Will a game run faster on a computer with more ram than a game with less ram Will I have an advantage over someone with less ram playing the same game

Yes you will have a slight advantage as the computer with less RAM will display the game in a lower framerate, in extreme cases it will make the games jump frames and therefore miss gameplay. However if you want to play online then the best way to get an advantage is to have an extremely fast internet connection. This minimizes lag and stops the game freezing as much online.