Any statisticians about? Your analysis is needed!! I'm currently putting the finishing touches on a program that I created in response to something that came up on another forum I frequent. There is someone there who claims that they have the ability to influence the results of video games, and the state of stoplights while they drive, through their magical power. They are not joking. I have created a little game to test this out. The game occurs in rounds. Each round, a frog is dropped onto a board. The frog hops towards a stoplight. When the frog nears the stoplight, it randomly turns either green or red (lightState = (rand() % 2 == 0 ? RED_LIGHT : GREEN_LIGHT); ) If the light is green, the frog hops past safely and does a little backflip to show just how happy he is. If the light turns red... well, what do you think happens? Before each round, the player is asked to select what they think the outcome will be - whether the frog lives, or suffers an untimely demise. The game keeps track of how many times the player guesses correctly or incorrectly, and how many times each stoplight color comes up. Afterwards, I'm asking the player to mail me an encrypted file that contains this information. I'll decrypt and post the results. My question to those of you with experience in statistics is: What is the lowest number of rounds I should insist that the game be played before I accept their results? Obviously, the more the better, but there's just so many times you can watch a frog get splattered before the novelty is gone. How many times, minimum, do I have to have them play before we can fairly safely rule out a lucky streak, and determine that it's probably magic at work? I'm serious. Help me out, here, I've never had a statistics course, and I'm sure there's a lot of interesting mathematics behind analyzing this.