Agent Smith going rogue and Neo not choosing the door to the source when he met the Architect were not something the machines had anticipated, as the previous anomalies all behaved in a way that they predicted. Neo did all these based on what the Oracle told him. Since the events happening during the time of Neo (in the Matrix and the real world) were something unanticipated, anything might have happened in the final battle with Smith. Yet the Oracle did what she did, and even allowed Agent Smith to infect her. Did she already know by this point that things would somehow work out in favour of the humans, also in such a way that the machine world does not get completely destroyed by Smith as well? Or is this what the Architect meant by "the dangerous game" at the end?
Did the Oracle somehow know the fight between Neo and Smith would work out in favour of the humans?
Did she already know by this point that things would somehow workout in favour of the humans, also in such a way that the machine world does not get destroyed as well?
Probably not. But I'm sure she believed. This is what the final lines of the film were referring to:
Seraph : Did you always know?
The Oracle: Oh, no. No, I didn't.
But I believed.
As to why not, that would be because:
We can never see past the choices we don't understand.
- The Oracle, The Matrix Reloaded
The Oracle had already been taken over by Agent Smith before Neo, Trinity and Morpheus had met up with The Logos which means Niobe had not yet understood her choice to help Neo by giving him her ship, so he could go to the Source to fight for the humans.
With this in mind, there's no way that The Oracle could know for sure about there being a fight in the Matrix or Neo's offer of peace with The Machines which lead to everyone (who survived the attack on Zion) being saved.
Or is this what the Architect meant by the dangerous game in the end?
It's possible. There isn't a lot of context but The Oracle certainly told all the humans exactly what they needed to hear for things to work out in the end. The danger of course being that she may have 'died' along with every other program and human attached to The Matrix.