Rolling to win!
Question
Suppose you are playing a game with a fair die (e.g. no bias for any one side), and your expected payout based on the # you roll is in the table below:
| Roll | Payout |
|---|---|
| 6 | $4 |
| 5 | $2 |
| 4 | $1 |
| 3 | $0 |
| 2 | $0 |
| 1 | $0 |
Given the above table, is it worth it to play this game?