I actually looked at them now. I am sorry to have assumed that they were equivalent to the Newcomb problem by adding assumptions from the Newcomb problem. So Game 1 is equivalent to the Newcomb problem but Game 1 isn’t equivalent to Game 2 or Game 3. Game 2 and Game 3 are equivalent and one should OB in Game 2/3 and TB in Game 1.
The assumption being what I wrote earlier:
the fact that you can win at least $1,000,000 is (causally) independent of your choice.
Game 1 and the Newcomb problem satisfy this, Game 2 and Game 3 don’t.