Mathematical evaluations are conducted to determine long term outcome of probability based applications. Long term outcomes may be determined by a number of factors within the application.
Example: A game based on probabilities has a Return To Player or RTP (total win/initial bet) that converges to a specific value after playing a million games or more. The RTP determines the long term profit from the game. As it is important to know this value accurately, mathematical evaluations are used to determine the RTP.
Mathematical evaluations are usually done on a spreadsheet. Where spreadsheet based calculations are not possible, simulations are used.