There are 64 teams who play single elimination tournament, hence 6 rounds, and you have to predict all the winners in all 63 games. Your score is then computed as follows: 32 points for correctly predicting the final winner, 16 points for each correct finalist, and so on, down to 1 point for every correctly predicted winner for the first round. (The maximum number of points you can get is thus 192.) Knowing nothing about any team, you flip fair coins to decide every one of your 63 bets. Compute the expected number of points.
I'm not exactly sure how to do this...
I assume everything is independent...
Working backwards, in the final, there is 1 game and a 50% chance of winning, in the semi-final, there are 2 games each with a 50% chance of winning, etc.
$$E[Points]= (1/2)\cdot 32 + (1/2)\cdot (1/2)\cdot 16 +$$
Is this the right approach?