Reading over this the first thing that sprang to mind is doing an FFT over the sequences and using the spectral flatness as a marker to eliminate simple ones. You could then do PCA on them along with some true pseudorandom sequences and plot, similar to Scy and William's method. I'm not 100% as these sequences are a tad short. Perhaps I'll give this a go however.
Ok so I found time to try this out.
Treating this like an audio signal makes sense, so that we can use analytical tools available in audio signal processing.
The overall challenge is effectively to try and determine whether each sample is white noisey enough.
Why? Think about what white noise is in this context. It's a pure random process. We're trying to determine if there are any particular patterns or skews to each sequence, or if the noise isn't 'white' enough.
If someone put down a completely repeatable sequence, say: [0,1,0,1,0,1,0,1,0,1...] If you were ... (read more)