Hah, nice one. For people not getting the joke, adding two random numbers reduces the randomness and concentrates the results around a mean.
Interestingly, the perception that adding random numbers together results in even more random numbers is behind the popularity of the scam game "razzle". In razzle there's usually a board containing an array of depressions each lined up with a different value onto which is dropped a number of marbles (there are other ways to play as well, including dice). The important part is the scoring board. After each toss the values where all the marbles landed are added up and then a board is consulted to see how many "points" are scored from that value. The game is easy, get to 10 points and you win. However, there are two tricks. First, the scoring board is arranged in non sequential order. This is to conceal the fact that the group of middle numbers do not win any points. In actuality it is very difficult to win any points, since the probabilities are all concentrated in the middle. Second, because of the scattered nature of the scoring board it's very easy for the person running the game to cheat in your favor by "accidentally" giving you points when you shouldn't have earned them. The scam then works fairly simply. People pay money for each throw, and they are given the opportunity to win a high value prize. For the early throws the operator goes quickly and fudges the score lookups, building up points for the player that they haven't actually used, and giving them an unwarranted confidence in the game. After the player gets within a point or so of winning the operator then lets stops cheating and lets them play completely fairly on their own, at which point they have odds of worse than a thousand to one of winning (keeping in mind that it costs money for every throw).