This question has been bothering me for a while because I can't think of a way to disprove it.
Question
If I randomly generate "entries" to a skill-based contest, can I assume that over a large number of iterations, they'll be evenly distributed, even if all the other entries are attempting to win?
My Thinking
Lets say I have 100 marbles. 99 are black, and 1 is white. If I put them all in a bag, and then pull marbles until I get a white one, over a large sample size, I'd assume that the white marble will typically come somewhere around the 50th pull.
Now however, lets say instead, I'm playing one of those "Guess how many beans are in this jar" games. 99 other people enter and actually try to guess based on what they see in the jar, but I pick a completely random number (lets bound it to keep it reasonable, so say I pick between 1 - 1,000,000). Can I still assume that over a large sample size, I'd be around the 50th most accurate?
What I'm Unsure Of
Because other people are trying to use skill and I'm still random, does my distribution change? If so, is there any way to adjust it based on math, or would I need to have some number to judge how accurate the 99 others are (i.e. what their "edge" is)?