I want to figure out a way/formula by which I can compute the probability of the sum of n random numbers to be greater than X. All the random numbers fall in the range of [−1000,−1.01]∪{0}∪[1.01,1000] and step size is 0.01
Each random number is chosen independently.
Use Case: I am working on the development project of a gaming engine. For each round a player is awarded a random score in the range of [−1000,−1.01]∪{0}∪[1.01,1000]. In the beginning, player can make a bet that after n rounds of the play the total sum of his score will be X. I just want to get the probability of the accuracy of his bet.
Current Progress - I was able to somehow get the results using brute force approach (n rolling dice problem), however the brute force method is taking lots of computation power. I want an efficient formulae/solution (in terms of computation)
I don't know if Convolutions is the right approach for it.
Thanks for the help, in advance!