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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)?

user52989
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  • When you say "they'll be evenly distributed," do you mean the wins will be evenly distributed? – setholopolus Dec 22 '16 at 16:33
  • Your distribution will certainly change if you are choosing randomly and others are using skill (for example glancing at the jar will give them an edge on guessing how many beans are in it). How much of an advantage depends on a LOT of different things--you would need to know the chance of winning of every single person in the contest in order to make good predictions about your chance of winning by random guessing. – setholopolus Dec 22 '16 at 16:35
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    How many beans are really in the jar? If there are three beans, and you randomly guess a positive integer below a million, chances are you'll be the least correct by a large margin. So in order to expect to be somewhere in the middle, you need to choose your distribution using skill. – Arthur Dec 22 '16 at 16:36

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