Predict the break-even read count for Anthropic prompt caching given the 1.25x / 0.1x rates

**Anthropic's prompt caching pricing:** writing a prefix to the cache costs 1.25x the normal input rate (a 25% premium over uncached). Each subsequent read costs only 0.1x, a 90% discount. **Break-even calculation.** Compare the cumulative cost of cached vs uncached over the same number of total requests (1 write + N reads vs N+1 fresh requests): - Cached total: `1.25 + 0.1 * N` - Uncached total: `1.0 * (N + 1)` Setting cached <= uncached: $$1.25 + 0.1N \le 1.0 + 1.0N$$ Solving: $$0.25 \le 0.9N \implies N \ge 0.278$$ Since N must be a positive integer, caching wins from the very first read. The intuition: the write is 1.25x but the read is 0.1x, so by the time you've paid 1.25 + 0.1 = 1.35x you've replaced 2x of uncached cost, already a 32% saving. The '~2 reads to break even' figure that floats around online compares cached cost against cached without the premium. It is not the right comparison. The right comparison is cached vs uncached, and caching wins on read one.

**The inequality.** Cached cost over (1 write + N reads) is `1.25 + 0.1N` input units. Uncached cost over the same N+1 requests is `1.0 * (N+1) = N+1`. The break-even is where they're equal: $$1.25 + 0.1N = N + 1$$ $$0.25 = 0.9N \implies N = 0.278$$ Since N is an integer count of reads, the smallest N satisfying cached strict less than uncached is **N = 1**. At N=1, cached = 1.35 vs uncached = 2.0, cached wins by 32.5%. At N=10, cached = 2.25 vs uncached = 11.0, cached wins by 80%. The practical implication is striking. *Any* system prompt that fires more than once is cheaper to cache. If you have a 4K-token system prompt at standard Claude input rates and it fires 100 times a day, your input cost on that prefix drops from 400K-tokens-equivalent (uncached) to ~40.25K-tokens-equivalent (1 write + 99 reads). Roughly a 90% saving on that prefix's input bill. The common confusion, 'caching pays off after about 2 reads', comes from comparing the cached recipe against a hypothetical 'cached without the write premium' baseline, which is not a real option. Against the *real* uncached baseline, caching wins immediately. Watch the engineering details: TTL on Anthropic's cache is 5 minutes (default) or 1 hour (extended), so a prefix that fires once an hour with default TTL never benefits. Cache breakpoints (`cache_control` markers) demarcate cached vs variable regions; misplacing them caches the wrong things or fails to cache at all.