I've done this exact thing before -- writing a Monte Carlo simulation where stats and algebra would have given me the same answer. I think it was less phobia and more that I'm completely out of practice with math and stats by hand, but spend enough time in code to be comfortable with it.

I knew my code would give me the right answer and I lacked the confidence in math, where even if I did do it by hand, I would have written the code to check it. The less time-risk way won.