[Siegmund]

Second hand is a very common suggestion.

For simple 1/2 or 1/4-type choices, you can use things like whether your hole cards / first board card / whatever you pick is red or black.

Do you keep your chips all in neat stacks except for one leftover pile? Another way to get a random number between 1 and 10 or 12 or 20. Not quite uniform, and if you consciously manipulate the chips a lot, not the best choice.