Math Expected Value? We are making a casino game and need to determine expected value to see if we will be profitable. My teacher says our expected value must be a small positive number so that it is fair and that the casino is making money.
HOWEVER, if you were to calculate the expected value, for example, rolling a die, assuming landing on a 1 will take away 5 points, and anything else gives you no points. Therefore your expected value will be negative. Therefore meaning you will LOSE money and the house should gain money. 
So shouldn't a negative expected value be better for the casino?
Thanks in advance!
 A: You're considering the expected value from the perspective of the player while your teacher is considering the expected value from the perspective of the casino. The two expected values will have the same magnitude but differ in sign. Using your terminology, a negative expected value would indeed be better for the casino (the player would 'expect' to lose a little money, so the casino would gain money).
A: Your question doesn't make a lot of sense because you haven't defined your problem thoroughly enough. From the perspective of the Casino, you want a small positive expected value if the random variable tracks dollars gained and you want the perspective of the gambler to be negative.
Suppose the random variable $X$ tracks the profit gained from paying 2 dollars to play the coin flip game where if you flip heads, you make two dollars, and if you flip tails you get nothing. Then $X = 0$ if H and $X = -2$ if T. So, the expected value is negative for the gambler, they lose money playing this game on average. But for the casino, if $X$ tracks the profit gained from letting a player play this game, then $X = 0$ if H and $X = 2$ if T. In this case, the casino has a positive expected value from letting a player play this game, the casino makes money on average.
A: It depends on how you look at it. Your teacher probably asked for the expected money that the house gains: It should be a small positive. But, the expected money that poor people like us should gain should be a small negative. Or, the expected money that poor people like us should lose should be a small positive, etc.
A: You can think about expected value in one of two ways: 
1) From the perspective of the Player.
2) From the perspective of the Casino. 
For example, if a player bets $\$1$, and his chance of winning is $0.49$, then his expected value is $\$0.98$. But the Casino's chance of winning is $0.51$, so the Casino's expected value is $\$1.02$!
Note that the Player and the Casino both have their own piles of money.
