This is why, when someone asks me to pick a random number, I try to think of some random process going on in my surroundings, and from there derive the random number.
A common tactic for Poker players who want to make some of their actions in a common scenario random (call in one instance, or perhaps re-raise instead) is to look at their wrist watch, and depending on where the second hand is they can simulate a coin flip or a dice roll.
https://www.youtube.com/watch?v=tP-Ipsat90c
TLDW: We don't pick numbers at random. At all. We're so bad at it that you can make money off this fact.