Final answer:
The casino makes money by having a negative expected value for the player. On average, for every $1 you bet on roulette, you can expect to lose 8 cents.
Step-by-step explanation:
To understand how the casino makes money, we can calculate the expected value of playing the roulette game. The expected value is calculated by multiplying the probability of winning by the amount won and subtracting the probability of losing multiplied by the amount lost.
In this case, the probability of winning is 1/38 since there are 38 numbers on the roulette wheel including 0 and 00. The amount won is $180, and the amount lost is $5.
Using these values, we can calculate the expected value:
Expected value = (1/38)(180) - (37/38)(5) = -0.0789
Therefore, the expected value of playing the roulette game is approximately -$0.08. This means that, on average, for every $1 you bet, you can expect to lose 8 cents. This is how the casino makes money in the long run.