Is there a game on an iPhone that's a strategy game where every choice we make affects how you play the game?
A good game on iPhone where every choice you make affects how you play the game is the Pandemic 2 game. The Pandemic 2 is a very addictive game and can be played freely online. Another great game is the Conquer game.
Try Qonqer, its really cool.
Try Sims free play. :)