[BruceZ]

[ QUOTE ]
Hey Jim , just to let you know , you are getting 5:1 against rolling a particular number from a die not 6:1 like you said .

The probability should be 1/6 that you roll a particular number which means odds against of (6-1):1.
I know it's been awhile since you've taken stats but these are some of the mistakes that people make .

[/ QUOTE ]

He's saying that he's getting PAID 6:1 when his number comes up, not that the odds against rolling his number are 6:1. The odds against rolling his number are 5:1, and that's why he has a positive EV. His EV equations show that he wins 6x when his number comes up, and this has probability 1/6 or odds of 5:1 against, and he loses x when it doesn't come up, and this has probability 5/6.