Question

Game 1 gives you 200 points every time you score. Game 2 doubles your points every time you score (2, 4, 8, and so on). In which game do you think you will you earn more points?

Answer 1

Its depends on how many times you score during the game 

in second game the number of points increases  as a geometric sequence
with common ratio 2

so for example if you score ten times in first game you get 2000 points


if you score 10 times in Game 2 you score   2 * (2^10) - 1  =  2046 points

so playing 10 or more games  is best with Game 2.  Any less plays favours gane 1.