The Generator's Curse: Search-Size Scaling of Backtest Overfitting in Technical FX Rule Libraries

No-code and large-language-model generators have made it inexpensive to synthesise large libraries of technical trading rules, and vendors routinely advertise a champion backtest drawn from such a search. The scientific question is not whether that champion looks attractive in sample, but how the quality of the selection itself behaves as the search intensity N grows. We study this question on EURUSD, GBPUSD, USDJPY and AUDUSD, measuring the combinatorial probability of backtest overfitting (PBO) and the in-sample and out-of-sample Sharpe ratios of the selected winner, net of round-turn transaction costs and under next-bar execution. On a declared library of 92 hand-specified rules built from European Central Bank reference rates over 2010–2025, increasing N raises the in-sample Sharpe of the selected rule on EURUSD and GBPUSD while the PBO of the search approaches 0.79 and the mean out-of-sample Sharpe of that rule is negative; the same library is rank-stable on AUDUSD, where the PBO is approximately 0.21. A single 2019 holdout can disagree with the combinatorial estimate. Replicating the protocol on a declared moving-average-and-RSI strategy family (N=500, S=16) on two independent daily tapes, Yahoo Finance and Twelve Data, confirms that the mean out-of-sample Sharpe of selected winners across combinatorial paths, rather than the holdout of a single champion, is the quantity of interest, and that heterogeneity across pairs and across data vendors is itself part of the finding. We make no claim of deployable alpha and we do not evaluate a commercial product. The results are reported at the level of historical, prototype evaluation. The author is CEO of Techain.