why does the number of posts one makes usually advance by one after each post but sometimes doesn't?
The post counts aren't necessarily updated instantly, rather the counts are updated at set intervals. This helps to alleviate some of the processing load and increase the overall speed of the site.
I'm not sure off the top of my head what the interval is exactly, but it's relatively short I believe, which is why the updating often appears to be nearly instantaneous, as you just happened to make your post just prior to the scheduled interval.