What if I don think the die rolls or coin flips look very random?
Sometimes people email me to say that they feel the Die Roller produces too many repeated numbers (e.g., that it is hard to roll five dice without getting two or more identical rolls) or that the Coin Flipper produces too many heads or tails when used with several coins. Such concerns are great illustrations of how difficult it is for humans to deal with randomness. Our brains are so good at finding patterns that we tend to see them even where they aren’t. (This is why statistical tests are useful and why the Real-Time Statistics for RANDOM.ORG’s numbers are published online.) So let’s do the math for an example where we’re rolling five dice. Intuitively, you may expect that the five rolls should come up different a lot of the time. (At least this is what people often mention in emails.) So what’s the chance of all the five rolls being different? The first die is trivial. Any of the six possible values is fine (none will result in duplicates), giving a probability of 6⁄6 = 1. After you
