reasoning, which is central to many quant prep exercises.

It trains your ability to compress past information into the minimal state needed to describe the future, and to translate a narrative description into a rigorous probabilistic model. In doing so, it sharpens intuition for randomness, expected behavior of patterns, and quantitative comparison of competing events.

This matters for a quant interview because trading, execution, and risk systems often hinge on interpreting streams of data. Mastering such pattern probability problems shows you can model stochastic processes cleanly and reason under uncertainty, key skills for high-level quant interviews.

What it tests

Problems that ask for the probability of one sequence appearing before another in a random process (like coin tosses) are governed by the structure of Markov chains and absorbing states. The key is to model the process as a set of states that capture all the relevant history needed to determine which sequence could occur next. Each state summarizes the minimal information required to predict the next possible transitions and their probabilities. By setting up equations for the probability of winning from each state, and identifying which are absorbing (where the process ends), you can solve for the desired probability. This approach works because the Markov property ensures that the future only depends on the current state, not the full past history, so the problem reduces to solving a system of equations based on transition probabilities.