In this game, cavalry counters archers, archers counters infantry and infantry counters cavalry. This is true, but there are some facts to prove them wrong.
We're talking about real life facts here. So, no doubt about the fact that archers can pick off infantries, strong infantries can block cavalries and cavalries are too fast for archers.
But in fact, sometimes, the infantries can't withstand the cavalries' charges and lost. In the late Ming Dynasty, a rebel leader is heavily defeated by the Manchus, as the rebel troops are mostly infantries, while the Manchus are mostly cavalries and the former can't withstand the latter's charges. (probably because the terrain is not suitable for the infantries to block them or that the Manchu cavalries are archers as well. )
Cavalries can also be countered by archers at some cases. Let's say, if the cavalries are fast, why not shoot their horses? Cavalries are nothing without their horses, so yea. There are many warfare around the world where the cavalries are bullied by archers, or the opposite situation.
Like I said at first, war is a complicated thing. It all depends on the situation. What do you think?