Jason vs Vishnu's Coin War

This classic coin-flip gambling problem is about the long-run chance that one player is ruined before the other when their fortunes evolve as a symmetric random walk. It sits at the intersection of probability theory and stochastic processes, a staple theme in quant prep and probability interviews. Candidates must recognize the structure behind seemingly simple betting games and relate it to well-known probabilistic models.

It trains understanding of fair games, hitting probabilities, and the behavior of random walks with absorbing states. You practice working with martingales, stopping times, and invariance properties that stay true throughout the game. It also reinforces intuition about how initial capital and symmetry shape risk, ruin, and long-term outcomes in stochastic systems.

This matters for quant interviews because market-making, risk, and derivatives roles all rely on modeling wealth, PnL, and exposure as stochastic processes. Interviewers use this style of question to see if you can connect intuitive gambling setups to rigorous tools like martingales and optional stopping, which underpin pricing, hedging, and risk-neutral valuation. Showing you can do this smoothly is key to standing out in competitive quant interviews and making your quant prep effective.

What it tests

This class of problems is governed by the concept of martingales and the linearity of expectation in symmetric random walks with absorbing barriers. When two players repeatedly exchange a fixed amount based on a fair random process, the expected value of either player's fortune remains constant until one is ruined. The probability of one player being ruined before the other is determined by the initial proportion of their fortunes relative to the total, because the process is fair and memoryless. This is a consequence of the optional stopping theorem: the expected value at the stopping time (when the game ends) must equal the initial expected value, provided the process is bounded and fair. The underlying structure is that the probability of absorption at a given boundary is proportional to the relative distance from the starting point to the opposite boundary, reflecting the fairness and symmetry of the process.