Smart trades with AI

So, in trade You-AI:
1gpt - 30g
42g - 1gpt
lux - 240g/6gpt
240g/8gpt - lux
strat - 45g/1gpt+3g
ambasy - 1gpt
25g - ambasy

That are pretty much basics. But there also seem to be some trades that don't add mathematically yet still work.

5 strat (225g) - lux (240g)
2 age above RA - 6 gpt overpay from your side (180g instead of supposed 200g)

Are there any others way to get extra value out of trades?

Well, such gains are usually very small. I bother with such transactions only when I'm extremely low on cash or it's the early game.

These values are dependent on your relations and in case of strategic resources, the era you are in. Sometimes you can get some money for opening your borders and this part of a deal can also make it cheaper in general.

You may be more interested in fact that when AI has a diplomat in your capital, you can trade them your votes for gold. If you don't care one way or another in a resolution, just check which one pays better. If you are decided on one of possibilities, it never hurts to check whether AI will be willing to pay you for what you are already willing to do. It isn't usually of any use before atom era, though.

The AI also does funny things with trades. Strat resources seem to deteriorate in value - horses seem to worth less over time. Sometimes, however, I have AI willing to pay me 5gpt for 5 horses even into atomic age. Don't know why.

Maybe they still have some mounted units kicking about, and maybe they're low on horses. It depends on the units and amount of Strategic Resources they have.