Probability of casino earning a certain amount
**Problem**
In a game of dice at a casino, a player throws two dice. There is no initial cost of playing.
If the player gets a 2 or a 12, the player wins $\$200$.
If the player gets a 7, the player wins $\$20$.
If the player gets anything else, the player pays $\$a$ to the casino.
The casino wants to set $a$ such that they, in the long run, make $\$5$ per game. Find the appropriate value for $a$.
**My progress**
Let's call the casino earnings per game $X$.
I've found $P(X=-20) = \frac16$.
Also, $P(X=-200) = \frac1{18}$.
This leaves $P(X=a) = \frac79$.
I assume I'm supposed to use these probabilities as weights, but I can't get a foothold in the calculations.