Here is a simple card trick you can perform informally, courtesy of the British YouTube channel Numberphile. James Grady shares a simple prediction that can be accomplished thanks to something called The Proizvolov Identity. (Don’t worry, I hadn’t heard of it either.)
Take a look:
As an ex-mathematician, I find these small tricks charming. They aren’t well suited to performing in a show, but as something fun to share with friends, the offer a wonderful small pleasant mystery.
The concept of symmetry in math, where you can make changes that have no impact, is closely related to the idea of choice in magic, where you often get to make choices that don’t affect the outcome of the trick. (And providing a moderately irritating counterexample to proponents of free will.)