Roll'Em

For a game of Roll'Em, the player rolls four 6-sided dice. If the same number shows up on all four dice (a

four-of-a-kind) the player wins $200; if only three of the dice have the same number (a three-of-a-kind)

the player wins $15; and if four numbers in a row are rolled (a straight), the player wins $30; otherwise

the player loses $6 (the cost to play).

No one has bothered to calculate the theoretical probabilities of each event, but Melvin has kept track

of all the rolls from the previous years and found that out of 600 rolls, a four-of-a-kind has shown up

three time, a three-of-a-kind has shown up 56 times, and a straight has shown up 30 times.

*Use empirical data for all parts of Roll'Em; do NOT use theoretical probabilities.

• Find the odds against a four-of-a-kind.

• Find the odds against a three-of-a-kind.

Find the odds against a straight.

• Using the data given, what is the expected value of Roll'Em?