HMD 436 Test #2 Name______________________

April 8, 2002

 

Consider a three reel single-line slot machine with weighted reels. The following table shows the total weights per reel for each symbol.

Symbol

Reel 1

Reel 2

Reel 3

Bar

3

2

1

Bell

4

3

2

Plum

5

4

3

Orange

6

5

4

Blank

14

18

22

Total

32

32

32

1. 3 bars pays 1200, 3 bells pays 400, 3 plums pays 100, and 3 oranges pays 75, all per coin bet. Use the following table if you wish or Excel to determine the player’s expected return. (15 points total)

Payline

Combinations

Pays

Return

3 bars

1200

3 bells

400

3 plums

100

3 oranges

75

Total

 

 

 

Total return = _________________

 

 

 

 

Total combinations = __________________

 

 

 

 

Expected return = ____________________

 

2. Consider a modified keno game in which there are 60 balls in the chamber, of which 15 will be drawn at random. The pick 6 game pays 1 for matching 3, 10 for matching 4, 100 for matching 5, and 1000 for matching 6. Use the following table if you wish or Excel for your work. (20 points total)

Match

Combinations

Pays

Return

3

1

4

10

5

100

6

1000

Total

 

 

 

 

 

 

 

Total return = ___________________

 

 

 

 

Total combinations = ____________________

 

 

 

 

Expected return = _____________________

 

 

3. Consider a game of Derby with the following pay table. You may use the following table or Excel for your own work. (15 points total)

Quinella

Pays

Fair probability

True probability

Return

1,2

95

1,3

4

1,4

9

1,5

37

2,3

21

2,4

49

2,5

200

3,4

2

3,5

8

4,5

19

Total

 

 

Fair probability of 1,2 quinella ______________________

 

 

 

 

Sum of all ten fair probabilities _______________________

 

 

 

Actual probability of 1,2 win _______________________

 

 

 

Expected return of 1,2 win ________________________

 

4. Consider the Royal Match side bet played with 5 decks. (20 points total)

How many combinations are there for a "royal match", in other words a suited king and queen?

 

 

 

How many combinations are there for a "easy match", in other words any two suited cards besides a royal match?

 

 

 

How many combinations are there for two non-suited cards?

 

 

 

Use the following table or Excel to determine the total return.

Hand

Combinations

Pays

Value

Royal match

25

Easy match

2.5

Non-suited

-1

Total

Total value = ____________________

 

 

 

Total combinations = ____________________

 

 

 

Player’s expected value = _______________________

 

 

  1. What is the probability of 2 suited sevens as the first two cards and then a non-seven as the third card in a 7-deck shoe of normal 52-card decks? (5 points)

    2.  

     

     

  2. What is the probability the player will get two queen of hearts in his first two cards and then the dealer gets a blackjack in a 4-deck game? (5 points)

    3.  

     

     

  3. Consider a game of Pairplus in Three Card Poker with a modified 75-card deck of 15 ranks and 5 suits. (15 points total)

 

 

 

How many combinations are there for a straight (not including a straight flush)?___________________

 

 

 

 

How many combinations are there for a flush (not including a straight flush)?___________________

 

 

 

How many combinations are there for a pair?___________________

 

8. Consider the same modified deck as in problem 7. The casino uses 8 such decks in Casino War. What is the probability that a hand will result in a double tie (the first two cards tie and then the second two cards tie)? (5 points)