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# Average Rate of Reoccurrence Distribution

Topic closed. 7 replies. Last post 10 years ago by JADELottery.

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The Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
3680 Posts
Online
 Posted: November 7, 2006, 1:11 pm - IP Logged

Average Rate of Reoccurrence Distribution

Reference - Combinatorial Distribution

Average Rate of Reoccurrence Distribution - Ar(n,r,c,z) = C(n,r) / D(n,r,c,z)

The average rate of reoccurrence is the average number of draws or index counts between random selections of n items take r at a time. This is directly related to common terms of Skip, Hit. The average rate of reoccurrence will be used in another function to describe a generalized rate of reoccurrence for all items in a combinatorial random selection. Here's an example of 49 numbers taken 6 at a time, n = 49 and r = 6. Looking at item or number 5 in column 1, the number 5 will on average reoccur about once every 12.88 selections or draws in column 1.

 C Z 1 2 3 4 5 6 1 8.17 2 9.12 78.40 3 10.20 42.85 921.20 4 11.45 31.28 328.49 14125.07 5 12.88 25.75 175.98 3695.51 317814.00 6 14.53 22.66 113.31 1548.60 65041.00 13983816.00 7 16.44 20.82 81.21 812.07 22196.53 2330636.00 8 18.66 19.73 62.47 487.24 9744.82 665896.00 9 21.25 19.13 50.55 320.14 4994.22 249711.00 10 24.29 18.89 42.50 224.66 2845.71 110982.67 11 27.86 18.94 36.84 165.76 1752.36 55491.33 12 32.08 19.25 32.72 127.25 1145.28 30268.00 13 37.09 19.78 29.67 100.89 784.73 17656.33 14 43.08 20.54 27.39 82.18 558.79 10865.44 15 50.26 21.54 25.68 68.48 410.88 6984.92 16 58.92 22.78 24.41 58.21 310.44 4656.62 17 69.44 24.30 23.49 50.34 240.11 3201.42 18 82.30 26.14 22.87 44.22 189.53 2259.83 19 98.13 28.35 22.51 39.40 152.33 1632.10 20 117.75 30.99 22.38 35.54 124.41 1202.60 21 142.29 34.15 22.47 32.45 103.08 901.95 22 173.22 37.94 22.77 29.95 86.54 687.20 23 212.58 42.52 23.28 27.94 73.53 531.02 24 263.20 48.06 24.03 26.32 63.17 415.58 25 329.00 54.83 25.03 25.03 54.83 329.00 26 415.58 63.17 26.32 24.03 48.06 263.20 27 531.02 73.53 27.94 23.28 42.52 212.58 28 687.20 86.54 29.95 22.77 37.94 173.22 29 901.95 103.08 32.45 22.47 34.15 142.29 30 1202.60 124.41 35.54 22.38 30.99 117.75 31 1632.10 152.33 39.40 22.51 28.35 98.13 32 2259.83 189.53 44.22 22.87 26.14 82.30 33 3201.42 240.11 50.34 23.49 24.30 69.44 34 4656.62 310.44 58.21 24.41 22.78 58.92 35 6984.92 410.88 68.48 25.68 21.54 50.26 36 10865.44 558.79 82.18 27.39 20.54 43.08 37 17656.33 784.73 100.89 29.67 19.78 37.09 38 30268.00 1145.28 127.25 32.72 19.25 32.08 39 55491.33 1752.36 165.76 36.84 18.94 27.86 40 110982.67 2845.71 224.66 42.50 18.89 24.29 41 249711.00 4994.22 320.14 50.55 19.13 21.25 42 665896.00 9744.82 487.24 62.47 19.73 18.66 43 2330636.00 22196.53 812.07 81.21 20.82 16.44 44 13983816.00 65041.00 1548.60 113.31 22.66 14.53 45 317814.00 3695.51 175.98 25.75 12.88 46 14125.07 328.49 31.28 11.45 47 921.20 42.85 10.20 48 78.40 9.12 49 8.17

Presented 'AS IS' and for Entertainment Purposes Only.
Any gain or loss is your responsibility.

Order is a Subset of Chaos
Knowledge is Beyond Belief
Wisdom is Not Censored
Douglas Paul Smallish
Jehocifer

United States
Member #32007
February 6, 2006
57 Posts
Offline
 Posted: November 7, 2006, 2:01 pm - IP Logged

I love the list. Is it good for every state? Would make for a great referance tool.

Good job.

Dragon Dreamer

United States
Member #32007
February 6, 2006
57 Posts
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 Posted: November 7, 2006, 2:06 pm - IP Logged

Need one for 39 numbers.

I am not that great in math to figure it out my-self.

Dragon Dreamer

The Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
3680 Posts
Online
 Posted: November 7, 2006, 2:25 pm - IP Logged

Need one for 39 numbers.

I am not that great in math to figure it out my-self.

Dragon Dreamer

 C Z 1 2 3 4 5 6 1 6.50 2 7.48 49.40 3 8.65 27.69 456.95 4 10.05 20.77 166.16 5483.40 5 11.73 17.59 90.87 1453.93 95959.50 6 13.75 15.95 59.80 617.92 19773.47 3262623.00 7 16.20 15.12 43.85 328.89 6797.13 543770.50 8 19.20 14.81 34.56 200.47 3007.03 155363.00 9 22.89 14.88 28.70 133.93 1553.63 58261.13 10 27.47 15.26 24.80 95.67 892.89 25893.83 11 33.20 15.93 22.13 71.93 554.87 12946.92 12 40.41 16.90 20.28 56.33 366.18 7061.95 13 49.60 18.19 19.01 45.63 253.51 4119.47 14 61.41 19.84 18.19 38.03 182.52 2535.06 15 76.76 21.93 17.71 32.48 135.81 1629.68 16 96.96 24.56 17.55 28.34 103.92 1086.45 17 123.89 27.88 17.65 25.22 81.48 746.94 18 160.33 32.07 18.04 22.85 65.28 527.25 19 210.44 37.41 18.71 21.04 53.31 380.79 20 280.58 44.30 19.69 19.69 44.30 280.58 21 380.79 53.31 21.04 18.71 37.41 210.44 22 527.25 65.28 22.85 18.04 32.07 160.33 23 746.94 81.48 25.22 17.65 27.88 123.89 24 1086.45 103.92 28.34 17.55 24.56 96.96 25 1629.68 135.81 32.48 17.71 21.93 76.76 26 2535.06 182.52 38.03 18.19 19.84 61.41 27 4119.47 253.51 45.63 19.01 18.19 49.60 28 7061.95 366.18 56.33 20.28 16.90 40.41 29 12946.92 554.87 71.93 22.13 15.93 33.20 30 25893.83 892.89 95.67 24.80 15.26 27.47 31 58261.13 1553.63 133.93 28.70 14.88 22.89 32 155363.00 3007.03 200.47 34.56 14.81 19.20 33 543770.50 6797.13 328.89 43.85 15.12 16.20 34 3262623.00 19773.47 617.92 59.80 15.95 13.75 35 95959.50 1453.93 90.87 17.59 11.73 36 5483.40 166.16 20.77 10.05 37 456.95 27.69 8.65 38 49.40 7.48 39 6.50

Presented 'AS IS' and for Entertainment Purposes Only.
Any gain or loss is your responsibility.

Order is a Subset of Chaos
Knowledge is Beyond Belief
Wisdom is Not Censored
Douglas Paul Smallish
Jehocifer

United States
Member #32007
February 6, 2006
57 Posts
Offline
 Posted: November 7, 2006, 2:56 pm - IP Logged

Thanks Doug.

That was quick.

Dragon Dreamer

Mid-Missouri
United States
Member #644
August 31, 2002
4271 Posts
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 Posted: November 7, 2006, 3:07 pm - IP Logged

Doug,

If you have time could you do one for 44 numbers?

TIA,

Bryan  :)

The Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
3680 Posts
Online
 Posted: November 7, 2006, 4:02 pm - IP Logged

Doug,

If you have time could you do one for 44 numbers?

TIA,

Bryan  :)

 1 2 3 4 5 6 1 7.33 2 8.30 63.07 3 9.42 34.85 662.20 4 10.73 25.75 238.16 9050.07 5 12.26 21.46 128.73 2381.60 181001.33 6 14.06 19.13 83.68 1004.13 37152.91 7059052.00 7 16.19 17.81 60.57 529.96 12719.01 1176508.67 8 18.72 17.12 47.08 320.14 5602.42 336145.33 9 21.74 16.85 38.52 211.86 2881.25 126054.50 10 25.37 16.91 32.77 149.80 1647.77 56024.22 11 29.74 17.25 28.75 111.41 1018.62 28012.11 12 35.05 17.85 25.88 86.25 668.47 15279.33 13 41.55 18.70 23.79 69.00 460.02 8912.94 14 49.54 19.81 22.29 56.74 329.09 5484.89 15 59.44 21.23 21.23 47.77 243.17 3526.00 16 71.83 22.98 20.52 41.04 184.70 2350.67 17 87.44 25.14 20.11 35.91 143.65 1616.08 18 107.31 27.78 19.96 31.94 114.08 1140.76 19 132.86 31.00 20.06 28.84 92.28 823.89 20 166.08 34.96 20.40 26.39 75.88 607.07 21 209.78 39.86 20.98 24.47 63.35 455.31 22 268.06 45.95 21.83 22.98 53.61 346.90 23 346.90 53.61 22.98 21.83 45.95 268.06 24 455.31 63.35 24.47 20.98 39.86 209.78 25 607.07 75.88 26.39 20.40 34.96 166.08 26 823.89 92.28 28.84 20.06 31.00 132.86 27 1140.76 114.08 31.94 19.96 27.78 107.31 28 1616.08 143.65 35.91 20.11 25.14 87.44 29 2350.67 184.70 41.04 20.52 22.98 71.83 30 3526.00 243.17 47.77 21.23 21.23 59.44 31 5484.89 329.09 56.74 22.29 19.81 49.54 32 8912.94 460.02 69.00 23.79 18.70 41.55 33 15279.33 668.47 86.25 25.88 17.85 35.05 34 28012.11 1018.62 111.41 28.75 17.25 29.74 35 56024.22 1647.77 149.80 32.77 16.91 25.37 36 126054.50 2881.25 211.86 38.52 16.85 21.74 37 336145.33 5602.42 320.14 47.08 17.12 18.72 38 1176508.67 12719.01 529.96 60.57 17.81 16.19 39 7059052.00 37152.91 1004.13 83.68 19.13 14.06 40 181001.33 2381.60 128.73 21.46 12.26 41 9050.07 238.16 25.75 10.73 42 662.20 34.85 9.42 43 63.07 8.30 44 7.33

Presented 'AS IS' and for Entertainment Purposes Only.
Any gain or loss is your responsibility.

Order is a Subset of Chaos
Knowledge is Beyond Belief
Wisdom is Not Censored
Douglas Paul Smallish
Jehocifer

The Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
3680 Posts
Online
 Posted: December 2, 2006, 5:30 am - IP Logged

The average rate of reoccurrence shows why it's not a wise choice to bet on the combination {01, 02, 03, 04, 05, 06}. Yes, I'm fully aware the every combination has an equal probability of being drawn as a whole. However, there are sub numbers, combinations, and probabilities within the whole combination that determine the outcome of a combination. Looking at the number 6 and referring to the above table for a 6/49 lottery, the number 6 can occur in any of the 6 columns. Each column has a different rate of reoccurrence, shown below, Table 1.

Table 1

 Z 1 2 3 4 5 6 6 14.53 22.66 113.31 1548.6 65041 1.39838e+07

The 1st column has an average rate of reoccurrence of 14.53 and the 6th column has an average rate of reoccurrence of 13983816.00. It shows the number 6 is more likely to reoccur in the 1st column than in the 6th column. The same is true for the other columns 2 through 5; with column 2 having a better reoccurrence and decreasing reoccurrence to the 5th column. The higher the number, the less likely it will reoccur in that column.

There is also competition of reoccurrence between numbers in the 6th column. Shown below, Table 2, is the 6th column for the average rate of reoccurrence and the corresponding numbers. As the the number (Z) increases, the average rate of reoccurrence decreases in column 6. The number 49 has an average rate of reoccurrence in the 6th column of 8.17. This means the number 49 reoccurs on average about once every 8.17 draws. The number 6 in the 6th column reoccurs on average about once every 13983816.00 draws. Also, there are many other numbers with lesser rates, meaning they reoccur more often than the number 6 in the 6th column.

Table 2

 Z 6 6 1.39838e+07 7 2.33064e+06 8 665896 9 249711 10 110983 11 55491.3 12 30268 13 17656.3 14 10865.4 15 6984.92 16 4656.62 17 3201.42 18 2259.83 19 1632.1 20 1202.6 21 901.95 22 687.2 23 531.02 24 415.58 25 329 26 263.2 27 212.58 28 173.22 29 142.29 30 117.75 31 98.13 32 82.3 33 69.44 34 58.92 35 50.26 36 43.08 37 37.09 38 32.08 39 27.86 40 24.29 41 21.25 42 18.66 43 16.44 44 14.53 45 12.88 46 11.45 47 10.2 48 9.12 49 8.17

Symmetry also shows there is an equally valid combination of {44, 45, 46, 47, 48, 49}. Yet, you don't hear many people boasting about how their going to play that combination; even though that combination has the same symmetric properties as the {01, 02, 03, 04, 05, 06} combination.

Presented 'AS IS' and for Entertainment Purposes Only.
Any gain or loss is your responsibility.