The IceCube Neutrino Observatory is a cubic-kilometer-scaled detector located at the Geographic South Pole. The calibration of the directional reconstruction of neutrino-induced muons and the pointing accuracy of the detector have to be verified. For these purposes, the moon is used as a standard candle to not rely exclusively on simulated data: Cosmic rays get absorbed by the moon, which leads to a deficit of cosmic-ray-induced muons from the lunar direction that is measured with high statistics. The moon shadow analysis uses an unbinned maximum-likelihood method, which has been methodically improved, and uses a larger detector compared to previous analyses. This allows to observe the shadow with a large significance per month. In the first part, it is found that incorporating a moon disk model, a coordinate-dependent uncertainty scaling and an improved background estimation increase the significance compared to a previous more simplistic analysis. In the second part, the performance of two new directional muon reconstruction algorithms is verified.