Where o is the public order gain, g is the number of garrison troops present, and p is the population:

o ≈ –2.8 + 701g / p
o + 2.8 ≈ 701g / p
g ≈ p(o + 2.8) / 701

If we want +20% public order, which is what monthly games give, then:

g ≈ 22.8p / 701 ≈ .0325p

If we want to express this in terms of number of peasant units required:

g = 60u
60u ≈ .0325p
u ≈ .00054p ≈ p / 1845

In other words, to get +20% public order, you need one peasant unit per 1,845 people. The cost of that is:

c = 100u
u = c / 100
c / 100 ≈ p / 1845
c ≈ p / 18.5

Therefore, given that monthly games cost 200 (IIRC), using garrisons is more profitable when

c < 200
p / 18.5 < 200
p < 3689

I'm too lazy to do daily games now. Maybe I'll do them tomorrow.

-Simetrical