You could put 1-2 turns of research into Communism yourself, HC would be more likely to give the tech after that. You did a great job on that war. I didn't have much time to check your earlier save and make useful comments, but it looks like you were in a tough spot. Earlier wars went a bit unlucky with Washington et al., but nobody took HC from you this time
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What now? I mean, you can probably win space. I don't know much about that approach. If I can win space, I might aswell win domination. Not being afraid of modern warfare. Due to my playstyle (and map choice, since continent or isolation games can't be swiped with just cuirs... usually) I end up with Artillery, Tanks and Bombers more often than not. It's always quite messy. But also rewarding when you manage to take out a 20-city-deity-monster at tech parity... in an era when their bonuses are at their highest.
I would consider two approaches in your position:
a) bee-line Mass Media and gift it to Washington or Sitting Bull. Farm everything and grow your cities. JC and Stalin should vote for you, if needed you could switch them back into religion and/or favorite civics. I am pretty sure you can get there first.
b) Go for the military win. Sitting Bull + Stalin should be enough. Sitting Bull is easy and Stalin, well... Infantry/Artillery should be good enough. And rather familiar to play with, just a beefed up version of your cannon war really. Key is to acknowledge how Railroads and Aircraft change the dynamic of the war though. One wrong step into their territory and your SoD will just be gone. I mean this is always true to some extent, but it becomes even more unforgiving. So soak up his offensive units in your own territory before moving into flatland just like that.
After that it's not a big deal though. You can pump out enough units to take down anything. You might want two stacks since the AI will likely focus all their airships on "one side" and your secondary army could move way quicker without being bombed.
You are almost even in tech so that should work nicely. If you were at a bigger disadvantage I would go for Tanks+Marine (defense vs Gunships and Anti-Tanks) +Fighters+Bombers. That would work even against Modern Armor and anything while being more elegant. Fighters, then Bombers and mop up. Takes a bit more time to set up but after your aircraft is ready and the first city falls it plays a lot like cavalry with mobile siege. Fighters bomb city culture (+distract his aircraft), Bombers do the collateral and tanks finish the job at good odds. Works like a charm, especially when the main SoD is down.
I never saw a need to go further down the tech tree. Maybe once or twice every 100 deity games. The different unit choices are kind of overwhelming and it's a slog, sure, but also fun in its own way.
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As you can probably tell from the details, I would go for b). Or try a) and if you fail on that, make a transition to b). Until then your cities should be set up and you would want to have Radio anyway (for Bombers), so it's not a big deal. Still early and Stalin / JC are not known to climb the tech tree too quickly.
But because I do stuff like this almost every game, I feel a bit burned out right now. Going to build up energy. My dream is to win 100 deity games in a row, going with first maprolls. Then I can claim to have a 100% win ratio and retire
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