Unless they've changed things, the tradition policy that gives cultural buildings will give the lowest one (not yet built), and if none is available, give you the lowest one once it is researched.
I sometimes used to take advantage of this to get a nice bunch of hammers, taking the policy when I had the monuments and using the hammers to instead get amphitheaters or whatever comes next (can depend on Civ).
But I just noticed that Cultural buildings have been nerfed. Its questionable whether the amphitheater is even worth much around the time you build it (the free maintenance is nice).
I wondered what people usually do (feel free to outline situations that change your behavior):
a) Get the policy to get 4 free monuments
b) Get the policy after getting 4 monuments so that the subsequent culture building is free (one might have to delay middle of tradition policy for this, and that is a hard sell to me).
c) Put a monument in the capitol, use the policy to get free monuments in other cities.
Realistically, the choice is between C and A for me.
I sometimes used to take advantage of this to get a nice bunch of hammers, taking the policy when I had the monuments and using the hammers to instead get amphitheaters or whatever comes next (can depend on Civ).
But I just noticed that Cultural buildings have been nerfed. Its questionable whether the amphitheater is even worth much around the time you build it (the free maintenance is nice).
I wondered what people usually do (feel free to outline situations that change your behavior):
a) Get the policy to get 4 free monuments
b) Get the policy after getting 4 monuments so that the subsequent culture building is free (one might have to delay middle of tradition policy for this, and that is a hard sell to me).
c) Put a monument in the capitol, use the policy to get free monuments in other cities.
Realistically, the choice is between C and A for me.