Most massive stellar mass to embedded cluster mass (m_max − M_ecl) relation. Red stars denote the observational data listed in Table A.1. Here, 10⁶ synthetic clusters are stochastically sampled from the canonical IMF (the a23m150 IMF model in Table 1), resulting in the density map. The darkness of the region is proportional to the number of the synthetic clusters in that region divided by the total number of synthetic clusters in the same M_ecl bin. The average m_max and standard deviation of m_max for each M_ecl bin are plotted as the red solid and the blue dashed curves, respectively. The solid line indicates the M_ecl = m_max limit and the horizontal dashed line indicates the m_up limit of 150 M_⊙ (see Sect. 7.4.4).