OK, a respite from my last two posts about the Research Excellence Framework. The following question occurred to me, I make no promise that it is interesting.
Suppose you repeatedly roll a fair die and write down the sequence of numbers you get. I'm going to delete numbers from the sequence according to the following rule. Let X be the first number in the sequence. I delete the first block of consecutive X's (which will usually just be the single X of course), then I delete the second block of consecutive X's, but retain everything in between. Then I do the same thing to the rest of the sequence of dice rolls - it will start with some Y not equal to X, so I get rid of the first two blocks of consecutive Y's and continue.
For example, I would delete the bold-face elements of the following:
And the question is, is the sequence of undeleted numbers indistinguishable from a completely random sequence? Seems to work for 2-sided dice (coins).