If it was random I expect to see runs of 4, 5, all the way to 7 to 9 zeros or ones What I found was that 'cheaters' are very reluctant to write long runs, and when they do write long runs, they far under-estimate the frequency of those long runs. Since I already know that some groups are already going to cheat, I challenge the students to cheat and will give them a bonus mark (it's a meaningless mark, and is more for bragging rights) if they cheated successfully, (also they don't have to redo the exercise) When I go over to check the results, what I do is to look for runs 4 or more of 0s or 1s, and see if they are present. I asked my students as a group to flip a some coins for a total of 400 coin flips, and write 0 if it's tails and 1 if it is heads. That is one thing I did with my statistics class years ago when I was a TA.