Craps and the Pass Line: Two Dice, One Point and a House Edge of 1.41 %

36 ways two dice can fall

wins on the come-out craps sets a point

Ways to make each sum

Numbers on the right: ways out of 36, and how often the sum came up in your rolls.

The chance to win the pass line, branch by branch

Branch	Gets there	Then wins	Together

"Then wins" for a point p: only rolls of p or 7 decide, so the chance is ways(p) ÷ (ways(p) + 6). The house edge for an even-money bet is the chance to lose minus the chance to win: 251/495 − 244/495 = 7/495 = 1.41 %.

	Simulated	Exact