The reason that some numbers come up more frequently is that it is extremely unlikely that each will come up the same number of times. If there are 50 different lotto numbers and 5 are picked per drawing for infinite time, the probability of ever having each number appear with exactly the same frequency (not counting at the beginning when each has appeared zero times) is less than 2.7e-20.
To get the same number of each, you need a multiple of 50 draws. If you don’t have 1 of each after 50 draws, the chances of ever equalizing everthing gets progressively worse with time.
The fraction of the the time that each number appears will gradually approach similar values, but even that would take many drawings for the relative frequency of each number to be very close. The standard deviation in the relative frequency of each number is approximately sqrt(M/N) where M is the number of different balls in the lotto game, and N is number of times a ball was randomly selected.
If M=50 different numbers, and data was selected for 20000 drawings (that’s over 50 years of one drawing per day) of 5 numbers each, N=5*20000=100000. The standard deviation of relative frequency is around sqrt(50/100000)=0.022 or 2.2 percent. So each ball would have been picked an average of 2000 (100000/50) times with a standard deviation of 44 (2.2 percent of 2000).
