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We describe how a novel online change-point detection algorithm, called Poisson-FOCuS, can be used to optimally detect gamma-ray bursts within the computational constraints imposed by miniaturized satellites such as the upcoming HERMES-Pathfinder constellation. Poisson-FOCuS enables testing for gamma-ray burst onset at all intervals in a count time series, across all timescales and offsets, in real time and at a fraction of the computational cost of conventional strategies. We validate an implementation with automatic background assessment through exponential smoothing, using archival data from Fermi-GBM. Through simulations of lightcurves modeled after real short and long gamma-ray bursts, we demonstrate that the same implementation has higher detection power than algorithms designed to emulate the logic of Fermi-GBM and Compton-BATSE, reaching the performance of a brute-force benchmark with oracle information on the true background rate, when not hindered by automatic background assessment. Finally, using simulated data with different lengths and means, we show that Poisson-FOCuS can analyze data twice as fast as a similarly implemented benchmark emulator for the historic Fermi-GBM on-board trigger algorithms.