Black hole formation efficiency, ϵ_BH, (left) computed by Eq. (3) against the initial mass of the cluster, M_i, normalized by the critical mass, M_crit, calculated via Eq. (1). Different types of star clusters are represented by distinct colors: black symbols for the first star clusters (yellow symbols data from Reinoso et al. 2020, represent models with external potential, calculated via Eq. 2), red symbols for GCS and blue symbols for NSCS. The final stellar mass is estimated neglecting mass loss via Eq. (4). Right: The black hole formation efficiency ϵ_BH computed by Eq. (3) against the current mass of the cluster, M_i, normalized by the critical mass, M_crit, calculated from Eq. (1), including an approximate correction for mass loss.