This is cool info, thanks. > Since it looks to follow whichever pattern already exists, and de bruijn sequences minimize existing patterns, it always beats the

This is cool info, thanks. > Since it looks to follow whichever pattern already exists, and de bruijn sequences minimize existing patterns, it always beats the game. I'm pretty sure this isn't true though. A de bruin sequence doesn't guarantee that the order of the n-patterns is random, only that the number of unique n-length patterns is maximized. Indeed, the algorithm you mention puts n-subsequences with many 0's in the front, and subsequences with many 1's in the back. Sure, every n-length subsequence appears only once, but because the order of the subsequences does follow a predictable pattern, your total sequence is still pretty predictable. This disparity isn't noticeable when n is small (you chose n=6), so you can comfortably beat the game. But pick a large n and your sequence becomes rather predictable. Try n=20. In that case, the generated sequence S has length |S|=32,768=2^15. In the first half, there are 9098 0's and 7286 1's. In the second half these numbers are exactly the opposite. Throw this sequence into the game, and you end up with a prediction accuracy of 50%. Not worse than random, but you didn't beat the game either.