Based on my friends, the care/don't care dichotomy cuts orthogonally to the math/no math dichotomy. Most people, whether good or bad at math, can understand that the chances are the same. It's some other independent aspect of your brain that determines whether it intensely matters to you to do things "the right way" or if you can accept the symmetry of the situation. I hereby nominate some OCD-like explanation. I'd be interested in seeing whether OCD correlated with your friends' behavior.

As a data point, I am not OCD and don't care if you cut the deck.