Questions: A popular casino table game is three-card poker. One aspect of the game is the "pair plus" bet in which a player is paid a dollar amount for any hand of a pair or better, regardless of the hand the dealer has. The table available below shows the profit and probability of various hands of a player playing the 5 pair plus bet. Complete parts (a) and (b) below. (a) What is the expected profit when playing the 5 pair plus bet in three-card poker? The expected profit is - (Round to two decimal places as needed.) (b) If you play the game for 4 hours with an average of 35 hands per hour, how much would you expect to lose? Expect to lose (Round to two decimal places as needed.)

A popular casino table game is three-card poker. One aspect of the game is the "pair plus" bet in which a player is paid a dollar amount for any hand of a pair or better, regardless of the hand the dealer has. The table available below shows the profit and probability of various hands of a player playing the 5 pair plus bet. Complete parts (a) and (b) below. (a) What is the expected profit when playing the 5 pair plus bet in three-card poker? The expected profit is - (Round to two decimal places as needed.) (b) If you play the game for 4 hours with an average of 35 hands per hour, how much would you expect to lose? Expect to lose (Round to two decimal places as needed.)
Transcript text: A popular casino table game is three-card poker. One aspect of the game is the "pair plus" bet in which a player is paid a dollar amount for any hand of a pair or better, regardless of the hand the dealer has. The table available below shows the profit and probability of various hands of a player playing the $\$ 5$ pair plus bet. Complete parts (a) and (b) below. (a) What is the expected profit when playing the $\$ 5$ pair plus bet in three-card poker? The expected profit is $-\$$ $\square$ (Round to two decimal places as needed.) (b) If you play the game for 4 hours with an average of 35 hands per hour, how much would you expect to lose? Expect to lose \$ $\square$ (Round to two decimal places as needed.)
failed

Solution

failed
failed

Solution Steps

Step 1: Calculate the Expected Profit for Each Outcome

To find the expected profit, multiply each profit by its corresponding probability.

  • Straight flush: \(200 \times 0.0022 = 0.44\)
  • Three of a kind: \(150 \times 0.0024 = 0.36\)
  • Straight: \(30 \times 0.0326 = 0.978\)
  • Flush: \(20 \times 0.0496 = 0.992\)
  • Pair: \(5 \times 0.1694 = 0.847\)
  • Other: \(-5 \times 0.7439 = -3.7195\)
Step 2: Sum the Expected Profits

Add all the expected profits calculated in Step 1 to get the total expected profit.

\[0.44 + 0.36 + 0.978 + 0.992 + 0.847 - 3.7195 = -0.1025\]

Final Answer

The expected profit when playing the $5 pair plus bet in three-card poker is \(-\$0.10\).

Step 3: Calculate the Expected Loss Over 4 Hours

First, calculate the number of hands played in 4 hours.

\[35 \text{ hands/hour} \times 4 \text{ hours} = 140 \text{ hands}\]

Next, multiply the number of hands by the expected loss per hand.

\[140 \text{ hands} \times -\$0.10 = -\$14.00\]

Final Answer

If you play the game for 4 hours with an average of 35 hands per hour, you would expect to lose \(\$14.00\).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
A box contains ten cards labeled Q, R, S, T, U, V, W, X, Y, and Z. One card will be randomly chosen. What is the probability of choosing a letter from U to Z ? Write your answer as a fraction. 6/10
failedAnswered
What is the volume of the solid of revolution generated by revolving the area bounded by y=x, y=-x+4, and y=0 about the y-axis? (A) 4 pi / 5 units ^3 (B) 10 pi / 5 units ^3 (C) 2 pi units ^3 (D) 16 pi units ^3
failedAnswered
Graph the line with the given slope m and y-intercept b. m=2/3, b=-1
failedAnswered
Christer excels at planning and staffing. Bohai is a talented problem-solver and project coordinator. Ines's proficiency is in aligning people, motivating teams, and inspiring project participants. Whose skill set would make them the best candidate for a project leadership position? a Christer b Bohai c Ines d They would be considered equally qualified candidates.
failedAnswered
Which is the stronger base? CH3CH2CH2COO^- CH3CH2CH2NH2