Questions: Determine a casino's expected net income from a 24-hour period at a single roulette table if the casino's total overhead for the table is 30 per hour and if customers place a total of 5,000 on single-number bets, 4,000 on two-number bets, 4,000 on four-number bets, 2,000 on six-number bets, 7,000 on low-number bets, and 8,000 on red-number bets. (Assume the expected value of each of these 1 bets in roulette is 0.053.) 88.8

Solution Steps

To determine the casino's expected net income from a 24-hour period at a single roulette table, we need to calculate the expected income from each type of bet and subtract the total overhead cost. The expected income from each type of bet is the product of the total amount bet and the expected value per dollar bet. The total overhead cost is the hourly overhead multiplied by the number of hours in a day.

The expected income from each type of bet can be calculated using the formula:

\[ \text{Expected Income} = \sum (\text{Total Amount Bet} \times \text{Expected Value per Dollar}) \]

Substituting the values:

\[ \text{Expected Income} = (5000 + 4000 + 4000 + 2000 + 7000 + 8000) \times 0.053 = 1590.0 \]

The total overhead cost for the casino can be calculated as follows:

\[ \text{Total Overhead} = \text{Overhead per Hour} \times \text{Total Hours} = 30 \times 24 = 720 \]

The expected net income is determined by subtracting the total overhead from the expected income:

\[ \text{Expected Net Income} = \text{Expected Income} - \text{Total Overhead} = 1590.0 - 720 = 870.0 \]

Final Answer