Claude's subscription plans offer better value than the API, but the extent of that value varies significantly across tiers. The 20× plan may seem appealing with its high session limits, but it actually only doubles the weekly usage compared to the 5× plan. The 5× plan stands out as the best deal, providing a six times higher session limit than the Pro plan and over eight times the weekly limit. This makes it a sweet spot for users looking for a balance between cost and functionality. When comparing subscription costs to API pricing, the savings are substantial. For example, the Pro plan costs $20 per month and offers a value equivalent to $163 in API costs, while the Max 5× plan at $100 provides around $1,354 in value. The Max 20× plan, priced at $200, offers an equivalent API cost of $2,708. The calculations also show that cache reads are free in the subscription plans, further increasing their value. In practical scenarios, a warm cache can push the value of the Max 5× plan to over 36 times that of the API, demonstrating the significant advantages of using the subscription service. The author details how they extracted precise usage values from Claude's system. By examining the SSE responses from the generation endpoint, they identified unrounded float values that hinted at the underlying limits. They employed a method involving the Stern-Brocot tree to derive the simplest fractions from these floats, allowing for accurate estimates of the service's real limits. This approach highlights a deeper investigation into Claude's usage metrics beyond the rounded values presented on the official site.