It is well-known that when you ask a person to construct a random sequence, say of zeroes and ones, the sequence they create differs in systematic ways from a “truly random” sequence. For example, they exhibit regression to the mean: the person constructing the sequence is too careful to make sure that the short-run averages are 50-50 resulting in too-frequent alternations between zero and one.
Knowing this, here is a simple bet you can use as a money pump at parties. Tell someone to write down a random sequence of heads and tails, and bet them that you can guess the numbers in their seqeunce. A simple strategy that correctly predicts more than 50% of the time is to randomly guess the first number and then guess that each subsequent number is the opposite of the previous. But if you study this article (and its links), you can refine your strategy and do even better.
And soon, as icing on the cake, you can offer your victim favorable odds, say you pay $1.10 every time you are wrong and she pays you $1.00 every time you are right. You will still make money.
Then after you have relieved your fellow revelers of their pocket cash, and they want to turn the tables on you, remember to use one of the coins you have just won to construct your sequence in a truly random fashion.
Cheap Talk 
2 comments
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June 20, 2009 at 3:44 pm
mike
Reminds me of this recent post:
http://chrisblattman.blogspot.com/2009/06/randomization-in-tropics.html
Basically, Blattman is disappointed in the randomization of his study because the results do not have the properties that he wants. In other words, similar to the people at the party, he chose his random number generator in the mistaken belief that any given random string will have similar properties to the full set of random strings taken as a whole.
One wonders if a ‘hand-crafted’ random string, which has the desired properties, would not have been the better way to go for situations like that.
You really only need/want ‘truly random’ numbers in situations where the string will be attacked; ie: the operative property of such a number is that it is unknown to the attacker.
June 20, 2009 at 7:37 pm
ZBicyclist
Second time I’ve run into this type of thing today. Over on Gelman’s blog, he’s had a couple of posts on other people’s work which show that Iranian election results tend to have too many 7’s in both early and late digits. This may indicate fraud.
Remember the old party trick in which you ask somebody to pick a number between 1 and 10? 7 tends to be disproportionately chosen, so you can potentially use this fact to win money from your friends, assuming you have an abundance of extra friends.
http://www.stat.columbia.edu/~cook/movabletype/archives/2009/06/the_devil_is_in.html#comments