Humans are terrible when it comes to randomness. They're bad at recognizing it; they are terrible at producing it. I think most people realize this so I'm not going to go on about it at any length. Instead, I want to provide an example which I find amusing.
Years back, a video game named Fire Emblem came out for the Game Boy Advance handheld console. It was a tactical role-playing game in which units fight one another. Whenever units attacked one another, they had a chance to hit and a chance to get a "critical hit." As is common in anything with randomness, people often complained about how they were unlucky in it. Quite often, people would say they thought the game's random number generator (RNG) was biased.
They were right. Kind of. You see, the game developers knew people feel this way when playing games. They knew no matter how perfectly random results might be, people would think they saw patterns in it. To try to reduce the unpleasantness this creates, the developers decided to rig the chance to hit rolls. Instead of rolling one random number from 1-100 for the percent chance to hit, they made it so the game rolled two numbers from 1-100 and averaged them.
Yeah, that's right. If you have a displayed 99% chance to hit, the only way you'd miss is if you rolled the 1% chance twice, If the opponent had a displayed 10% chance to hit, their actual chance to hit would be much lower. Yet people playing the game routinely complained about the RNG being biased against them.
I thought that was amusing enough to share.