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 $50 per hour and if customers place a total of $7,000 on single-number bets, $4,000 on two-number bets, $4,000 on four-number bets, $3,000 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.)
To determine the casino's expected net income from a 24-hour period at a single roulette table, we need to calculate the total amount wagered and subtract the expected value of those bets.
Step 1: Calculate the total amount wagered.
Total amount wagered = $7,000 + $4,000 + $4,000 + $3,000 + $7,000 + $8,000
Total amount wagered = $33,000
Step 2: Calculate the expected value of the bets.
Expected value = (-$0.053) * total amount wagered
Expected value = (-$0.053) * $33,000
Expected value = -$1,749.00
Step 3: Calculate the net income.
Net income = total amount wagered - expected value
Net income = $33,000 - (-$1,749.00)
Net income = $34,749.00
Step 4: Calculate the overhead cost for 24 hours.
Overhead cost = total overhead per hour * number of hours
Overhead cost = $50 * 24
Overhead cost = $1,200.00
Step 5: Calculate the expected net income.
Expected net income = net income - overhead cost
Expected net income = $34,749.00 - $1,200.00
Expected net income = $33,549.00
Therefore, the casino's expected net income from a 24-hour period at a single roulette table is $33,549.00.