Okay, so I have played 122 backgammon practice matches against an "advanced" AI opponent so far, which should play a solid game. 71 of those games have been lost, but we're not here for that. We are mostly interested in the error rate, which is calculated mathematically, so greater deviations from the optimal play will have a much bigger impact than smaller ones. It doesn't matter how easy or hard any move was to find - if a much better move exists, it counts as a big mistake.
The software gives you a player rating whenever you run a full analysis, which I always do at the end of a match. Once again, the deviation matters, so one big mistake can easily offset many perfect decisions, and may be enough to get you stuck with a very bad rating, even when everything else was good.
I have prepared a graph of my error rates per game with the thresholds for the ratings included. The red dashed line would be my overall error rate, which currently puts me at the upper end of "Casual Player". It would be nice to get it up to "Intermediate", at least.

Wild fluctuations, as you can see - but that's because single big mistakes, which can happen quite easily from time to time, have a very big impact on your rating, as I explained above, resulting in those sharp single game downward spikes.
A breakdown can be found below. "Intermediate" is still the most common rating, but it gets dragged down by the bad games.


Here is a breakdown of my unforced moves, all the moves where I was left with a decision to make. If it doesn't hit the thresholds for "doubtful", "bad" or "very bad", I will consider it "acceptable", regardless of whether it was perfect or just not enough of a deviation to hit the thresholds, and also regardless of how difficult it was to find - some of the acceptable moves may have been no-brainers anyway, others may have been very strong plays.


Back to the results: I am losing, for what it's worth, but I am playing against strong opponents and the outcomes do not matter anyway.


Here is a graph that assigns a value of +1 for every win and -1 for every loss, further illustrating the way things are currently going results-wise:

So it is not going very well so far, but not terribly either. Many mistakes have been avoided, some difficult strong moves have been found. Besides, it is mostly supposed to train me for poker situations, rather than turning me into a great backgammon player. I should already be able to hold my own in casual games, at least.