Here are a few things that I have found to be really important to winning on immortal BTS. I have arranged them into what I consider to be the most important first. Any agreement, expansion on my comments or disagreements are welcome.
1. Control Barbs. They are treacherous on immortal. They are relentless. They are worse than on deity because the AI don't settle the land as quickly immortal.
2. Wonders can be a big trap. Generally, if you want a wonder, you really have to prioritize it.
3. Plan your economy from the beginning to avoid falling behind in tech. Whether it be form luxury or seafood resources, cottage or specialist, you can't over expand trying to grab as much land as possible unless you can finance that first trade tech, whether it be Alphabet, aesthetics or CoL.
4. Expand as allowed by the AI. If the AI is close, find a strategic resource and go to war early. If there are no close AI, REX and develop.
5. Deny the AI strategic resources. I am not big on choking, but this in one option. Chose an AI to attack that you can easily pillage their resources. It is generally better to let the AI develop their cities a bit before taking them.
6. Carefully plan diplomacy. Cultivate friendships to ensure trade partners and carefully watch anyone you anger.
Most of the top games played involve heavy warring early, and often. And, of course, play the map.
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