Hybrid metal-halide perovskites have potential as cost-effective gain media for laser technology because of their superior optoelectronic properties. Although lead-halide perovskites have been most widely studied to date, tin-based perovskites have been proposed as a less toxic alternative. In this Letter, we show that amplified spontaneous emission (ASE) in formamidinium tin triiodide (FASnI3) thin films is supported by an observed radiative monomolecular charge recombination pathway deriving from its unintentional doping. Such a radiative component will be active even at the lowest charge-carrier densities, opening a pathway for ultralow light-emission thresholds. Using time-resolved THz photoconductivity analysis, we further show that the material has an unprecedentedly high charge-carrier mobility of 22 cm2 V-1 s-1 favoring efficient transport. In addition, FASnI3 exhibits strong radiative bimolecular recombination and Auger rates that are over an order of magnitude lower than for lead-halide perovskites. In combination, these properties reveal that tin-halide perovskites are highly suited to light-emitting devices.