Please note: this is not homework.
This is related to a previous question I have asked, Calculate number of sequences in frequency matrix.
Please refer to this image:
(also the image presented on this StackOverflow question: Plot weighted frequency matrix)
The plot is from Boring, E. G. (1941). Statistical frequencies as dynamic equilibria. Psychological Review, 48(4), 279.
For the full matrix there are $2^{36}$ paths through the full matrix. Boring states:
Frequency matrix converging upon one-sixth. The diagram is for inter- dependent events with a limiting frequency of one-sixth. There are only 1,947,792 sequences in this matrix
My question: Since I am reproducing the plot but for 25 trials (instead of 36) how do I calculate the relevant figure for 25 trials rather than for 36 (which is what Boring gives)