I did the math between now and the end of samsara according to the Kadampa teachings. It yielded some interesting results.
First, I assumed a starting point where beings are equally distributed in the six realms plus one Buddha for all of samsara (not accurate, but some people struggle to accept that 99% of all beings are already in hell, so to humor them, I did an even distribution). I then assumed a starting rate of virtue for each type of being depending on the realm they occupy. At the end of each period beings go up or they go down a realm based on the percentage of virtue of that realm.
I then assumed a certain percentage of humans attain enlightenment in each period. To calculate the attain enlightenment/human ratio I took the total number of humans on earth divided by the number who I’m estimating attain enlightenment (7.6 billion people, 30,000 Kadampas, 2,500 of whom attain enlightenment = 0.00003% enlightenment rate). With each increase in the number of Buddhas, I assume the amount they bless the minds of living beings goes up 1%, thus increasing the rate of virtue for the human, animal, hungry ghost, and hell realms. I did not assume the virtue rate goes up for beings in the demi-god and god realms because then they get stuck in those realms and never attain a human rebirth. Presumably, Buddhas would bless their minds to take human rebirths.
In the beginning, as would be expected, almost everyone falls into the lower realms, in particular the hell realm because once you take rebirth in the lower realms, it is almost impossible to get out. But gradually over time, the number of Buddhas increases, who are then able to bless the minds of the beings in the lower realms more and more effectively. After about 23% of time between now and the end of samsara, due to all the blessings of the now more numerous Buddhas, the lower realms are emptied and almost everyone is in the upper realms. At that time, there is a big spike in the number of humans who start attaining enlightenment at faster rates, again thanks to increased blessings from the Buddhas.
We then start a very long period where we wait for Gods and demi-gods to burn up their merit to fall down into the human realm, where then a growing percentage of them attain enlightenment. At around the 75% of time mark, there is an exponential growth in the number of Buddhas who then so outnumber humans, they reach an efficiency where anybody who reaches the human realm attains enlightenment in that life.
Once that stage is reached, there are still about 700,000 remaining beings who just refuse to let go of their pleasures in the demi-god and god realms, ignoring their spiritual guides who go and visit them there. But eventually, enough of them fall back into the human realm, drip by drip, where they then attain enlightenment.
After about 100 periods, essentially all of samsara is emptied except about 12,500 of the last stragglers.
Let me know if you have suggestions on how to change the assumptions of the model. Obviously, this is all an estimate, but it does paint a pretty accurate picture of how things are likely to unfold between now and the end of samsara based upon my understanding of the Kadampa teachings.