[split] Verbose cipher?

[MichelleL11]

One thing I'd like to hear more statistics-savvy people's opinion on is why some glyphs appeared more effective than others. For example EVA-e was always underwhelming...

I think that Farmerjohn's math is the answer to this -- although I am not such a mathematician to be able to explain it.  But I'm going to try anyway and don't laugh too hard everyone.
   

It seems to say that the impact of changing two letters into a single letter X will depend on the probability of both letters being substituted for (with two probabilities being equal and so having the value of p/2, will result in at least some positive impact on entropy) (e.g. in Koen's experiments the dot will move up the Y axis).

This increase is maxed out when each letter substituted in takes the place of two letters of equal probabilities (e.g. subbing out a four-gram with a bigram?) then entropy will increase by 1 (e.g., the dot in the experiment will move up the Y axis maximally).

And to make it even more ideal, if the substitution discussed above is performed AND both probabilities are "independent of context" (not sure that that means) you'll get an equivalent change in (h1-h2) (h1 alone? -- I'm confused on this point)* and thus won't lose your progress by messing with the X axis (e.g., the dot will move up the Y axis but won't move across the X axis).

Finally, trying to apply this to the EVA-e issue -- perhaps the probabilities of this letter are such that it cannot achieve a value of p/2 in relation to the other letters that will be substituted with it -- and thus it does not have a positive effect on entropy?

*I seem to recall that you graphed your results differently at different times although I had trouble finding it on your blog again -- Koen can you comment on this and does this fit into Farmerjohn's discussion?