A Monte Carlo simulation exploring uncertainties in standard stellar evolution theory on the red giant branch of metal-poor globular clusters has been conducted .
Confidence limits are derived on the absolute V -band magnitude of the bump in the red giant branch luminosity function ( \mathrm { M _ { V, { \mathrm { b } } } } ) and the excess number of stars in the bump , \mathrm { R _ { b } } .
The analysis takes into account uncertainties in the primordial helium abundance , abundance of alpha-capture elements , radiative and conductive opacities , nuclear reaction rates , neutrino energy losses , the treatments of diffusion and convection , the surface boundary conditions , and color transformations .

The uncertainty in theoretical values for the red giant bump magnitude varies with metallicity between +0.13 / -0.12 mag at \hbox { $ [ \mathrm { Fe } / \mathrm { H } ] $ } = -2.4 and +0.23 / -0.21 mag at \hbox { $ [ \mathrm { Fe } / \mathrm { H } ] $ } = -1.0 .
The dominant sources of uncertainty are the abundance of the alpha-capture elements , the mixing length , and the low-temperature opacities .
The theoretical values of \mathrm { M _ { V, { \mathrm { b } } } } are in good agreement with observations .
The uncertainty in the theoretical value of \mathrm { R _ { b } } is \pm 0.01 at all metallicities studied .
The dominant sources of uncertainty are the abundance of the alpha-capture elements , the mixing length , and the high-temperature opacities .
The median value of \mathrm { R _ { b } } varies from 0.44 at \hbox { $ [ \mathrm { Fe } / \mathrm { H } ] $ } = -2.4 to 0.50 at \hbox { $ [ \mathrm { Fe } / \mathrm { H } ] $ } = -1.0 .
These theoretical values for \mathrm { R _ { b } } are in agreement with observations .