For the commissioning process of the OPAL nuclear reactor of the Australian Nuclear Science and Technology Organization (ANSTO), the thermal neutron flux is measured through the activity measurement of an activated Au wire, Au-Al (0.112% of Au) alloy wire and Au foil. The absolute activities of ¹⁹⁸Au in the form of Au wire, Al-Au wire and Au foil were determined using the conventional 4πβ - γ coincidence-counting method. Monte Carlo simulation technique was employed to simulate the complicated absorption and attenuation processes of electrons and gamma photon interactions with the surrounding materials. The Monte Carlo calculated probabilities of escape beta particles, internal conversion electrons and photon-interaction generated photoelectrons and Compton electrons were used to determine the correction term of the coincidence equation. The corrections for the Au wire (length: 8.000 mm, radius: 0.064 mm), Al-Au wire (length: 7.690 mm, radius: 0.255 mm) and Au foil (thickness: 0.025 mm, radius: 3.000 mm) were found to be 5.2%±0.1%, 2.6%±0.1% and 4.2%±0.2% respectively. The study demonstrates that the Monte Carlo calculation for the correction term of the coincidence equation can be applied to the absolute activity determination of radionuclides with well-defined source geometries with an uncertainty of better than 1%.