Large language model (LLM) agents for portfolio management learn from past experiences: each experience stored in memory is credited with the outcome of decisions that used it. In financial markets the outcome is dominated by the market move on that date, so the credit ends up tracking the market rather than the specific experience, causing these agents to underperform a simple equal‑weight ($1/N$) portfolio. We ask how an agent can credit an experience only for the change it induces. The answer is to put memory on trial: generate two drafts of the same decision, one with the experience and one without, both facing the same market; the shared market outcome cancels out, leaving the difference as the experience’s contribution. MemTrial drafts each decision with eight combinations of retrieved experiences, selected by a fractional factorial design, and assigns each experience a Banzhaf value—the average of those differences. Because each date appears only once and each draft is a noisy LLM sample, the per‑date credits are noisy and may not generalize to new dates. MemTrial therefore pools credits across dates and similar experiences using a hierarchical Bayesian model, acts on them only after they have predicted unseen dates, and otherwise stays anchored to a conservative reference such as $1/N$. On four benchmarks MemTrial not only exploits valuable experiences (the best of 15 methods on a semi‑synthetic benchmark with known experience quality) but also limits its losses when its values do not hold (at most 2.2% below $1/N$ on PortBench and InvestorBench, versus 15%–38% for the best experience‑learning agent). Averaged over five settings it improves the utility of the best experience‑learning agent by 21.2%, and with eight LLMs it beats every LLM‑based baseline on InvestorBench.
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