The "law of thirds" says that if you spin a roulette wheel once for every number on the wheel, about 1/3 of the numbers will never occur.
1/3 is really a pretty poor estimate. A much better one would be 1/e =~ 36.79%. The true percentage, in double-zero roulette, is 36.30%.
The following table shows the probability of 1 to 38 distinct numbers being observed in 38 spins of double-zero roulette.
Law of Thirds -- Double-Zero Roulette
Distinct
Numbers Probability 10.000000000 20.000000000 30.000000000 40.000000000 50.000000000 60.000000000 70.000000000 80.000000000 90.000000000 100.000000000 110.000000000 120.000000000 130.000000005 140.000000124 150.000001991 160.000022848 170.000191281 180.001186530 190.005519547 200.019434593 210.052152293 220.107159339 230.169042497 240.204864337 250.190490321 260.135436876 270.073211471 280.029838199 290.009063960 300.002020713 310.000323888 320.000036309 330.000002742 340.000000132 350.000000004 360.000000000 370.000000000 380.000000000 Total1.000000000
The table shows the most likely outcome is 24 distinct numbers at 20.49%. The average is 24.20656478.
Some quacks make the argument that the player should observe the first nine distinct outcomes and then bet on them, under the incorrect belief that they are more likely to occur than other numbers. This is strictly not true! The wheel and ball do not have a memory. On a fair wheel, every number is equally likely and the past does not matter.