I have wasted endless hours of my life playing historical strategy games since 1970, first as board games and then on computers. Troy Goodfellow at Flash of Steel has a fascinating look at games which involve the Papacy:
Popes are also generally not playable characters, and when they are, they come with major strings attached. Papal power is a spasmodic interference in play, either through the mechanics of being a Trump (a power that players compete for so they can use it against their enemies), a Vendor (a mechanic that distributes tasks and rewards to stimulate certain types of play and progress) or a Disruptor (a mechanic serves to keep games challenging or hasten resolution of stalemates.)
Medieval Total War II is probably the best exemplar here, and the one most familiar to readers of this blog, though certainly not the first. You can’t play the Pope in MTW2 – and you can’t even easily direct who assumes that role once the old pope dies – but he is always in your face, both in good ways and bad. First, as a Vendor, the Pope is one of two sources of “missions” for Catholic rulers (alongside local nobles). The Pope’s missions are connected to religious stuff, generally – build a church, convert a province, etc – and rewards for accomplishing his minor missions are on par with those nobles will provide. The Pope is a Disruptor by calling Crusades and then demanding your king or princes participate, drawing resources and armies away from where you would rather have them (you can always say no, but there’s a price). And the Pope further disrupts through Excommunication, putting leaders beyond the protection of the church and freeing you to act against them.
Go here to read the fascinating rest.The papacy spans a huge portion of recorded history. Popes had had to meet challenges of all sorts in all the historical periods covered by two millenia. Games on the subject, so long as they are not Catholic bashing, I find fascinating.