[QUOTE=standby my man;7082223]In random data, you EXPECT to see sequences of data that don't look random at all, including consistent patterns. It may be counterintuitive, but if you didn't see those patterns, the data wouldn't really be random! I think you are equating random with "completely irregular." But in fact that's not random. Data's not really random unless it doesn't look random at times. (I know, my head is starting to spin too.)

A couple years ago, Apple had to change the "shuffle" algorithm on the iPod to make it LESS random because people didn't think it was random enough. Mathematically, the expectation is high that you'll hear the same song two or three times in a row now and then, even if you have a lot of songs and are shuffling randomly among them. But if you have one thousand songs and hear the same one twice in a row, intuitively you think it's not random at all. So Apple adjusted the algorithm, making it LESS random by minimizing the chance of those TRULY random artifacts from happening. They did this by reducing the chance that a song is played if it has recently been played. That makes the algorithm completely unrandom, but to people, the result will seem more random.

You are noticing patterns. In random data you expect to have noticeable patterns. That doesn't change the fact that the data is still random.

Here's another example of this paradox in play. If you gather 23 complete, random strangers together in a room, what are the chances that at least two of the strangers will have the exact same birthday? Mathematically, the chance is more than 50%. But that doesn't seem intuitive to us: after all, there's only 23 people, but 365 days. I'd bet that most people, upon discovering that two people had the same birthday, would consider it an amazing coincidence. It's not. It would be more of a coincidence if two people DIDN'T have the same birthday! (If the number rises to 60 random people in a room, statistically there is a greater than 99% chance that at least two will have the same birthday.)

The only thing that is not random about slot machines is that the algorithm is adjusted to, over time, pay back a certain percent of the take-in in an adjustable way. Within that constraint, the manner in which the slot machine does it is completely random. A lot of math, research, engineering and regulation guarantees that. The beauty of statistics is that even in random data, we will see things that we swear aren't random at all because they're such an "amazing coincidence." And that's part of what makes slot machines addicting. If the manufacturers adjusted the algorithms to *appear* more random by in fact being *less* random (like Apple did with the iPod), that would decrease the fun of slot machines because you would no longer have those hot or cold runs that make slot machines exciting. Mathematically, in random data you expect hot and cold runs and every other possibility of pattern or non-pattern, over time, at some time.