Best to look at this is terms a cycle. A cycle is how long it takes on average to hit a specific hand. A royal cycle for JOB is about 40,000 hands. A four deuce cycle is about 4900 hands in deuces wild.
Now we can ask "What are the chances of going 0 for 1 or 0 for 2 cylces" the odds will be the same for any type of hand.
For example if the odds of going 0 for 3 cycles is 1 in 20, that would correspond to 3x40,000 = 120,000 hands for a royal, and 3x4900=14,700 hands for hitting four deuces.
Chances of hitting zero hits for
1 cycle : 1 in 2.7
2 cycles : 1 in 7.4
3 cycles : 1 in 20
4 cycles : 1 in 55
5 cycles : 1 in 148 (this would be 200,000 hands for a royal or 24,500 hands for four deuces)
6 cycles : 1 in 403
7 cycles : 1 in 1096
8 cycles : 1 in 2981
9 cycles : 1 in 8103
10 cycles : 1 in 22026
11 cycles : 1 in 59874
12 cycles : 1 in 162755
13 cycles : 1 in 442413
14 cycles : 1 in 1202604
15 cycles : 1 in 3269017
I once went 0-9 cycles trying to hit a four of a kind. A 1 in 8103 shot.
One million hands is 25 royal cycles. Chances of going this many hands with no royal are 1 in 72 billion. If you played 700 hands an hour, 24 hours a day, it would take 11,741 years just to play 72 billion hands.
TomSki