GAM470 Name__________________

March 8, 2005 Homework

For problems 1 to 8 consider a side bet on a single-deck blackjack game.

1. How many combinations are there for a suited ace/jack blackjack?
2.

3. How many combinations are there for a non-suited ace/jack blackjack?
4.

5. How many combinations are there for any other suited blackjack?
6.

7. How many combinations are there for all other blackjacks (non-suited and non-ace/jack)?

5. How many combinations are there for non-blackjacks?

1. How many combinations are there of any two cards in a single deck?
2.

3. Based on the answers to 1-5 determine the total return for the game for all combinations.
4.  Hand Combinations Pays Return Suited ace/jack BJ . 50 . Other ace/jack BJ . 25 . Other suited BJ . 25 . Any other BJ . 10 . Non-BJ . -1 . Total
5. Divide the total return by the total combinations to get the expected value of this side bet.
6.

7. You have a drawer with drawer with 10 white socks and 6 black socks. You reach in and draw 5 at random without replacement. What is the probability you draw a full house (three of one color and two of the other)?
8.

9. A keno game has 50 numbers. The casino will draw 10 of them. You pick 5 numbers. What is the probability you catch exactly 2 of them?
10.

Problems 11-16: Consider a side bet called "Fantastic Fives." The game uses five decks of 52-cards each. The player is paid according to his own initial two cards and the dealer’s up card.

11. How many combinations are there for three suited fives?
12.

13. How many combinations are there for three non-suited fives?
14.

15. How many combinations are there for two fives, which are suited?
16.

17. How many combinations are there for two fives, which are not suited?
18.

19. How many combinations are there for one five?

Fill in the following table to find the expected value of the game, which is the total return divided by the total combinations.

 Hand Combinations Pays Return Three sutied fives . 2000 . Three fives . 200 . Two suited fives . 50 . Two unsuited fives . 20 . One five . 1 . No fives . -1 . Total . . .

16. What is the expected value?