I'm sure you're right when you say the house has a 1.41% advantage on a line bet. I, however, calulated the advantage to be 2.25%. Here is my reasoning.
A line bet can be won or lost either on the opening roll or once a point has been estalished. There is a 33.3% chance that the opening roll will produce a win or loss (2,3,7,11,or 12 i.e. 12 ways out of 36 possible ways). The expected return on a $1 bet if there is a win or loss on the opening roll is $0.33. (8 ways to win and 4 ways to lose nets a +4/12 or .33). There is a 66.7% chance that a point will be established. The expected return if this event occurs is -$0.20. (6 ways to lose and 4 ways to win nets -2/10 or -.20. 4 ways to win is the average winning ways of 4,5,6,8,9,10).
Therefore: 33.3% X (expected return if opening roll produces a win or loss) + 66.7% X (expected return if a point is established) =.333(.33)+.667(-.20)= -.0225 or -2.25%.
I assume I made an error somewhere. It seems reasonable what I did.
|