Anybody know what kind of effect ...

It makes a city cost more to bribe. Other than that, I`m not sure.

[St Leo]

It either doubles the price directly or halves the distance to the capital and doubles it that way, I am not sure which.

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St. Leo
http://ziggurat.sidgames.com/
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[DarthVeda]

What kind of effect does a Courthouse have on spies and diplomats?

[Smash]

Doubles the cost.

In my experience the courthouse has NO effect on anything else(steal tech,sabotage, etc).It should.Or some other improvement should.Thats why in MP there is no realistic defense to dip raping.