As someone who has studied several statistics courses for my major, I have grappled many times with the concept of randomness. At first look it seems easy enough to define: an event is said to have a random outcome if each possible outcome is equally likely to take place. Throw a die, and if it’s a fair one, then each of its six faces should have equal chances of showing up. If the die’s outcome is truly random, then over many tries the different possible results should show up with relatively the same frequency; throw a die six thousand times and the face with the four dots should come out around a thousand times. The same goes for all the other faces.
But people have more complicated thinking, and this clarity of definition is difficult to attain for some. If at the very start of your attempt to throw a die six thousand times, you come up with six dots for four times in a row, you would doubt the die’s randomness, wouldn’t you? The basic definition of randomness, however, does not actually imply that the same results cannot be achieved consecutively. Even if all the other faces possess equal likeliness of appearance, it does not guarantee them actual occurrence, especially in a small number of tries.