Last Man's Roll 2

What this sequential-sum probability question tests

This is a medium-difficulty probability question that asks you to reason about the final outcome of a cumulative process. Rather than computing a single expectation, you must identify which terminal state is most probable—a shift in perspective that often surprises candidates.

The core skill is recognizing that the "last roll" is not uniformly distributed across all possible final sums. Instead, you need to think about which outcomes are reachable from each position just before the goal, and weight them by the probability of landing in that pre-goal state. This combines conditional probability with careful case analysis.

• Absorption barriers and boundary conditions
• Distribution of sums from rolling multiple dice
• Backward induction: reasoning from the goal state
• Symmetry and asymmetry in terminal outcomes