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Still on my first real game (after playing all the tutorials very slowly, trying to learn everything).

Spymaster lets you run various missions, which all seem pretty good, and have good chance of success!
You can steal research, slander nations, or infiltrate them to reveal the map.
Opinion doesn't seem to do much here, maybe lower costs a bit, but the success rate is like 60-70% on these!!!

Then we have the agents you can assign in foreign citys, after quite cumbersome use of your scouts first setting up a agent network there.
And the agents have their own, quite crappy missions.
They can only run treachery or insurrection in their city, and with real low success rates (way below 50%).
And I see no way to get it higher, caues influencing the agents does nothing except lower the already low mission cost.

So, to sum it up, what's the use of agents?
This question / problem has been solved by nolegskittenimage
Having an agent provides full visibility of the city territory, which in itself is absolutely huge. They also passive provide bonus yields according to their stats, which can be a significant source of science in particular. The missions are very powerful, treachery inflicts 10 HP of damage when it succeeds and any damage on a city prevents hurrying builds. when the mission fails, more often than not you still get the assigned character back, you only have to re-establish the spy network and with a scout around, that's instantaneous.

Missions like treachery have their rate of success based on courage, which makes heroes and particularly strong courage hero courtiers (great soldiers usually) particularly strong agents if you're looking to use missions.
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nolegskitten: Having an agent provides full visibility of the city territory, which in itself is absolutely huge. They also passive provide bonus yields according to their stats, which can be a significant source of science in particular. The missions are very powerful, treachery inflicts 10 HP of damage when it succeeds and any damage on a city prevents hurrying builds. when the mission fails, more often than not you still get the assigned character back, you only have to re-establish the spy network and with a scout around, that's instantaneous.

Missions like treachery have their rate of success based on courage, which makes heroes and particularly strong courage hero courtiers (great soldiers usually) particularly strong agents if you're looking to use missions.
Oh, I thought full visibility was instant, as soon as you got the network, but maybe need an Agent assigned also...

Ah ok, I didn't think of them also getting passive yields, that's ok I guess, if no other place to put them.

Man, this game...it really needs to better explain what rating/archetype/opinion will affect what.
I did not see anywhere that the low successrate of the agent missions would be affected by courage!

Guess future patches always add something good, so maybe some day it will have more clear information about stuff like that, as well as an option to resize the tiny overlay info you can show on the map...
I have to clarify, different missions get boosted by different stats, courage boosts treachery but Insurrection is boosted by charisma for instance. This is mostly only conveyed through tooltips tho, and Charisma can be pretty scarce on agent candidates. Also, schemers get a flat +20% chance on all agent missions (but they tend to have low courage).
I have just started doing agent missions (still learning the basics), this information will certainly come in handy! ;)
To answer the original question "what's the use of agents?", I think the most obvious answer is still missing:
It's the yields. An agent creates 5% of the assigned city's output in science/civics/training/money per stat point of wisdom/charisma/courage/discipline respectively, and Schemers get a flat 20% on top. This is incredibly huge if you assign high wisdom Schemers to enemy capitals, and clearly overshadows any and all other uses that agents can have.