What would the payoff odds have to be for a pass line bet
in order for the bet to be totally fair with no house edge ?
A fair game is one where every player's expectation is zero.
Let p = probability to win = 244 / 495 [ shown previously ]
Then E = ( kB ) * p + ( -B ) * ( 1 - p ) = kBp - B + Bp
E = 0 → kBp = B - Bp = B * ( 1 - p ) → k = ( 1 - p ) / p = ( 1 / p ) - 1
We need k = 251 / 244 = 1.02868852....
The payoff odds would have to be about 1.03 to 1.