Any math wizards? I would like confirmation

[FreeRoulette]

Hey All,

I would like someone to confirm my results.

On a double zero wheel, spin until all numbers come up.
Count how many spins it takes until the next number comes up.

For example, If the following numbers came up
2
10
12
12
14

Four numbers came up, and 14 took 2 spins to appear after the 3rd number 12 came up.

The following is the average number of spins it takes for the next number to display using 10 million trials.

1) 1
2) 1.026848
3) 1.055713
4) 1.085443
5) 1.117322
6) 1.151022
7) 1.187317
1.226022
9) 1.267451
10) 1.310417
11) 1.357984
12) 1.40847
13) 1.461565
14) 1.520706
15) 1.58364
16) 1.650701
17) 1.727872
18) 1.8086
19) 1.897021
20) 2.00035
21) 2.10782
22) 2.238503
23) 2.378271
24) 2.531304
25) 2.713461
26) 2.922626
27) 3.166293
28) 3.454441
29) 3.803622
30) 4.216614
31) 4.750645
32) 5.439951
33) 6.342094
34) 7.62275
35) 9.486869
36) 12.676807
37) 18.986925
38) 38.014091

So if you wait and play the last 8 numbers, then on average it should win in 4.750645 spins?
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