All optical switching (AOS) of magnetization exhibits a high potential for ultrafast and energy-efficient memory applications. Many works have been carried out in the area of AOS, including its observation in a wide variety of ferromagnetic or ferrimagnetic materials, and the exploration of the parameters for the achievements of AOS such as the laser fluence and helicity, and duration of laser pulses. A large majority of all optical helicity-independent single-shot switching (AO-HIS) has been observed in Gd-based rare-earth transition-metal ferrimagnets. It is then necessary to explore the unique role of Gd in AO-HIS mechanism, compared with other rare-earth elements. Here, we engineered Gd 1−x−y Tb y Co x alloys and investigated the influence of the Tb concentration on the magnetization dynamics via static Kerr microscope and time-resolved magneto-optical Kerr effect (TR-MOKE) measurements. The ultrafast demagnetization time at low fluence is found to be independent of Tb concentration, while both the range of laser fluence and pulse duration allowing for AO-HIS becomes narrower with increasing the Tb concentration. The TR-MOKE signal K / K_sat ∼ 10 ps after the laser pulse excitation decreases with increasing either the Tb concentration or the pulse duration. The fact that AO-HIS is prohibited by increasing the Tb content is explained by considering a larger damping for Tb than Gd in atomistic simulations. Our results are well explained by the fact that angular momentum can be transferred from Gd to Co resulting in the magnetization switching, whereas for Tb it is dissipated through the lattice due to the large spin-orbit coupling, instead of being transferred between Tb and Co.