## 5 Discussion  
As shown in Section 4.2, the results of the deterministic race simulation do not indicate that they often do not represent the most likely outcome of a race. Additionally, the theoretically fastest strategy for a race often turns out to be fragile when probabilistic effects are considered. Consequently, race simulations should include these effects, which can be evaluated using MCS. Thus, the strategy engineer can benefit from information on the position distribution and robustness of different race strategies against unforeseen events.  
The significance of the MCS results depends on the accurate modeling of the probabilistic influences. Therefore, we extended existing ideas (e.g., using Bayesian inference for accidents and failures) and developed new approaches (determination of FCY phases, modeling of safety cars, starting performance) to improve on the points criticized in the literature. Of note is the FCY phase implementation, which affects the drivers equally regardless of their respective race progress. The SCG concept allows the realistic modeling of safety cars despite the lap-wise discretization. The example in the results section outlines that the approach represents reality well. The separate consideration of accidents and failures increases model accuracy and strengthens the cause-effect relationship with the FCY phases. Finally, the presented model for the starting performance does not distort probabilities for drivers starting predominantly at the front or back of the starting grid. The database with the seasons 2014-2019 allows a significantly improved and extended parameterization compared to the literature.  
There are, however, some inaccuracies. In reality, at the end of an SC phase, lapped drivers may often catch up one lap to restore the correct ranking of the drivers for the re-start. This behavior cannot be simulated due to lap-wise discretization. For the same cause, an SC in the simulation does not start directly in front of the leader, but at a particular race time. However, this disadvantage was largely eliminated by increasing the first SCG lap time, so that the drivers quickly catch up with their SCG. Another inaccuracy is that we can currently only consider one driver per accident that causes an SC phase. This could be eliminated if more detailed data were available, which would allow us to analyze accidents involving several cars. A thorough analysis of the conditional probability for VSC phases after failures would also be desirable in that case.  
The computing time of the race simulation was kept at a similar level despite the extensions. For obtaining the results of Monte Carlo simulations even faster, the introduction of Latin Hypercube sampling could be investigated in the future. Presumably, this reduces the number of simulation runs required to achieve a defined maximal deviation. Regarding our future research, we aim to focus on the optimization of race strategy using the developed race simulation. The challenge is that the basic strategy before a race cannot be determined independently for a single team since every team aims for an optimum. Consequently, the mutual effects must be taken into account. Furthermore, during a race, the basic strategy needs to be quickly adapted to the current race situation, for example, in the case of an SC. This requires a solution that can provide the results very quickly.