From a computational linguistics and token-economics perspective, the value of the Max tier is closely tied to the math of context window decay. When developers run agentic loops (such as Claude Code), the model must read and write code in multiple steps. Each step appends new data to the prompt history. This causes the token count to grow rapidly. On a standard Pro plan, a single complex task can exhaust the entire 5-hour budget in under an hour. The 5x and 20x multipliers are not just luxury additions; they are necessary to prevent state-space collapse during multi-step reasoning tasks.