Optimal Bets for World Series Winner

This question is set in a sequential betting game on the outcome of a finite playoff series with a fixed maximum number of games. You control how much of your wealth to stake on each individual game, knowing that each game is an even double-or-nothing bet on a particular team. The objective is to design a dynamic betting schedule that forces a prescribed final wealth level if the team ultimately wins the series, and a different prescribed final wealth level if it loses, regardless of the exact win–loss path. Variants of this style sometimes appear in quantitative trading or derivatives roles that care about dynamic replication and path-insensitive payoffs.

Solving it leans on state-based reasoning and backward planning on a finite probability tree. You need to label states by current score and current wealth, and then reason recursively from terminal outcomes back to earlier games. The interviewer is looking for comfort with dynamic programming, invariants along all branches, and the Markov viewpoint that only the current game count matters. They also watch how you translate a payoff condition into equations at each node, and whether you can systematically design a self-financing strategy that achieves a path-independent terminal result.

What it tests

This class of problems is governed by the principle of backward induction in deterministic state processes, where you must guarantee a fixed outcome regardless of the sequence of intermediate events. The core idea is to treat the process as a tree of states, each representing a possible history, and to work backward from the terminal states with known outcomes. At each non-terminal state, you select actions (here, bet sizes) that ensure, no matter which branch is taken next, the resulting payoffs can be recursively combined to always yield the desired final value. This is possible because the process is Markovian: the only relevant information at each step is the current state, not the path taken to get there. The reason this works is that, by construction, you can always solve for the required action at each node to maintain the invariant that the eventual outcome is locked in, regardless of the random sequence of wins and losses.