I want to learn of good ways by which to generate $\{0,1 \}$-sequences in my head which are (pseudo)random with uniform distribution, so that I may simulate flipping a fair two-sided, standard coin. I want to do this because sometimes, I need to pick an option randomly, but I have no equipment (such as a coin or a random number generator) handy - and I am scared of having cognitive biases creep in.

The trick/constraints in this challenge include(s):

- the fact that I am not an exceptionally skilled mental calculator and I may need to generate these numbers under pressure or quickly;
- I want the sequence (if it is pseudorandom) to have a fairly large period so that I can generate values many times in the same situation (say, in order to make several consecutive decisions over the course of a few seconds or minutes) without falling into an apparent pattern. I may add other constraints too. But the basic idea is that the method needs to be robust and versatile, but also reasonable in human situations.

And, of course, it has to be free of cognitive biases or other failings, except for calculation accuracy and possibly choosing the initial values.

Bonus points if it generalizes easily to $\{0, 1, \ldots, n \}$-sequences for small $n$, such that the method is still easy (etc.) to use

Thank you very much