clacam
clacam
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Joined: Sep 30, 2012
September 30th, 2012 at 9:57:39 AM permalink
Hi everyone, I am a new member and I have a probobilities question.
Can anyone help me to write the formula to calculate on a 37 numbers roulette wheel
the correct odds of the expected repetitions of numbers at any time between spins 10 and 37.

ie: at spin 17 there should be 4.22 repetitions.
I consider a second repetition a number that has come up three times.

I thank you for your help.
clacam
clacam
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Joined: Sep 30, 2012
October 1st, 2012 at 1:43:24 PM permalink
No help?
Ibeatyouraces
Ibeatyouraces
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Joined: Jan 12, 2010
October 1st, 2012 at 2:11:23 PM permalink
deleted
DUHHIIIIIIIII HEARD THAT!
7craps
7craps
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Joined: Jan 23, 2010
October 1st, 2012 at 2:19:03 PM permalink
"Can anyone help me to write the formula to calculate on a 37 numbers roulette wheel
the correct odds of the expected repetitions of numbers at any time between spins 10 and 37."


Guido111 has a post about this. I can not find a link to it, maybe you can.

Here is a link to his Excel workbook for 37 and 38 wheels.
http://www.pulcinientertainment.com/info/37euro-roulette.xls
It uses the BINOMDIST() function in Excel
Very easy to see how it is done.


It shows
spins  no hit   unique#  repeats
17 23.22 13.78 3.22

Here is more of it, no math sorry
Spins	not	unique	repeat
hit numbers
1 36.00 1.00 0.00
2 35.03 1.97 0.03
3 34.08 2.92 0.08
4 33.16 3.84 0.16
5 32.26 4.74 0.26
6 31.39 5.61 0.39
7 30.54 6.46 0.54
8 29.72 7.28 0.72
9 28.91 8.09 0.91
10 28.13 8.87 1.13
11 27.37 9.63 1.37
12 26.63 10.37 1.63
13 25.91 11.09 1.91
14 25.21 11.79 2.21
15 24.53 12.47 2.53
16 23.87 13.13 2.87
17 23.22 13.78 3.22
18 22.60 14.40 3.60
19 21.98 15.02 3.98
20 21.39 15.61 4.39
21 20.81 16.19 4.81
22 20.25 16.75 5.25
23 19.70 17.30 5.70
24 19.17 17.83 6.17
25 18.65 18.35 6.65
26 18.15 18.85 7.15
27 17.66 19.34 7.66
28 17.18 19.82 8.18
29 16.72 20.28 8.72
30 16.26 20.74 9.26
31 15.82 21.18 9.82
32 15.40 21.60 10.40
33 14.98 22.02 10.98
34 14.58 22.42 11.58
35 14.18 22.82 12.18
36 13.80 23.20 12.80
37 13.43 23.57 13.43


A quick computer simulation
I show 13.78 unique numbers in 17 spins
That sure looks to be 3.22 repeats on average.
My sim data below.
It is for unique numbers for 17 spins
subtract that from 17 for the repeats
       group         middle     freq  freq/100
----------------------------------------------
6.50 <= x < 7.50 7.00 3 0.00%
7.50 <= x < 8.50 8.00 64 0.01%
8.50 <= x < 9.50 9.00 972 0.10%
9.50 <= x < 10.50 10.00 7678 0.77%
10.50 <= x < 11.50 11.00 38119 3.81%
11.50 <= x < 12.50 12.00 120823 12.08%
12.50 <= x < 13.50 13.00 238388 23.84%
13.50 <= x < 14.50 14.00 291452 29.15%
14.50 <= x < 15.50 15.00 209963 21.00%
15.50 <= x < 16.50 16.00 80096 8.01%
16.50 <= x < 17.50 17.00 12442 1.24%

----------------------------------------------
grouped data
items: 1000000

minimum value: 7.00
first quartile: 13.00
median: 14.00
third quartile: 15.00
maximum value: 17.00

mean value: 13.78
midrange: 12.00

range: 10.00
interquartile range: 2.00
mean abs deviation: 1.08

sample variance (n): 1.81
sample variance (n-1): 1.81
sample std dev (n): 1.34
sample std dev (n-1): 1.34

----------------------------------------------
cumulative
----------------------------------------------
6.50 <= x < 7.50 7.00 3 0.00%
7.50 <= x < 8.50 8.00 67 0.01%
8.50 <= x < 9.50 9.00 1039 0.10%
9.50 <= x < 10.50 10.00 8717 0.87%
10.50 <= x < 11.50 11.00 46836 4.68%
11.50 <= x < 12.50 12.00 167659 16.77%
12.50 <= x < 13.50 13.00 406047 40.60%
13.50 <= x < 14.50 14.00 697499 69.75%
14.50 <= x < 15.50 15.00 907462 90.75%
15.50 <= x < 16.50 16.00 987558 98.76%
16.50 <= x < 17.50 17.00 1000000 100.00%

----------------------------------------------

winsome johnny (not Win some johnny)
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