if .5 is completely random, what does it mean that I got it down to 0.4781666666666667? I may have gotten it lower than that, but got tired of taking screenshots. Eventually I ended up back around .53
It means you were able to fake the algorithm out. Consider a very simple algorithm that guesses based on your previous two characters:
df d
dd d
fd f
ff f
This is presumably much simpler than what the page is doing, but will nonetheless work pretty well on humans by looking for alternations and long runs.
This algorithm is trivially defeated (chance of guessing 0) by the string
ffddffddffdd
Since that holds a pattern just long enough to get the algorithm to guess based on it and then switches.
For a little while, either intentionally or not, you must have been doing a more sophisticated version of this.
With perfect knowledge, it should be possible to get it down to 0.
Any random result series has such "unlikely" occurrences -- you can get 100 6 in a row by throwing dice for example, it's just rare. It's the long term convergence that matters.
This algorithm is trivially defeated (chance of guessing 0) by the string
ffddffddffdd
Since that holds a pattern just long enough to get the algorithm to guess based on it and then switches.
For a little while, either intentionally or not, you must have been doing a more sophisticated version of this.
With perfect knowledge, it should be possible to get it down to 0.