A developer who goes by she-llac just published a detailed breakdown of Claude's internal credit system, extracted from what appears to be a floating-point oversight in Anthropic's API responses. The analysis suggests Claude's subscription plans deliver dramatically more value than equivalent API usage, with the $100/month Max plan coming out to roughly 13.5 times what you'd pay at API rates.
The suspiciously precise float
Here's the trick: Claude's generation endpoint returns usage data as unrounded doubles. Not rounded percentages like the official usage page shows, but raw floats like 0.16327272727272726. That number looks suspicious because it is. It's a fraction converted to decimal, and the underlying fraction can be recovered.
She-llac used a Stern-Brocot tree, a binary search structure over all positive rationals, to find the simplest fraction within the float's rounding bucket. When you take multiple samples and compute their lowest common denominator, you converge on the true limit. In this case: 3,300,000 credits for a five-hour session on the Max 5× plan.
The math gets a bit involved. IEEE-754 floats have a fixed mantissa, so each decimal value represents a tiny interval of rationals that would round to it. For values between 0 and 1, that interval is roughly 10⁻¹⁷ wide. The Stern-Brocot search finds the simplest fraction in that bucket, and after a few samples the LCM stops growing. That's your limit.
What the numbers actually say
The credit-to-token conversion isn't one-to-one. Each model has different input and output rates, mirroring API pricing ratios:
| Model | Input credits/token | Output credits/token |
|---|---|---|
| Haiku | 0.133 | 0.667 |
| Sonnet | 0.4 | 2.0 |
| Opus | 0.667 | 3.333 |
Output costs 5× input. Opus costs 5× Haiku. Standard API ratios. The interesting bit is what this implies for actual monthly throughput:
| Tier | Monthly price | Monthly credits | Equivalent API cost |
|---|---|---|---|
| Pro | $20 | 21.7M | $163 (8.1× value) |
| Max 5× | $100 | 180.6M | $1,354 (13.5× value) |
| Max 20× | $200 | 361.1M | $2,708 (13.5× value) |
That last column is the kicker. The Max plans deliver roughly 13.5 times more value than paying Anthropic directly for tokens.
But wait. It gets worse (for API users).
Cache reads are free
On the API, cached prompt reads cost 10% of the standard input price. Every time Claude Code makes a tool call, it re-reads the conversation context. Ten calls, ten cache reads. The 10% adds up fast.
On subscription plans? Cache reads cost nothing. Zero credits.
She-llac worked through the math on a realistic agentic scenario: 100K tokens cached, 1K new tokens per call, 1K output. On API pricing with a warm cache, each request runs about $0.08. On the Max 5× plan, you could make over 10,000 such requests per week, which pencils out to $3,667/month in equivalent API value.
For a hundred bucks.
That's 36.7× the API price for the same work. The caching discount alone shifts the economics dramatically.
The 5× plan overdelivers
The naming is misleading. The Max 5× plan doesn't give you 5× Pro usage. According to the recovered limits, it gives you:
- 6× the session limit (3.3M credits vs 550K)
- 8.33× the weekly limit (41.7M vs 5M)
The Max 20× plan, meanwhile, actually delivers closer to 16.67× the weekly throughput of Pro. The asterisk on "20× more usage" is doing a lot of work.
How startups are supposed to compete with this
If Anthropic is selling subscriptions at 13–37× better unit economics than their own API, how does anyone building a coding agent on top of Claude compete?
The answer might be that they don't. Not on price, anyway. Anthropic is clearly subsidizing heavy users on the consumer plans, likely because subscriptions create stickier revenue than pay-as-you-go API usage. The Pro plan at $20/month delivers $163 in API-equivalent value, which suggests Anthropic is eating significant losses on power users to lock in monthly recurring revenue.
For developers hitting Claude Code hard, the subscription plans are the obvious choice. The Max 5× plan seems to be the sweet spot: nearly 14× API value, generous weekly limits, and you're not paying $200/month for a 2× throughput increase that mostly affects session limits rather than total weekly capacity.
Will the floats stay unrounded?
She-llac expects Anthropic will probably round those SSE responses once this analysis gets attention. The claude-counter extension she built to track usage relies on the unrounded data for precision, so losing it would be annoying.
But the broader point stands regardless. Claude's subscription plans are wildly underpriced relative to API rates, especially for agentic workloads where cache efficiency matters. If you're using Claude Code and paying by the token, you're leaving money on the table.
