The Big Six
In the Big Six game, you can place a 1-dollar bet to toss 2 fair six-faced dice for a chance to increase it by the multiple of 6. The amounts of gain or loss depend on the pips as followed:
- 2-6 pips: -12 $
- 7-9 pips: +6 $
- 10-12 pips: +12 $
Moreover, if both dice show up the same number, the amount of money earned or lost will be doubled. For example, if both dice have 6 on their faces, you can win the maximum jackpot of 24 dollars!
What is the expected value of this 1-dollar bet? Submit your answer in the nearest 3 decimal places.
Bonus: Is this game worth a gamble?