When rolling two six sided dice, the possible outcomes
(each with probability 1/36) are :

 rolls                                          total    odds
 ---------------------------------------------------------------
 (1,1)                                           2       1/36
 (1,2), (2,1)                                    3       2/36
 (1,3), (2,2), (3,1)                             4       3/36
 (1,4), (2,3), (3,2), (4,1)                      5       4/36
 (1,5), (2,4), (3,3), (4,2), (5,1)               6       5/36
 (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)        7       6/36
 (2,6), (3,5), (4,4), (5,3), (6,2)               8       5/36
 (3,6), (4,5), (5,4), (6,3)                      9       4/36
 (4,6), (5,4), (6,4)                            10       3/36
 (5,6), (6,5)                                   11       2/36
 (6,6)                                          12       1/36

Craps rules:
 1st roll: 
   7, 11 wins
   2, 3, 12 loses
   4, 5,6, 8, 9, 10 sets "point"
 following rolls:
   point wins
   7 loses
   anything else continues

So the ways to win with their probabilities are :

  
--- way to win -------------- odds --------------------

   7 on roll 1 :              6/36
  11 on roll 1 :              2/36
  
  4 on roll 1 & 
  (not 4, not 7) for n rolls &
  4 on roll n+2               3/36 * (27/36)**n * 3/36

  5 on roll 1 & 
  (not 5, not 7) for n rolls &
  5 on roll n+2               4/36 * (26/36)**n * 4/36

  6 on roll 1 & 
  (not 6, not 7) for n rolls &
  6 on roll n+2               5/36 * (25/36)**n * 5/36

  8 on roll 1 & 
  (not 8, not 7) for n rolls &
  8 on roll n+2               5/36 * (25/36)**n * 5/36

  9 on roll 1 & 
  (not 5, not 7) for n rolls &
  9 on roll n+2               4/36 * (26/36)**n * 4/36

  10 on roll 1 & 
  (not 10, not 7) for n rolls &
  10 on roll n+2              3/36 * (27/36)**n * 3/36

For all the continued rolls, for the total probability
we need to sum a series like (1 + x + x**2 + x**3 + ...)
which we can derive from the following trick:

  S       = 1 + x + x**2 + x**3 + ... + x**N
  x*S     =     x + x**2 + x**3 + ... + x**N + x**(N+1)
  ----------------------------------
  S*(1-x) = (1 - x**(N+1))

so 

 S = (1 - x**(N+1)) / (1 - x)

For an infinte sum, this becomes just S = 1/(1-x).

So the total probability of winning is

 6/36 + 2/36 + 
 (3/36)**2 * 1/(1 - 27/36) +
 (4/36)**2 * 1/(1 - 26/36) +
 (5/36)**2 * 1/(1 - 25/36) +
 (5/36)**2 * 1/(1 - 25/36) +
 (4/36)**2 * 1/(1 - 26/36) +
 (3/36)**2 * 1/(1 - 27/36)


The complicated terms all simplify nicely, like this:

   4/36 * 4/36 * 1/( 36/36 - 26/36) 
 = 4/36 * 4/36 * 1/(10/36)
 = 4/36 * 4/36 * 36/10
 = 4/36 * 4/10

Simplying the last six terms and grouping them gives

 = 8/36 + 2 * (3/36 * 3/9  +  4/36 * 4/10  +  5/36 * 5/11)
 = 2 * (1/9 + (1/12 * 1/3) + (1/9 * 2/5) + (5/36 * 5/11))
 = 2 * (1/9 + 1/36 + 2/45 + 25/396) 
 = 244/495 
 = 0.49292929...