Serve soup from two pots A and B. Each operation reduces (A, B) by one of 4 choices. Find probability A empties first (or tie counts as 0.5).
For small , use DP: = probability A empties first from state . observation: on average, A decreases faster than B (operations favor reducing A). For large , probability approaches 1. improvement: for , return 1.0 directly. The error is negligible. This bounds the DP state space.