Does persistent memory accumulated from previous attempts help an LLM agent solve new problems, and does memory design affect that benefit? We study programmatic Chinese-character drawing across five agent conditions attempting the same 668 items. Accumulated memory produces modest aggregate gains despite substantial growth in the memory stores: free-form notes improve first-attempt success by 4.6 percentage points, while a design combining free-form memory with reusable code improves it by 2.8 points. The two designs do not differ significantly overall, but the code bank shows a suggestive advantage on later, harder items. A separate post-hoc comparison finds a much larger improvement when the code-bank agent receives privileged, target-specific structural supervision. The agent can therefore exploit highly informative structural guidance, although the privileged per-item information does not establish what could have been learned from experience alone. These results suggest that memory design may affect where accumulated experience becomes useful, even when its average benefit is modest.

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