To Play or Not to Play? That is the Question. I am very bad at problems involving expected return and was hoping some one could help me out.
You are offered a chance to play a game for $48 against 99 other players(100 including you) the game consists of 16 rounds and in each round you have 4 chances to win. The first winner picked in each round gets 30 dollars, the second winner gets 50 dollars, the third gets 30 dollars, and the fourth gets 100 dollars. It is also possible for one person to win more than one of the prizes in one round. The question is what is the expected payout of playing this game?
Note: All rounds are independent of each other and each player has an equal chance to win each prize in each round.

Your expected winnings for a round are:
$$(1/100)\cdot 30 + (1/100)\cdot 50 + (1/100)\cdot 30 + (1/100) \cdot 100 = \frac{21}{10}$$
Do this 16 times. You expect to win 
$$16 \cdot \frac{21}{10} \$= \frac{168}{5} \$= 33.6 \$$$
Not worth the money.
Payout is $-48\$ + 33.6\$ = -14.4\$$
