Triple 7's in Craps

We can ignore any roll other than a 6,7 or 8 for now.

There are 6 ways to throw a 7
5 ways each for the 6&8
7 before a 6 or 8 = 6/16 = .375
3 times in a row
=.375^3 (.375*.375*.375) = 0.052734375
or 1 in 18.96 trials

But each trial is not 1 roll long (of 6,7 and 8s only)

That is the sum of a geometric series
1+(6/16)+(6/16)^2 = 1.515625 = length of each trial

Multiply the two together
18.96 * 1.515625 = 28.74074074 the average number of rolls of 6,7,8s

For the average number of total rolls (your total wait time)
28.74074074 * (36/16) = 64.667 rolls on average


For 4 in a row just extend the math
(6/16)^4 = 0.019775391 or 1 in 50.56790123 (1/0.019775391)
The length of each trial
1+(6/16)+(6/16)^2+(6/16)^3 = 1.568359375

product = 79.30864198 (50.56790123*1.568359375)
This is just the average number of 6,7 and 8s

now Times 2.25
(2.25 is the average number of rolls to see either a 6,7 or 8)
178.44 = average number of total dice rolls

A quick look at the Zumma Craps Tester Book (35097 actual dice roll file) shows
at least 3 in a row 7s before a 6 or 8 happened 536 times, avg=65.48
at least 4 in a row 7s before a 6 or 8 happened 196 times, avg=179.07