My strategy at conquer man 1v1 has worked pretty well for me (might have just been luck tho).
What I do is, first I check who has better chances in getting the cupcake and CM (usually the same person) and if its me, I take them and fortify and build an army next to a diamond but I dont take it. If not, I search for a good spot for a base and start conquering his areas near it. But the most important thing is to focus on the small battles. If you find some outcast territories where you have 2 areas bordering an enemy, deploy 1 on each and take it over, especially when after that those areas are surrounded by neutrals. The thing is to keep raiding his outcast areas while hes busy growing and fortifying his main base to protect the cupcake and CM, if he has it, which usually leads to him taking over neutrals which you should avoid, as it gives the opponent who only attacks you an advantage. Also try to trick him into taking an alien and a diamond, especially if you have spoils, then take the diamond and fortify it. Eventually the -3 troops will have weakened him enough for you to break through to the cupcake and CM. If youre the one who has them, just counter what I proposed.
