Thread Rating:

Right.

There are folks who claim they can "read" random numbers like a fortune teller "reads" your hand. Sadly I can't do either.

I don't know of a single case of clairvoyance that is documented - in ANYTHING that has a random probability of happening. This applies to gambling and investing. But maybe there is a case documented? If so I'd love to get a link. (Stocks go up because there is inflation in an economy and some companies do a good job, but no super secret technical indicator that exists. A monkey throwing darts at the WSJ will out perform 80% of the Wizards of Wall street; I remember reading actual studies of monkeys doing just that)

That leaves AP. This seems to be the last bastion for folks to brag they can "beat Roulette" and never have to prove it. How would they prove it since the wheel at a particular Roulette table may have been swapped out for maintenance, like a diamond mark wearing down or chipping off.

Certainly AP doesn't work in online Roulette since there is no wear or tear on the circuit board.

So I ask if anyone has a documented case of anyone being able to demonstrate AP for Roulette in an open casino? I mean where someone demonstrated this ability over and over again to witnesses and the witnesses filed sworn affidavits with a penalty of perjury that could be used in a court of law as evidence of this ability)

Thanks for any input........

That is because such stories get good media play but when the dart-throwing monkeys do poorly, its not quite such a newsworthy item.Quote:MauiSunsetA monkey throwing darts at the WSJ will out perform 80% of the Wizards of Wall street; I remember reading actual studies of monkeys doing just that)

>So I ask if anyone has a documented case of anyone being able to demonstrate AP for Roulette in an open casino?

Of course not. Wheels used to be less finely manufactured and wheels used to be less strictly monitored. Also maintenance personnel were allowed to move a table for vacuuming purposes from time to time with no leveling or testing being conducted. Those days are long past!

The "annunciator" or "marquee" or "history display" shows the latest "x" spins but that information is not discarded. Its part of the monitoring situation.

Do people win on weird premonitions sometimes? Sure. Do you have repeats and missing numbers? Of course but often its in the mind of the observer more than anything else. Can you bet on "repeats" Sure? You might even win. Of course you can also bet on a "missing number" being "due" and win on that from time to time.

Random? I don't know if its a random wheel or not, but usually its random enough! Random enough for the casino that can hire all those statisticians and all those computer experts, but apparently its never random enough for someone who wants to sell you his secret super-duper technique for detecting wheel bias.

Quote:FleaStiff

...

>So I ask if anyone has a documented case of anyone being able to demonstrate AP for Roulette in an open casino?

Of course not. Wheels used to be less finely manufactured and wheels used to be less strictly monitored. Also maintenance personnel were allowed to move a table for vacuuming purposes from time to time with no leveling or testing being conducted. Those days are long past!

...

OK, the maintenance folks move a Roulette table for a poker tournament and place it somewhere else. There is a "bubble level" on all regulated Roulette tables, required by the local gaming commission, that I play at and it's part of the compass which is used to detect Roulette balls with a magnetic core. Every time I check that bubble, which is part of my ritual before sitting down at a new table, that bubble is dead center. I ask the dealer where that leveling bubble is and they show me - I have every right to see it; it's no big deal.

I guess the Roulette wheel could have been damaged in transit but every time I see a Roulette table moved the Roulette wheel is removed so that $3,000 wheel isn't hurt.

Maybe at cheap casinos they move the Roulette wheels around and none of the players care if they feel like the table is doing a Titanic but not the places I gamble at....

do a search and you will find the last flame war on this subject.

mrjjj is the resident expert on AP roulette, perhaps you should speak with him.

Quote:WongBooh dear god, not another AP roulette thread....

do a search and you will find the last flame war on this subject.

mrjjj is the resident expert on AP roulette, perhaps you should speak with him.

Mr J has deleted and modified many of my posts on other websites over this topic; so there is no need to debate this with him.

I'm simply asking for any verifiable cases of folks using AP or Reading Random Numbers "beating Roulette". If this could be done then there should be sworn affidavits backing up the claims.

I know there are many scams out there over these topics but I can't find a single case that is documented to be true; just scam after scam.

That's all I'm asking for........

Quote:Gabes22If the numbers are truly random then there is no way to predermine their outcome. Now, there are cases of people finding biases in certain wheels finding that specific numbers come up with enough frequency to overcome the house edge on that particular number or set of numbers, however this takes hours and hours of studying the specific wheels and IMO might raise some suspicion in a casino.

Has any AP player ever demonstrated that wheels are so lopsided that observing 38 spins (American wheel) would give them some kind of edge?

If it takes 1 minute per spin, in Vegas this can be done because of automated chip sorting machines, then that would be just 38 minutes of standing around a table and writing down spins. The pit boss is going to have a chat with you.

Every Roulette player knows that what the Marquee shows is totally inaccurate - spins are posted wrong all the time so actual spins would have to be recorded.

Since there are 38 slots on the wheel and the "Roulette Law of Thirds" points out that 1/3 of those 38 spins won't even show up and 1/3 will be duplicates, triplicates, and quadrupedal occurrences that means another 12 or so spins or 50 spins - about 1 hours worth of Roulette spins.

AP players brag about winning at Roulette but their antics around a Roulette table would result in their removal from the casino.

So has any person or group bought a wheel and table, from the same sources as casinos do, and demonstrated this ability? I sure haven't ever seen this but maybe there is a case of this happening....

Quote:MauiSunsetWhen a Roulette player finally realizes that the Odds Table and the Payout Table can't be changed then the only way to "win" at Roulette is to "Understand Random Numbers", and/or to Play with an Advantage, "Advantage Play (AP)", by finding numbers that spin out too frequently and thus should be bet on.

Right.

There are folks who claim they can "read" random numbers like a fortune teller "reads" your hand. Sadly I can't do either.

I don't know of a single case of clairvoyance that is documented - in ANYTHING that has a random probability of happening. This applies to gambling and investing. But maybe there is a case documented? If so I'd love to get a link. (Stocks go up because there is inflation in an economy and some companies do a good job, but no super secret technical indicator that exists. A monkey throwing darts at the WSJ will out perform 80% of the Wizards of Wall street; I remember reading actual studies of monkeys doing just that)

That leaves AP. This seems to be the last bastion for folks to brag they can "beat Roulette" and never have to prove it. How would they prove it since the wheel at a particular Roulette table may have been swapped out for maintenance, like a diamond mark wearing down or chipping off.

Certainly AP doesn't work in online Roulette since there is no wear or tear on the circuit board.

So I ask if anyone has a documented case of anyone being able to demonstrate AP for Roulette in an open casino? I mean where someone demonstrated this ability over and over again to witnesses and the witnesses filed sworn affidavits with a penalty of perjury that could be used in a court of law as evidence of this ability)

Thanks for any input........

I brought this subject up before. A couple of my methods rely on playing repeaters and/or numbers that are hitting alot, call it whatever you wish.

Lets PRETEND (a real longshot) that the wheel is a bit bias and out of coincidence, I am betting on a few of those bias numbers. So what?

Why does my PLAN need a TITLE as to WHY I am betting on those numbers? My goal is to leave the casino with a profit REGARDLESS of why/how.

Ken

Quote:mrjjjI brought this subject up before. A couple of my methods rely on playing repeaters and/or numbers that are hitting alot, call it whatever you wish.

Lets PRETEND (a real longshot) that the wheel is a bit bias and out of coincidence, I am betting on a few of those bias numbers. So what?

Why does my PLAN need a TITLE as to WHY I am betting on those numbers? My goal is to leave the casino with a profit REGARDLESS of why/how.

Ken

My goal is to win the Powerball lottery by any means too.

Big deal......

Regarding the law of the third.

1. It's nonsense.

2. There is no such law.

3. I believe that nobody would ever mistake Mr. Jjj. for an AP player.

Quote:KeyserI have two wheels.

Regarding the law of the third.

1. It's nonsense.

2. There is no such law.

3. I believe that nobody would ever mistake Mr. Jjj. for an AP player.

Well, the law is for real - there is much statistics to prove it. Spin a wheel 38 times and 1/3, or about a dozen numbers will not show up and 1/3 will be duplicates, triplicates, and quadruplicates. But so what?

However, there is nothing you can do with it - it won't help at all in predicting the next number spun.

So if you want to see all 38 numbers appear, the Law of the Third of Random Numbers says you will have to spin more than 38 times, at least 1/3 more.

That's all it says.....

Quote:KeyserIn short, the law of the third is just another fools folly.

Of course.....

It may be a layman's law, but not a law my any known mathematician.Quote:MauiSunsetWell, the law is for real - there is much statistics to prove it. Spin a wheel 38 times and 1/3, or about a dozen numbers will not show up and 1/3 will be duplicates, triplicates, and quadruplicates. But so what?

In 38 spins, the average number of unique numbers hit is about 24.2 (24 or 25)

That means between 13 and 14 that have not hit in 38 spins

(12.67 would be 1/3)

The probability of that is just about 40%.

You can play with the distribution if you like

simulation results

`Unique numbers 38 spins 00 wheel`

group middle freq freq/100

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

14.50 <= x < 15.50 15.00 22 0.00%

15.50 <= x < 16.50 16.00 231 0.00%

16.50 <= x < 17.50 17.00 1815 0.02%

17.50 <= x < 18.50 18.00 11875 0.12%

18.50 <= x < 19.50 19.00 54722 0.55%

19.50 <= x < 20.50 20.00 194436 1.94%

20.50 <= x < 21.50 21.00 522880 5.23%

21.50 <= x < 22.50 22.00 1071966 10.72%

22.50 <= x < 23.50 23.00 1688953 16.89%

23.50 <= x < 24.50 24.00 2048494 20.48%

24.50 <= x < 25.50 25.00 1904317 19.04%

25.50 <= x < 26.50 26.00 1355333 13.55%

26.50 <= x < 27.50 27.00 732259 7.32%

27.50 <= x < 28.50 28.00 298308 2.98%

28.50 <= x < 29.50 29.00 90520 0.91%

29.50 <= x < 30.50 30.00 20202 0.20%

30.50 <= x < 31.50 31.00 3279 0.03%

31.50 <= x < 32.50 32.00 361 0.00%

32.50 <= x < 33.50 33.00 22 0.00%

33.50 <= x < 34.50 34.00 5 0.00%

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

grouped data

items: 10,000,000

minimum value: 15.00

first quartile: 23.00

median: 24.00

third quartile: 26.00

maximum value: 34.00

mean value: 24.21

midrange: 24.50

range: 19.00

interquartile range: 3.00

mean abs deviation: 1.54

sample variance (n): 3.71

sample variance (n-1): 3.71

sample std dev (n): 1.93

sample std dev (n-1): 1.93

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

cumulative

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

14.50 <= x < 15.50 15.00 22 0.00%

15.50 <= x < 16.50 16.00 253 0.00%

16.50 <= x < 17.50 17.00 2068 0.02%

17.50 <= x < 18.50 18.00 13943 0.14%

18.50 <= x < 19.50 19.00 68665 0.69%

19.50 <= x < 20.50 20.00 263101 2.63%

20.50 <= x < 21.50 21.00 785981 7.86%

21.50 <= x < 22.50 22.00 1857947 18.58%

22.50 <= x < 23.50 23.00 3546900 35.47%

23.50 <= x < 24.50 24.00 5595394 55.95%

24.50 <= x < 25.50 25.00 7499711 75.00%

25.50 <= x < 26.50 26.00 8855044 88.55%

26.50 <= x < 27.50 27.00 9587303 95.87%

27.50 <= x < 28.50 28.00 9885611 98.86%

28.50 <= x < 29.50 29.00 9976131 99.76%

29.50 <= x < 30.50 30.00 9996333 99.96%

30.50 <= x < 31.50 31.00 9999612 100.00%

31.50 <= x < 32.50 32.00 9999973 100.00%

32.50 <= x < 33.50 33.00 9999995 100.00%

33.50 <= x < 34.50 34.00 10000000 100.00%

computer results from some R code

`> draw.unique(1:38,38,38)`

Prob

u=1 3.531888016e-59

u=2 1.796050273e-46

u=3 1.059174006e-38

u=4 5.183421957e-33

u=5 1.695453233e-28

u=6 9.471698925e-25

u=7 1.493713473e-21

u=8 8.972474438e-19

u=9 2.4885921e-16

u=10 3.63239974e-14

u=11 3.061581311e-12

u=12 1.595200485e-10

u=13 5.409183238e-09

u=14 1.241901364e-07

u=15 1.99122433e-06

u=16 2.284767205e-05

u=17 0.0001912806707

u=18 0.001186529879

u=19 0.005519546762

u=20 0.01943459301

u=21 0.05215229288

u=22 0.1071593392

u=23 0.1690424973

u=24 0.2048643366

u=25 0.1904903213

u=26 0.1354368761

u=27 0.07321147122

u=28 0.02983819925

u=29 0.009063960064

u=30 0.002020712815

u=31 0.0003238875908

u=32 3.630885883e-05

u=33 2.741719853e-06

u=34 1.3225537e-07

u=35 3.767712201e-09

u=36 5.587491563e-11

u=37 3.417426033e-13

u=38 4.86120346e-16

Quote:MauiSunsetSo how many spins are needed for all 38 numbers to show up?

Nope27 Blog has a table

https://wizardofvegas.com/member/nope27/blog/

Roulette 00 Wheel "at least 1" number NOT hitting September 26th, 2010 at 11:21:44 am

the link there should be

https://wizardofodds.com/ask-the-wizard/roulette/

This is the coupon collectors problem

average: 160.66 spins

standard deviation: 46.66

part of the distribution

x prob[X=x] prob[X<x] prob[X>=x] prob[X<=x] prob[X>x]

65 0.00002 0.00005 0.99995 0.00007 0.99993

66 0.00003 0.00007 0.99993 0.00009 0.99991

67 0.00004 0.00009 0.99991 0.00013 0.99987

68 0.00005 0.00013 0.99987 0.00018 0.99982

69 0.00006 0.00018 0.99982 0.00024 0.99976

70 0.00008 0.00024 0.99976 0.00032 0.99968

71 0.00010 0.00032 0.99968 0.00042 0.99958

72 0.00013 0.00042 0.99958 0.00055 0.99945

73 0.00016 0.00055 0.99945 0.00071 0.99929

74 0.00019 0.00071 0.99929 0.00090 0.99910

75 0.00024 0.00090 0.99910 0.00114 0.99886

76 0.00029 0.00114 0.99886 0.00143 0.99857

77 0.00034 0.00143 0.99857 0.00177 0.99823

78 0.00041 0.00177 0.99823 0.00218 0.99782

79 0.00048 0.00218 0.99782 0.00266 0.99734

80 0.00056 0.00266 0.99734 0.00322 0.99678

81 0.00065 0.00322 0.99678 0.00387 0.99613

82 0.00075 0.00387 0.99613 0.00462 0.99538

83 0.00086 0.00462 0.99538 0.00548 0.99452

84 0.00098 0.00548 0.99452 0.00647 0.99353

85 0.00111 0.00647 0.99353 0.00758 0.99242

86 0.00125 0.00758 0.99242 0.00883 0.99117

87 0.00141 0.00883 0.99117 0.01024 0.98976

88 0.00157 0.01024 0.98976 0.01181 0.98819

89 0.00174 0.01181 0.98819 0.01355 0.98645

90 0.00192 0.01355 0.98645 0.01547 0.98453

91 0.00211 0.01547 0.98453 0.01759 0.98241

92 0.00232 0.01759 0.98241 0.01990 0.98010

93 0.00253 0.01990 0.98010 0.02243 0.97757

94 0.00274 0.02243 0.97757 0.02517 0.97483

95 0.00297 0.02517 0.97483 0.02814 0.97186

96 0.00320 0.02814 0.97186 0.03135 0.96865

97 0.00344 0.03135 0.96865 0.03479 0.96521

98 0.00369 0.03479 0.96521 0.03848 0.96152

99 0.00394 0.03848 0.96152 0.04241 0.95759

100 0.00419 0.04241 0.95759 0.04660 0.95340

101 0.00445 0.04660 0.95340 0.05105 0.94895

102 0.00471 0.05105 0.94895 0.05575 0.94425

103 0.00497 0.05575 0.94425 0.06072 0.93928

104 0.00523 0.06072 0.93928 0.06595 0.93405

105 0.00549 0.06595 0.93405 0.07143 0.92857

106 0.00575 0.07143 0.92857 0.07718 0.92282

107 0.00600 0.07718 0.92282 0.08318 0.91682

108 0.00626 0.08318 0.91682 0.08944 0.91056

109 0.00651 0.08944 0.91056 0.09596 0.90404

110 0.00676 0.09596 0.90404 0.10271 0.89729

111 0.00700 0.10271 0.89729 0.10971 0.89029

112 0.00724 0.10971 0.89029 0.11695 0.88305

113 0.00747 0.11695 0.88305 0.12442 0.87558

114 0.00769 0.12442 0.87558 0.13211 0.86789

115 0.00791 0.13211 0.86789 0.14002 0.85998

116 0.00812 0.14002 0.85998 0.14814 0.85186

117 0.00832 0.14814 0.85186 0.15646 0.84354

118 0.00851 0.15646 0.84354 0.16497 0.83503

119 0.00870 0.16497 0.83503 0.17367 0.82633

120 0.00887 0.17367 0.82633 0.18254 0.81746

121 0.00903 0.18254 0.81746 0.19157 0.80843

122 0.00919 0.19157 0.80843 0.20076 0.79924

123 0.00933 0.20076 0.79924 0.21009 0.78991

124 0.00947 0.21009 0.78991 0.21956 0.78044

125 0.00960 0.21956 0.78044 0.22916 0.77084

126 0.00971 0.22916 0.77084 0.23887 0.76113

127 0.00982 0.23887 0.76113 0.24869 0.75131

128 0.00991 0.24869 0.75131 0.25860 0.74140

129 0.01000 0.25860 0.74140 0.26859 0.73141

130 0.01007 0.26859 0.73141 0.27867 0.72133

131 0.01014 0.27867 0.72133 0.28880 0.71120

132 0.01019 0.28880 0.71120 0.29900 0.70100

133 0.01024 0.29900 0.70100 0.30923 0.69077

134 0.01028 0.30923 0.69077 0.31951 0.68049

135 0.01030 0.31951 0.68049 0.32981 0.67019

136 0.01032 0.32981 0.67019 0.34014 0.65986

137 0.01033 0.34014 0.65986 0.35047 0.64953

138 0.01033 0.35047 0.64953 0.36080 0.63920

139 0.01033 0.36080 0.63920 0.37113 0.62887

140 0.01031 0.37113 0.62887 0.38144 0.61856

141 0.01029 0.38144 0.61856 0.39173 0.60827

142 0.01026 0.39173 0.60827 0.40200 0.59800

143 0.01023 0.40200 0.59800 0.41222 0.58778

144 0.01018 0.41222 0.58778 0.42240 0.57760

145 0.01013 0.42240 0.57760 0.43254 0.56746

146 0.01008 0.43254 0.56746 0.44261 0.55739

147 0.01002 0.44261 0.55739 0.45263 0.54737

148 0.00995 0.45263 0.54737 0.46258 0.53742

149 0.00988 0.46258 0.53742 0.47245 0.52755

150 0.00980 0.47245 0.52755 0.48225 0.51775

151 0.00972 0.48225 0.51775 0.49197 0.50803

152 0.00963 0.49197 0.50803 0.50160 0.49840

153 0.00954 0.50160 0.49840 0.51114 0.48886

154 0.00945 0.51114 0.48886 0.52058 0.47942

155 0.00935 0.52058 0.47942 0.52993 0.47007

156 0.00925 0.52993 0.47007 0.53918 0.46082

157 0.00914 0.53918 0.46082 0.54832 0.45168

158 0.00904 0.54832 0.45168 0.55736 0.44264

159 0.00893 0.55736 0.44264 0.56628 0.43372

160 0.00881 0.56628 0.43372 0.57510 0.42490

161 0.00870 0.57510 0.42490 0.58380 0.41620

162 0.00858 0.58380 0.41620 0.59238 0.40762

163 0.00847 0.59238 0.40762 0.60085 0.39915

164 0.00835 0.60085 0.39915 0.60920 0.39080

165 0.00823 0.60920 0.39080 0.61742 0.38258

166 0.00811 0.61742 0.38258 0.62553 0.37447

167 0.00798 0.62553 0.37447 0.63352 0.36648

168 0.00786 0.63352 0.36648 0.64138 0.35862

169 0.00774 0.64138 0.35862 0.64912 0.35088

170 0.00761 0.64912 0.35088 0.65673 0.34327

171 0.00749 0.65673 0.34327 0.66422 0.33578

172 0.00737 0.66422 0.33578 0.67159 0.32841

173 0.00724 0.67159 0.32841 0.67883 0.32117

174 0.00712 0.67883 0.32117 0.68595 0.31405

175 0.00699 0.68595 0.31405 0.69294 0.30706

176 0.00687 0.69294 0.30706 0.69982 0.30018

177 0.00675 0.69982 0.30018 0.70656 0.29344

178 0.00663 0.70656 0.29344 0.71319 0.28681

179 0.00651 0.71319 0.28681 0.71970 0.28030

180 0.00638 0.71970 0.28030 0.72608 0.27392

181 0.00626 0.72608 0.27392 0.73235 0.26765

182 0.00615 0.73235 0.26765 0.73849 0.26151

183 0.00603 0.73849 0.26151 0.74452 0.25548

184 0.00591 0.74452 0.25548 0.75043 0.24957

185 0.00580 0.75043 0.24957 0.75623 0.24377

186 0.00568 0.75623 0.24377 0.76191 0.23809

187 0.00557 0.76191 0.23809 0.76747 0.23253

188 0.00545 0.76747 0.23253 0.77293 0.22707

189 0.00534 0.77293 0.22707 0.77827 0.22173

190 0.00523 0.77827 0.22173 0.78351 0.21649

191 0.00513 0.78351 0.21649 0.78863 0.21137

192 0.00502 0.78863 0.21137 0.79365 0.20635

193 0.00491 0.79365 0.20635 0.79857 0.20143

194 0.00481 0.79857 0.20143 0.80338 0.19662

195 0.00471 0.80338 0.19662 0.80809 0.19191

196 0.00461 0.80809 0.19191 0.81270 0.18730

197 0.00451 0.81270 0.18730 0.81721 0.18279

198 0.00441 0.81721 0.18279 0.82162 0.17838

199 0.00432 0.82162 0.17838 0.82593 0.17407

200 0.00422 0.82593 0.17407 0.83015 0.16985

201 0.00413 0.83015 0.16985 0.83428 0.16572

202 0.00404 0.83428 0.16572 0.83832 0.16168

203 0.00395 0.83832 0.16168 0.84227 0.15773

204 0.00386 0.84227 0.15773 0.84612 0.15388

205 0.00377 0.84612 0.15388 0.84990 0.15010

206 0.00369 0.84990 0.15010 0.85358 0.14642

207 0.00360 0.85358 0.14642 0.85718 0.14282

208 0.00352 0.85718 0.14282 0.86071 0.13929

209 0.00344 0.86071 0.13929 0.86415 0.13585

210 0.00336 0.86415 0.13585 0.86751 0.13249

211 0.00328 0.86751 0.13249 0.87079 0.12921

212 0.00321 0.87079 0.12921 0.87400 0.12600

213 0.00313 0.87400 0.12600 0.87713 0.12287

214 0.00306 0.87713 0.12287 0.88019 0.11981

215 0.00299 0.88019 0.11981 0.88318 0.11682

216 0.00292 0.88318 0.11682 0.88610 0.11390

217 0.00285 0.88610 0.11390 0.88894 0.11106

218 0.00278 0.88894 0.11106 0.89173 0.10827

219 0.00272 0.89173 0.10827 0.89444 0.10556

220 0.00265 0.89444 0.10556 0.89709 0.10291

221 0.00259 0.89709 0.10291 0.89968 0.10032

222 0.00253 0.89968 0.10032 0.90221 0.09779

223 0.00247 0.90221 0.09779 0.90467 0.09533

224 0.00241 0.90467 0.09533 0.90708 0.09292

225 0.00235 0.90708 0.09292 0.90943 0.09057

226 0.00229 0.90943 0.09057 0.91172 0.08828

227 0.00224 0.91172 0.08828 0.91395 0.08605

228 0.00218 0.91395 0.08605 0.91613 0.08387

229 0.00213 0.91613 0.08387 0.91826 0.08174

230 0.00208 0.91826 0.08174 0.92034 0.07966

231 0.00203 0.92034 0.07966 0.92236 0.07764

232 0.00198 0.92236 0.07764 0.92434 0.07566

233 0.00193 0.92434 0.07566 0.92627 0.07373

234 0.00188 0.92627 0.07373 0.92815 0.07185

235 0.00183 0.92815 0.07185 0.92998 0.07002

236 0.00179 0.92998 0.07002 0.93177 0.06823

237 0.00174 0.93177 0.06823 0.93351 0.06649

238 0.00170 0.93351 0.06649 0.93521 0.06479

239 0.00166 0.93521 0.06479 0.93687 0.06313

240 0.00162 0.93687 0.06313 0.93849 0.06151

241 0.00158 0.93849 0.06151 0.94007 0.05993

242 0.00154 0.94007 0.05993 0.94160 0.05840

243 0.00150 0.94160 0.05840 0.94310 0.05690

244 0.00146 0.94310 0.05690 0.94457 0.05543

245 0.00143 0.94457 0.05543 0.94599 0.05401

246 0.00139 0.94599 0.05401 0.94738 0.05262

247 0.00135 0.94738 0.05262 0.94873 0.05127

248 0.00132 0.94873 0.05127 0.95005 0.04995

249 0.00129 0.95005 0.04995 0.95134 0.04866

250 0.00125 0.95134 0.04866 0.95260 0.04740

251 0.00122 0.95260 0.04740 0.95382 0.04618

252 0.00119 0.95382 0.04618 0.95501 0.04499

253 0.00116 0.95501 0.04499 0.95617 0.04383

254 0.00113 0.95617 0.04383 0.95731 0.04269

255 0.00110 0.95731 0.04269 0.95841 0.04159

256 0.00108 0.95841 0.04159 0.95949 0.04051

257 0.00105 0.95949 0.04051 0.96053 0.03947

258 0.00102 0.96053 0.03947 0.96156 0.03844

259 0.00100 0.96156 0.03844 0.96255 0.03745

260 0.00097 0.96255 0.03745 0.96352 0.03648

261 0.00095 0.96352 0.03648 0.96447 0.03553

262 0.00092 0.96447 0.03553 0.96539 0.03461

263 0.00090 0.96539 0.03461 0.96629 0.03371

264 0.00087 0.96629 0.03371 0.96716 0.03284

265 0.00085 0.96716 0.03284 0.96802 0.03198

266 0.00083 0.96802 0.03198 0.96885 0.03115

267 0.00081 0.96885 0.03115 0.96966 0.03034

268 0.00079 0.96966 0.03034 0.97044 0.02956

269 0.00077 0.97044 0.02956 0.97121 0.02879

270 0.00075 0.97121 0.02879 0.97196 0.02804

271 0.00073 0.97196 0.02804 0.97269 0.02731

272 0.00071 0.97269 0.02731 0.97340 0.02660

273 0.00069 0.97340 0.02660 0.97409 0.02591

274 0.00067 0.97409 0.02591 0.97477 0.02523

275 0.00066 0.97477 0.02523 0.97543 0.02457

276 0.00064 0.97543 0.02457 0.97607 0.02393

277 0.00062 0.97607 0.02393 0.97669 0.02331

278 0.00061 0.97669 0.02331 0.97730 0.02270

279 0.00059 0.97730 0.02270 0.97789 0.02211

280 0.00058 0.97789 0.02211 0.97847 0.02153

281 0.00056 0.97847 0.02153 0.97903 0.02097

282 0.00055 0.97903 0.02097 0.97958 0.02042

283 0.00053 0.97958 0.02042 0.98011 0.01989

284 0.00052 0.98011 0.01989 0.98063 0.01937

285 0.00051 0.98063 0.01937 0.98113 0.01887

286 0.00049 0.98113 0.01887 0.98163 0.01837

287 0.00048 0.98163 0.01837 0.98211 0.01789

288 0.00047 0.98211 0.01789 0.98257 0.01743

289 0.00046 0.98257 0.01743 0.98303 0.01697

290 0.00044 0.98303 0.01697 0.98347 0.01653

291 0.00043 0.98347 0.01653 0.98391 0.01609

292 0.00042 0.98391 0.01609 0.98433 0.01567

293 0.00041 0.98433 0.01567 0.98474 0.01526

294 0.00040 0.98474 0.01526 0.98514 0.01486

295 0.00039 0.98514 0.01486 0.98552 0.01448

296 0.00038 0.98552 0.01448 0.98590 0.01410

297 0.00037 0.98590 0.01410 0.98627 0.01373

298 0.00036 0.98627 0.01373 0.98663 0.01337

299 0.00035 0.98663 0.01337 0.98698 0.01302

300 0.00034 0.98698 0.01302 0.98732 0.01268

301 0.00033 0.98732 0.01268 0.98765 0.01235

302 0.00032 0.98765 0.01235 0.98798 0.01202

303 0.00031 0.98798 0.01202 0.98829 0.01171

304 0.00031 0.98829 0.01171 0.98860 0.01140

305 0.00030 0.98860 0.01140 0.98890 0.01110

306 0.00029 0.98890 0.01110 0.98919 0.01081

307 0.00028 0.98919 0.01081 0.98947 0.01053

308 0.00028 0.98947 0.01053 0.98975 0.01025

309 0.00027 0.98975 0.01025 0.99002 0.00998

310 0.00026 0.99002 0.00998 0.99028 0.00972

311 0.00025 0.99028 0.00972 0.99053 0.00947

312 0.00025 0.99053 0.00947 0.99078 0.00922

313 0.00024 0.99078 0.00922 0.99102 0.00898

314 0.00024 0.99102 0.00898 0.99126 0.00874

315 0.00023 0.99126 0.00874 0.99149 0.00851

316 0.00022 0.99149 0.00851 0.99171 0.00829

317 0.00022 0.99171 0.00829 0.99193 0.00807

318 0.00021 0.99193 0.00807 0.99214 0.00786

319 0.00021 0.99214 0.00786 0.99235 0.00765

320 0.00020 0.99235 0.00765 0.99255 0.00745

321 0.00020 0.99255 0.00745 0.99274 0.00726

322 0.00019 0.99274 0.00726 0.99293 0.00707

323 0.00019 0.99293 0.00707 0.99312 0.00688

324 0.00018 0.99312 0.00688 0.99330 0.00670

325 0.00018 0.99330 0.00670 0.99347 0.00653

326 0.00017 0.99347 0.00653 0.99365 0.00635

327 0.00017 0.99365 0.00635 0.99381 0.00619

328 0.00016 0.99381 0.00619 0.99398 0.00602

329 0.00016 0.99398 0.00602 0.99413 0.00587

330 0.00015 0.99413 0.00587 0.99429 0.00571

331 0.00015 0.99429 0.00571 0.99444 0.00556

332 0.00015 0.99444 0.00556 0.99458 0.00542

333 0.00014 0.99458 0.00542 0.99473 0.00527

334 0.00014 0.99473 0.00527 0.99486 0.00514

335 0.00013 0.99486 0.00514 0.99500 0.00500

336 0.00013 0.99500 0.00500 0.99513 0.00487

337 0.00013 0.99513 0.00487 0.99526 0.00474

338 0.00012 0.99526 0.00474 0.99538 0.00462

339 0.00012 0.99538 0.00462 0.99550 0.00450

340 0.00012 0.99550 0.00450 0.99562 0.00438

341 0.00012 0.99562 0.00438 0.99574 0.00426

342 0.00011 0.99574 0.00426 0.99585 0.00415

343 0.00011 0.99585 0.00415 0.99596 0.00404

344 0.00011 0.99596 0.00404 0.99606 0.00394

345 0.00010 0.99606 0.00394 0.99617 0.00383

346 0.00010 0.99617 0.00383 0.99627 0.00373

347 0.00010 0.99627 0.00373 0.99637 0.00363

348 0.00010 0.99637 0.00363 0.99646 0.00354

349 0.00009 0.99646 0.00354 0.99656 0.00344

350 0.00009 0.99656 0.00344 0.99665 0.00335

351 0.00009 0.99665 0.00335 0.99673 0.00327

352 0.00009 0.99673 0.00327 0.99682 0.00318

353 0.00008 0.99682 0.00318 0.99690 0.00310

354 0.00008 0.99690 0.00310 0.99698 0.00302

355 0.00008 0.99698 0.00302 0.99706 0.00294

356 0.00008 0.99706 0.00294 0.99714 0.00286

357 0.00008 0.99714 0.00286 0.99722 0.00278

358 0.00007 0.99722 0.00278 0.99729 0.00271

359 0.00007 0.99729 0.00271 0.99736 0.00264

360 0.00007 0.99736 0.00264 0.99743 0.00257

361 0.00007 0.99743 0.00257 0.99750 0.00250

362 0.00007 0.99750 0.00250 0.99756 0.00244

363 0.00006 0.99756 0.00244 0.99763 0.00237

364 0.00006 0.99763 0.00237 0.99769 0.00231

365 0.00006 0.99769 0.00231 0.99775 0.00225

366 0.00006 0.99775 0.00225 0.99781 0.00219

367 0.00006 0.99781 0.00219 0.99787 0.00213

368 0.00006 0.99787 0.00213 0.99792 0.00208

369 0.00005 0.99792 0.00208 0.99798 0.00202

370 0.00005 0.99798 0.00202 0.99803 0.00197

371 0.00005 0.99803 0.00197 0.99808 0.00192

372 0.00005 0.99808 0.00192 0.99813 0.00187

373 0.00005 0.99813 0.00187 0.99818 0.00182

374 0.00005 0.99818 0.00182 0.99823 0.00177

375 0.00005 0.99823 0.00177 0.99828 0.00172

376 0.00005 0.99828 0.00172 0.99832 0.00168

377 0.00004 0.99832 0.00168 0.99837 0.00163

378 0.00004 0.99837 0.00163 0.99841 0.00159

379 0.00004 0.99841 0.00159 0.99845 0.00155

380 0.00004 0.99845 0.00155 0.99849 0.00151

381 0.00004 0.99849 0.00151 0.99853 0.00147

382 0.00004 0.99853 0.00147 0.99857 0.00143

383 0.00004 0.99857 0.00143 0.99861 0.00139

384 0.00004 0.99861 0.00139 0.99864 0.00136

385 0.00004 0.99864 0.00136 0.99868 0.00132

386 0.00003 0.99868 0.00132 0.99871 0.00129

387 0.00003 0.99871 0.00129 0.99875 0.00125

388 0.00003 0.99875 0.00125 0.99878 0.00122

389 0.00003 0.99878 0.00122 0.99881 0.00119

390 0.00003 0.99881 0.00119 0.99884 0.00116

391 0.00003 0.99884 0.00116 0.99888 0.00112

392 0.00003 0.99888 0.00112 0.99890 0.00110

393 0.00003 0.99890 0.00110 0.99893 0.00107

394 0.00003 0.99893 0.00107 0.99896 0.00104

395 0.00003 0.99896 0.00104 0.99899 0.00101

396 0.00003 0.99899 0.00101 0.99902 0.00098

397 0.00003 0.99902 0.00098 0.99904 0.00096

398 0.00003 0.99904 0.00096 0.99907 0.00093

399 0.00002 0.99907 0.00093 0.99909 0.00091

400 0.00002 0.99909 0.00091 0.99912 0.00088

401 0.00002 0.99912 0.00088 0.99914 0.00086

402 0.00002 0.99914 0.00086 0.99916 0.00084

403 0.00002 0.99916 0.00084 0.99918 0.00082

404 0.00002 0.99918 0.00082 0.99920 0.00080

405 0.00002 0.99920 0.00080 0.99923 0.00077

406 0.00002 0.99923 0.00077 0.99925 0.00075

407 0.00002 0.99925 0.00075 0.99927 0.00073

408 0.00002 0.99927 0.00073 0.99929 0.00071

409 0.00002 0.99929 0.00071 0.99930 0.00070

410 0.00002 0.99930 0.00070 0.99932 0.00068

411 0.00002 0.99932 0.00068 0.99934 0.00066

412 0.00002 0.99934 0.00066 0.99936 0.00064

413 0.00002 0.99936 0.00064 0.99937 0.00063

414 0.00002 0.99937 0.00063 0.99939 0.00061

415 0.00002 0.99939 0.00061 0.99941 0.00059

416 0.00002 0.99941 0.00059 0.99942 0.00058

417 0.00002 0.99942 0.00058 0.99944 0.00056

sim data

Max # of spins in this 1 million session sim was 710

group middle freq freq/100

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

53.50 <= x < 56.50 55.00 1 0.00%

56.50 <= x < 59.50 58.00 2 0.00%

59.50 <= x < 62.50 61.00 16 0.00%

62.50 <= x < 65.50 64.00 47 0.00%

65.50 <= x < 68.50 67.00 106 0.01%

68.50 <= x < 71.50 70.00 271 0.03%

71.50 <= x < 74.50 73.00 488 0.05%

74.50 <= x < 77.50 76.00 863 0.09%

77.50 <= x < 80.50 79.00 1422 0.14%

80.50 <= x < 83.50 82.00 2266 0.23%

83.50 <= x < 86.50 85.00 3280 0.33%

86.50 <= x < 89.50 88.00 4783 0.48%

89.50 <= x < 92.50 91.00 6302 0.63%

92.50 <= x < 95.50 94.00 8434 0.84%

95.50 <= x < 98.50 97.00 10460 1.05%

98.50 <= x < 101.50 100.00 12606 1.26%

101.50 <= x < 104.50 103.00 14931 1.49%

104.50 <= x < 107.50 106.00 17157 1.72%

107.50 <= x < 110.50 109.00 19381 1.94%

110.50 <= x < 113.50 112.00 21826 2.18%

113.50 <= x < 116.50 115.00 23488 2.35%

116.50 <= x < 119.50 118.00 25529 2.55%

119.50 <= x < 122.50 121.00 26965 2.70%

122.50 <= x < 125.50 124.00 28236 2.82%

125.50 <= x < 128.50 127.00 29345 2.93%

128.50 <= x < 131.50 130.00 30161 3.02%

131.50 <= x < 134.50 133.00 30876 3.09%

134.50 <= x < 137.50 136.00 30939 3.09%

137.50 <= x < 140.50 139.00 31179 3.12%

140.50 <= x < 143.50 142.00 30847 3.08%

143.50 <= x < 146.50 145.00 30209 3.02%

146.50 <= x < 149.50 148.00 29764 2.98%

149.50 <= x < 152.50 151.00 29197 2.92%

152.50 <= x < 155.50 154.00 28455 2.85%

155.50 <= x < 158.50 157.00 27244 2.72%

158.50 <= x < 161.50 160.00 26649 2.66%

161.50 <= x < 164.50 163.00 25277 2.53%

164.50 <= x < 167.50 166.00 24050 2.40%

167.50 <= x < 170.50 169.00 23143 2.31%

170.50 <= x < 173.50 172.00 22209 2.22%

173.50 <= x < 176.50 175.00 21102 2.11%

176.50 <= x < 179.50 178.00 20056 2.01%

179.50 <= x < 182.50 181.00 18876 1.89%

182.50 <= x < 185.50 184.00 17550 1.76%

185.50 <= x < 188.50 187.00 16717 1.67%

188.50 <= x < 191.50 190.00 15651 1.57%

191.50 <= x < 194.50 193.00 14634 1.46%

194.50 <= x < 197.50 196.00 14117 1.41%

197.50 <= x < 200.50 199.00 13001 1.30%

200.50 <= x < 203.50 202.00 12172 1.22%

203.50 <= x < 206.50 205.00 11479 1.15%

206.50 <= x < 209.50 208.00 10567 1.06%

209.50 <= x < 212.50 211.00 9954 1.00%

212.50 <= x < 215.50 214.00 9227 0.92%

215.50 <= x < 218.50 217.00 8482 0.85%

218.50 <= x < 221.50 220.00 7995 0.80%

221.50 <= x < 224.50 223.00 7306 0.73%

224.50 <= x < 227.50 226.00 7018 0.70%

227.50 <= x < 230.50 229.00 6496 0.65%

230.50 <= x < 233.50 232.00 5890 0.59%

233.50 <= x < 236.50 235.00 5557 0.56%

236.50 <= x < 239.50 238.00 5085 0.51%

239.50 <= x < 242.50 241.00 4745 0.47%

242.50 <= x < 245.50 244.00 4405 0.44%

245.50 <= x < 248.50 247.00 3960 0.40%

248.50 <= x < 251.50 250.00 3755 0.38%

251.50 <= x < 254.50 253.00 3521 0.35%

254.50 <= x < 257.50 256.00 3193 0.32%

257.50 <= x < 260.50 259.00 2960 0.30%

260.50 <= x < 263.50 262.00 2795 0.28%

263.50 <= x < 266.50 265.00 2611 0.26%

266.50 <= x < 269.50 268.00 2332 0.23%

269.50 <= x < 272.50 271.00 2119 0.21%

272.50 <= x < 275.50 274.00 1933 0.19%

275.50 <= x < 278.50 277.00 1917 0.19%

278.50 <= x < 281.50 280.00 1758 0.18%

281.50 <= x < 284.50 283.00 1519 0.15%

284.50 <= x < 287.50 286.00 1463 0.15%

287.50 <= x < 290.50 289.00 1297 0.13%

290.50 <= x < 293.50 292.00 1266 0.13%

293.50 <= x < 296.50 295.00 1203 0.12%

296.50 <= x < 299.50 298.00 1048 0.10%

299.50 <= x < 302.50 301.00 1019 0.10%

302.50 <= x < 305.50 304.00 904 0.09%

305.50 <= x < 308.50 307.00 860 0.09%

308.50 <= x < 311.50 310.00 782 0.08%

311.50 <= x < 314.50 313.00 736 0.07%

314.50 <= x < 317.50 316.00 691 0.07%

317.50 <= x < 320.50 319.00 667 0.07%

320.50 <= x < 323.50 322.00 553 0.06%

323.50 <= x < 326.50 325.00 554 0.06%

326.50 <= x < 329.50 328.00 444 0.04%

329.50 <= x < 332.50 331.00 458 0.05%

332.50 <= x < 335.50 334.00 398 0.04%

335.50 <= x < 338.50 337.00 375 0.04%

338.50 <= x < 341.50 340.00 325 0.03%

341.50 <= x < 344.50 343.00 323 0.03%

344.50 <= x < 347.50 346.00 291 0.03%

347.50 <= x < 350.50 349.00 270 0.03%

350.50 <= x < 353.50 352.00 267 0.03%

353.50 <= x < 356.50 355.00 244 0.02%

356.50 <= x < 359.50 358.00 224 0.02%

359.50 <= x < 362.50 361.00 192 0.02%

362.50 <= x < 365.50 364.00 203 0.02%

365.50 <= x < 368.50 367.00 184 0.02%

368.50 <= x < 371.50 370.00 160 0.02%

371.50 <= x < 374.50 373.00 111 0.01%

374.50 <= x < 377.50 376.00 129 0.01%

377.50 <= x < 380.50 379.00 118 0.01%

380.50 <= x < 383.50 382.00 98 0.01%

383.50 <= x < 386.50 385.00 92 0.01%

386.50 <= x < 389.50 388.00 100 0.01%

389.50 <= x < 392.50 391.00 74 0.01%

392.50 <= x < 395.50 394.00 91 0.01%

395.50 <= x < 398.50 397.00 73 0.01%

398.50 <= x < 401.50 400.00 48 0.00%

401.50 <= x < 404.50 403.00 58 0.01%

404.50 <= x < 407.50 406.00 58 0.01%

407.50 <= x < 410.50 409.00 49 0.00%

410.50 <= x < 413.50 412.00 48 0.00%

413.50 <= x < 416.50 415.00 43 0.00%

416.50 <= x < 419.50 418.00 38 0.00%

419.50 <= x < 422.50 421.00 43 0.00%

422.50 <= x < 425.50 424.00 30 0.00%

425.50 <= x < 428.50 427.00 31 0.00%

428.50 <= x < 431.50 430.00 24 0.00%

431.50 <= x < 434.50 433.00 28 0.00%

434.50 <= x < 437.50 436.00 28 0.00%

437.50 <= x < 440.50 439.00 26 0.00%

440.50 <= x < 443.50 442.00 19 0.00%

443.50 <= x < 446.50 445.00 25 0.00%

446.50 <= x < 449.50 448.00 9 0.00%

449.50 <= x < 452.50 451.00 21 0.00%

452.50 <= x < 455.50 454.00 12 0.00%

455.50 <= x < 458.50 457.00 17 0.00%

458.50 <= x < 461.50 460.00 16 0.00%

461.50 <= x < 464.50 463.00 14 0.00%

464.50 <= x < 467.50 466.00 12 0.00%

467.50 <= x < 470.50 469.00 15 0.00%

470.50 <= x < 473.50 472.00 11 0.00%

473.50 <= x < 476.50 475.00 5 0.00%

476.50 <= x < 479.50 478.00 9 0.00%

479.50 <= x < 482.50 481.00 7 0.00%

482.50 <= x < 485.50 484.00 13 0.00%

485.50 <= x < 488.50 487.00 8 0.00%

488.50 <= x < 491.50 490.00 4 0.00%

491.50 <= x < 494.50 493.00 7 0.00%

494.50 <= x < 497.50 496.00 6 0.00%

497.50 <= x < 500.50 499.00 6 0.00%

500.50 <= x < 503.50 502.00 5 0.00%

503.50 <= x < 506.50 505.00 3 0.00%

506.50 <= x < 509.50 508.00 3 0.00%

509.50 <= x < 512.50 511.00 4 0.00%

512.50 <= x < 515.50 514.00 1 0.00%

515.50 <= x < 518.50 517.00 5 0.00%

518.50 <= x < 521.50 520.00 0

521.50 <= x < 524.50 523.00 7 0.00%

524.50 <= x < 527.50 526.00 3 0.00%

527.50 <= x < 530.50 529.00 3 0.00%

530.50 <= x < 533.50 532.00 2 0.00%

533.50 <= x < 536.50 535.00 1 0.00%

536.50 <= x < 539.50 538.00 2 0.00%

539.50 <= x < 542.50 541.00 4 0.00%

542.50 <= x < 545.50 544.00 3 0.00%

545.50 <= x < 548.50 547.00 2 0.00%

548.50 <= x < 551.50 550.00 1 0.00%

551.50 <= x < 554.50 553.00 0

554.50 <= x < 557.50 556.00 2 0.00%

557.50 <= x < 560.50 559.00 0

560.50 <= x < 563.50 562.00 0

563.50 <= x < 566.50 565.00 1 0.00%

566.50 <= x < 569.50 568.00 0

569.50 <= x < 572.50 571.00 0

572.50 <= x < 575.50 574.00 1 0.00%

575.50 <= x < 578.50 577.00 2 0.00%

578.50 <= x < 581.50 580.00 0

581.50 <= x < 584.50 583.00 0

584.50 <= x < 587.50 586.00 1 0.00%

587.50 <= x < 590.50 589.00 1 0.00%

590.50 <= x < 593.50 592.00 0

593.50 <= x < 596.50 595.00 3 0.00%

596.50 <= x < 599.50 598.00 0

599.50 <= x < 602.50 601.00 1 0.00%

602.50 <= x < 605.50 604.00 0

605.50 <= x < 608.50 607.00 0

608.50 <= x < 611.50 610.00 1 0.00%

611.50 <= x < 614.50 613.00 0

614.50 <= x < 617.50 616.00 1 0.00%

617.50 <= x < 620.50 619.00 0

620.50 <= x < 623.50 622.00 0

623.50 <= x < 626.50 625.00 1 0.00%

626.50 <= x < 629.50 628.00 0

629.50 <= x < 632.50 631.00 0

632.50 <= x < 635.50 634.00 0

635.50 <= x < 638.50 637.00 0

638.50 <= x < 641.50 640.00 0

641.50 <= x < 644.50 643.00 0

644.50 <= x < 647.50 646.00 0

647.50 <= x < 650.50 649.00 1 0.00%

650.50 <= x < 653.50 652.00 0

653.50 <= x < 656.50 655.00 0

656.50 <= x < 659.50 658.00 0

659.50 <= x < 662.50 661.00 0

662.50 <= x < 665.50 664.00 0

665.50 <= x < 668.50 667.00 0

668.50 <= x < 671.50 670.00 0

671.50 <= x < 674.50 673.00 0

674.50 <= x < 677.50 676.00 0

677.50 <= x < 680.50 679.00 0

680.50 <= x < 683.50 682.00 0

683.50 <= x < 686.50 685.00 0

686.50 <= x < 689.50 688.00 0

689.50 <= x < 692.50 691.00 0

692.50 <= x < 695.50 694.00 0

695.50 <= x < 698.50 697.00 0

698.50 <= x < 701.50 700.00 0

701.50 <= x < 704.50 703.00 0

704.50 <= x < 707.50 706.00 0

707.50 <= x < 710.50 709.00 1 0.00%

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

grouped data

items: 1000000

minimum value: 55.00

first quartile: 128.00

median: 152.00

third quartile: 184.00

maximum value: 710.00

mean value: 160.63

midrange: 382.50

range: 655.00

interquartile range: 56.00

mean abs deviation: 35.61

sample variance (n): 2166.24

sample variance (n-1): 2166.25

sample std dev (n): 46.54

sample std dev (n-1): 46.54

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

cumulative

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

53.50 <= x < 56.50 55.00 1 0.00%

56.50 <= x < 59.50 58.00 3 0.00%

59.50 <= x < 62.50 61.00 19 0.00%

62.50 <= x < 65.50 64.00 66 0.01%

65.50 <= x < 68.50 67.00 172 0.02%

68.50 <= x < 71.50 70.00 443 0.04%

71.50 <= x < 74.50 73.00 931 0.09%

74.50 <= x < 77.50 76.00 1794 0.18%

77.50 <= x < 80.50 79.00 3216 0.32%

80.50 <= x < 83.50 82.00 5482 0.55%

83.50 <= x < 86.50 85.00 8762 0.88%

86.50 <= x < 89.50 88.00 13545 1.35%

89.50 <= x < 92.50 91.00 19847 1.98%

92.50 <= x < 95.50 94.00 28281 2.83%

95.50 <= x < 98.50 97.00 38741 3.87%

98.50 <= x < 101.50 100.00 51347 5.13%

101.50 <= x < 104.50 103.00 66278 6.63%

104.50 <= x < 107.50 106.00 83435 8.34%

107.50 <= x < 110.50 109.00 102816 10.28%

110.50 <= x < 113.50 112.00 124642 12.46%

113.50 <= x < 116.50 115.00 148130 14.81%

116.50 <= x < 119.50 118.00 173659 17.37%

119.50 <= x < 122.50 121.00 200624 20.06%

122.50 <= x < 125.50 124.00 228860 22.89%

125.50 <= x < 128.50 127.00 258205 25.82%

128.50 <= x < 131.50 130.00 288366 28.84%

131.50 <= x < 134.50 133.00 319242 31.92%

134.50 <= x < 137.50 136.00 350181 35.02%

137.50 <= x < 140.50 139.00 381360 38.14%

140.50 <= x < 143.50 142.00 412207 41.22%

143.50 <= x < 146.50 145.00 442416 44.24%

146.50 <= x < 149.50 148.00 472180 47.22%

149.50 <= x < 152.50 151.00 501377 50.14%

152.50 <= x < 155.50 154.00 529832 52.98%

155.50 <= x < 158.50 157.00 557076 55.71%

158.50 <= x < 161.50 160.00 583725 58.37%

161.50 <= x < 164.50 163.00 609002 60.90%

164.50 <= x < 167.50 166.00 633052 63.31%

167.50 <= x < 170.50 169.00 656195 65.62%

170.50 <= x < 173.50 172.00 678404 67.84%

173.50 <= x < 176.50 175.00 699506 69.95%

176.50 <= x < 179.50 178.00 719562 71.96%

179.50 <= x < 182.50 181.00 738438 73.84%

182.50 <= x < 185.50 184.00 755988 75.60%

185.50 <= x < 188.50 187.00 772705 77.27%

188.50 <= x < 191.50 190.00 788356 78.84%

191.50 <= x < 194.50 193.00 802990 80.30%

194.50 <= x < 197.50 196.00 817107 81.71%

197.50 <= x < 200.50 199.00 830108 83.01%

200.50 <= x < 203.50 202.00 842280 84.23%

203.50 <= x < 206.50 205.00 853759 85.38%

206.50 <= x < 209.50 208.00 864326 86.43%

209.50 <= x < 212.50 211.00 874280 87.43%

212.50 <= x < 215.50 214.00 883507 88.35%

215.50 <= x < 218.50 217.00 891989 89.20%

218.50 <= x < 221.50 220.00 899984 90.00%

221.50 <= x < 224.50 223.00 907290 90.73%

224.50 <= x < 227.50 226.00 914308 91.43%

227.50 <= x < 230.50 229.00 920804 92.08%

230.50 <= x < 233.50 232.00 926694 92.67%

233.50 <= x < 236.50 235.00 932251 93.23%

236.50 <= x < 239.50 238.00 937336 93.73%

239.50 <= x < 242.50 241.00 942081 94.21%

242.50 <= x < 245.50 244.00 946486 94.65%

245.50 <= x < 248.50 247.00 950446 95.04%

248.50 <= x < 251.50 250.00 954201 95.42%

251.50 <= x < 254.50 253.00 957722 95.77%

254.50 <= x < 257.50 256.00 960915 96.09%

257.50 <= x < 260.50 259.00 963875 96.39%

260.50 <= x < 263.50 262.00 966670 96.67%

263.50 <= x < 266.50 265.00 969281 96.93%

266.50 <= x < 269.50 268.00 971613 97.16%

269.50 <= x < 272.50 271.00 973732 97.37%

272.50 <= x < 275.50 274.00 975665 97.57%

275.50 <= x < 278.50 277.00 977582 97.76%

278.50 <= x < 281.50 280.00 979340 97.93%

281.50 <= x < 284.50 283.00 980859 98.09%

284.50 <= x < 287.50 286.00 982322 98.23%

287.50 <= x < 290.50 289.00 983619 98.36%

290.50 <= x < 293.50 292.00 984885 98.49%

293.50 <= x < 296.50 295.00 986088 98.61%

296.50 <= x < 299.50 298.00 987136 98.71%

299.50 <= x < 302.50 301.00 988155 98.82%

302.50 <= x < 305.50 304.00 989059 98.91%

305.50 <= x < 308.50 307.00 989919 98.99%

308.50 <= x < 311.50 310.00 990701 99.07%

311.50 <= x < 314.50 313.00 991437 99.14%

314.50 <= x < 317.50 316.00 992128 99.21%

317.50 <= x < 320.50 319.00 992795 99.28%

320.50 <= x < 323.50 322.00 993348 99.33%

323.50 <= x < 326.50 325.00 993902 99.39%

326.50 <= x < 329.50 328.00 994346 99.43%

329.50 <= x < 332.50 331.00 994804 99.48%

332.50 <= x < 335.50 334.00 995202 99.52%

335.50 <= x < 338.50 337.00 995577 99.56%

338.50 <= x < 341.50 340.00 995902 99.59%

341.50 <= x < 344.50 343.00 996225 99.62%

344.50 <= x < 347.50 346.00 996516 99.65%

347.50 <= x < 350.50 349.00 996786 99.68%

350.50 <= x < 353.50 352.00 997053 99.71%

353.50 <= x < 356.50 355.00 997297 99.73%

356.50 <= x < 359.50 358.00 997521 99.75%

359.50 <= x < 362.50 361.00 997713 99.77%

362.50 <= x < 365.50 364.00 997916 99.79%

365.50 <= x < 368.50 367.00 998100 99.81%

368.50 <= x < 371.50 370.00 998260 99.83%

371.50 <= x < 374.50 373.00 998371 99.84%

374.50 <= x < 377.50 376.00 998500 99.85%

377.50 <= x < 380.50 379.00 998618 99.86%

380.50 <= x < 383.50 382.00 998716 99.87%

383.50 <= x < 386.50 385.00 998808 99.88%

386.50 <= x < 389.50 388.00 998908 99.89%

389.50 <= x < 392.50 391.00 998982 99.90%

392.50 <= x < 395.50 394.00 999073 99.91%

395.50 <= x < 398.50 397.00 999146 99.91%

398.50 <= x < 401.50 400.00 999194 99.92%

401.50 <= x < 404.50 403.00 999252 99.93%

404.50 <= x < 407.50 406.00 999310 99.93%

407.50 <= x < 410.50 409.00 999359 99.94%

410.50 <= x < 413.50 412.00 999407 99.94%

413.50 <= x < 416.50 415.00 999450 99.94%

416.50 <= x < 419.50 418.00 999488 99.95%

419.50 <= x < 422.50 421.00 999531 99.95%

422.50 <= x < 425.50 424.00 999561 99.96%

425.50 <= x < 428.50 427.00 999592 99.96%

428.50 <= x < 431.50 430.00 999616 99.96%

431.50 <= x < 434.50 433.00 999644 99.96%

434.50 <= x < 437.50 436.00 999672 99.97%

437.50 <= x < 440.50 439.00 999698 99.97%

440.50 <= x < 443.50 442.00 999717 99.97%

443.50 <= x < 446.50 445.00 999742 99.97%

446.50 <= x < 449.50 448.00 999751 99.98%

449.50 <= x < 452.50 451.00 999772 99.98%

452.50 <= x < 455.50 454.00 999784 99.98%

455.50 <= x < 458.50 457.00 999801 99.98%

458.50 <= x < 461.50 460.00 999817 99.98%

461.50 <= x < 464.50 463.00 999831 99.98%

464.50 <= x < 467.50 466.00 999843 99.98%

467.50 <= x < 470.50 469.00 999858 99.99%

470.50 <= x < 473.50 472.00 999869 99.99%

473.50 <= x < 476.50 475.00 999874 99.99%

476.50 <= x < 479.50 478.00 999883 99.99%

479.50 <= x < 482.50 481.00 999890 99.99%

482.50 <= x < 485.50 484.00 999903 99.99%

485.50 <= x < 488.50 487.00 999911 99.99%

488.50 <= x < 491.50 490.00 999915 99.99%

491.50 <= x < 494.50 493.00 999922 99.99%

494.50 <= x < 497.50 496.00 999928 99.99%

497.50 <= x < 500.50 499.00 999934 99.99%

500.50 <= x < 503.50 502.00 999939 99.99%

503.50 <= x < 506.50 505.00 999942 99.99%

506.50 <= x < 509.50 508.00 999945 99.99%

509.50 <= x < 512.50 511.00 999949 99.99%

512.50 <= x < 515.50 514.00 999950 100.00%

515.50 <= x < 518.50 517.00 999955 100.00%

518.50 <= x < 521.50 520.00 999955 100.00%

521.50 <= x < 524.50 523.00 999962 100.00%

524.50 <= x < 527.50 526.00 999965 100.00%

527.50 <= x < 530.50 529.00 999968 100.00%

530.50 <= x < 533.50 532.00 999970 100.00%

533.50 <= x < 536.50 535.00 999971 100.00%

536.50 <= x < 539.50 538.00 999973 100.00%

539.50 <= x < 542.50 541.00 999977 100.00%

542.50 <= x < 545.50 544.00 999980 100.00%

545.50 <= x < 548.50 547.00 999982 100.00%

548.50 <= x < 551.50 550.00 999983 100.00%

551.50 <= x < 554.50 553.00 999983 100.00%

554.50 <= x < 557.50 556.00 999985 100.00%

557.50 <= x < 560.50 559.00 999985 100.00%

560.50 <= x < 563.50 562.00 999985 100.00%

563.50 <= x < 566.50 565.00 999986 100.00%

566.50 <= x < 569.50 568.00 999986 100.00%

569.50 <= x < 572.50 571.00 999986 100.00%

572.50 <= x < 575.50 574.00 999987 100.00%

575.50 <= x < 578.50 577.00 999989 100.00%

578.50 <= x < 581.50 580.00 999989 100.00%

581.50 <= x < 584.50 583.00 999989 100.00%

584.50 <= x < 587.50 586.00 999990 100.00%

587.50 <= x < 590.50 589.00 999991 100.00%

590.50 <= x < 593.50 592.00 999991 100.00%

593.50 <= x < 596.50 595.00 999994 100.00%

596.50 <= x < 599.50 598.00 999994 100.00%

599.50 <= x < 602.50 601.00 999995 100.00%

602.50 <= x < 605.50 604.00 999995 100.00%

605.50 <= x < 608.50 607.00 999995 100.00%

608.50 <= x < 611.50 610.00 999996 100.00%

611.50 <= x < 614.50 613.00 999996 100.00%

614.50 <= x < 617.50 616.00 999997 100.00%

617.50 <= x < 620.50 619.00 999997 100.00%

620.50 <= x < 623.50 622.00 999997 100.00%

623.50 <= x < 626.50 625.00 999998 100.00%

626.50 <= x < 629.50 628.00 999998 100.00%

629.50 <= x < 632.50 631.00 999998 100.00%

632.50 <= x < 635.50 634.00 999998 100.00%

635.50 <= x < 638.50 637.00 999998 100.00%

638.50 <= x < 641.50 640.00 999998 100.00%

641.50 <= x < 644.50 643.00 999998 100.00%

644.50 <= x < 647.50 646.00 999998 100.00%

647.50 <= x < 650.50 649.00 999999 100.00%

650.50 <= x < 653.50 652.00 999999 100.00%

653.50 <= x < 656.50 655.00 999999 100.00%

656.50 <= x < 659.50 658.00 999999 100.00%

659.50 <= x < 662.50 661.00 999999 100.00%

662.50 <= x < 665.50 664.00 999999 100.00%

665.50 <= x < 668.50 667.00 999999 100.00%

668.50 <= x < 671.50 670.00 999999 100.00%

671.50 <= x < 674.50 673.00 999999 100.00%

674.50 <= x < 677.50 676.00 999999 100.00%

677.50 <= x < 680.50 679.00 999999 100.00%

680.50 <= x < 683.50 682.00 999999 100.00%

683.50 <= x < 686.50 685.00 999999 100.00%

686.50 <= x < 689.50 688.00 999999 100.00%

689.50 <= x < 692.50 691.00 999999 100.00%

692.50 <= x < 695.50 694.00 999999 100.00%

695.50 <= x < 698.50 697.00 999999 100.00%

698.50 <= x < 701.50 700.00 999999 100.00%

701.50 <= x < 704.50 703.00 999999 100.00%

704.50 <= x < 707.50 706.00 999999 100.00%

707.50 <= x < 710.50 709.00 1000000 100.00%

Why do you keep bringing up the law of the third? Who's even trying to use it and why?

Quote:7crapsIt may be a layman's law, but not a law my any known mathematician.

In 38 spins, the average number of unique numbers hit is about 24.2 (24 or 25)

That means between 13 and 14 that have not hit in 38 spins

(12.67 would be 1/3)

The probability of that is just about 40%.

You can play with the distribution if you like`Unique numbers 38 spins 00 wheel`

group middle freq freq/100

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

14.50 <= x < 15.50 15.00 1 0.00%

15.50 <= x < 16.50 16.00 21 0.00%

16.50 <= x < 17.50 17.00 186 0.02%

17.50 <= x < 18.50 18.00 1222 0.12%

18.50 <= x < 19.50 19.00 5662 0.57%

19.50 <= x < 20.50 20.00 19492 1.95%

20.50 <= x < 21.50 21.00 52418 5.24%

21.50 <= x < 22.50 22.00 106767 10.68%

22.50 <= x < 23.50 23.00 168797 16.88%

23.50 <= x < 24.50 24.00 204829 20.48%

24.50 <= x < 25.50 25.00 190812 19.08%

25.50 <= x < 26.50 26.00 135407 13.54%

26.50 <= x < 27.50 27.00 73138 7.31%

27.50 <= x < 28.50 28.00 29826 2.98%

28.50 <= x < 29.50 29.00 9025 0.90%

29.50 <= x < 30.50 30.00 2026 0.20%

30.50 <= x < 31.50 31.00 338 0.03%

31.50 <= x < 32.50 32.00 30 0.00%

32.50 <= x < 33.50 33.00 2 0.00%

33.50 <= x < 34.50 34.00 1 0.00%

I agree it's not any kind of statistical law but it's a rule of thumb- about 1/3 of the nnumbers generated within a set will be missing due to duplicates. e.g. generating 1,000 numbers between 1 and 1,000 will have about 1/3 missing and 1/3 duplicates.

It's just interesting and tthe basis for the "Sleepping Dozen" nonsense in Roulette..

So how many spins are needed for all 38 numbers to show up?

Quote:KeyserMaui,

Why do you keep bringing up the law of the third? Who's even trying to use it and why?

It's that basis for hundreds of Roulette systems - there are chat rooms where everyone seems to believe in it.....

I guess if the Roulette wheel spun 38 times and all 38 numbers showed up, in a random order, that would probably mean something is rigged.....

If you're supposedly an aerospace engineer, then why are you hanging out on such a roulette system forum talking about the law of the third???

I'm a bad person...........

As an "aerospace engineer", what formula would you use to account for the decay of the spinning ball in relation to the spinning rotor?

Quote:KeyserMaui,

As an "aerospace engineer", what formula would you use to account for the decay of the spinning ball in relation to the spinning rotor?

Hell if I know, I haven't practiced AE since I started in computers in 1972 after getting out of the Air Force.

Doing a Google Search I find:

http://www.roulette.gmxhome.de/roulette[1].pdf <- I think this is what you want.

http://arxiv.org/pdf/1204.6412.pdf <- this looks cool

http://www.worldacademicunion.com/journal/SSCI/sscivol05no01paper02.pdf

If there was something to this there would be a lot of wealthy AEs out there..........

The pit boss will switch balls depending on how the crowds are doing. If it's slow then they use a ball that has a long spin time, if the tables are crowded they use a ball that slows down fast - more spins per hour.

So the AP gambler must determine which ball is being used while they gamble - in addition to temperature, moisture, static electricity, and even where the moon is at the time.

AP is total voodoo.........

How could static electricity possibly be a factor?

Static electricity builds up on your shoes as you walk - as you approach a Roulette table that charge is transferred to the table. During periods of low humidity you can even get a spark. That static charge builds up on the table and affects the spinning ball to some degree.

Humidity is probably a big factor too since it makes a hell of a difference in air density.

Then there is the oil on the fingers of the dealer.

Don't forget what happens as the ball jumps out of the track and bounces to the floor - all that gunk on the floor. Sure the dealer will wave the ball past the compass to make sure it doesn't have a magnetic core but I've yet to see a dealer clean the ball.

There is no way to use any kind of math to come up with any kind of forecast - none.....

Quote:MauiSunsetStatic electricity builds up on your shoes as you walk - as you approach a Roulette table that charge is transferred to the table. During periods of low humidity you can even get a spark. That static charge builds up on the table and affects the spinning ball to some degree.

Not in the way you've described it.

Quote:MauiSunsetThere is no way to use any kind of math to come up with any kind of forecast - none.....

Then why does the chief engineer for TCS Huxley say otherwise? I've seen the math, I know the formulas, I've seen the videos. Perhaps you should explain to him where he's in error.

Why is it that someone that pretends to be an aerospace engineer doesn't understand something as simple as the linear regression of a decaying ball on a track, and coefficient of restitution tests? I also don't understand your fascination with roulette system forums.

Quote:KeyserNot in the way you've described it.

Then why does the chief engineer for TCS Huxley say otherwise? I've seen the math, I know the formulas, I've seen the videos. Perhaps you should explain to him where he's in error.

Why is it that someone that pretends to be an aerospace engineer doesn't understand something as simple as the linear regression of a decaying ball on a track, and coefficient of restitution tests? I also don't understand your fascination with roulette system forums.

You sound just like all the other AP players on other Roulette chat rooms - like a UFO believer who happened to log into the wrong chat room.

A simple demonstration will clear all this up - Scotty, the Chief Engineer on the Enterprise, can easily demonstrate it live for us and clear all this up.

Oops wrong chat room - sorry..............

You believe that you can get an advantage over the casino by studying the physics and math behind a spinning wheel and spinning ball - I'm happy for you.

Maybe under strict controlled environments that's possible - but the casino is the real world and all your wonderful theories make no sense at all:

>That wheel is constantly slowing down, the spin last time was made at a faster rate than this one.

>And then the dealer spins the wheel faster to start the cycle all over again.

>The ball is let go at different speeds and the dealer does not look at the wheel to release it in the general area of the last spin.

>The pit boss can switch out white balls and you have brand new characteristics in play.

>The wheel used today may have been not the wheel at the same table yesterday - maintenance replaced it for some reason.

>The dealers take a break every hour and his/her 15 minute replacement spins the ball totally different.

You guys know all this stuff and always drag out mysterious people, formulas, computers, and processes and imply that they compensate for all the above.

BS - Roulette can't be beaten by mathematicians, physicists, engineers, or PhDs.

No matter how smart you are you can't beat Roulette - that's the sad truth. Einstein said it best:

"You cannot beat a roulette table unless you steal money from it"

No one has ever proven Einstein wrong on this subject - no one.....

P.S.

All I'm asking for is verifiable proof that AP has "beaten Roulette" in this post - certainly there should be proof somewhere.

Quote:Gabes22When I have heard of it working was in Europe with the "en prison" rule which has roughly 1/4 of the HE of an American wheel.

One would think that some AP guy who has made his millions/billions would put on a world demonstration and prove that AP does beat Roulette; take the credit and then retire with world adoration. The guy would easily get a reality show "Die Casino Die".

Sadly we must settle for rumors.........

AP folks are like UFO folks - "You should have been here yesterday".............

Exactly what my research has shone - lot's of wishful thinking but the same ol' losses like the rest of us, but with the smoke and mirrors.....

Quote:Gabes22LOL! Why are you ridiculing me for answering your question? It's not like I believe in AP roulette as I illustrated to you the only cases in which I have seen it work amount to what I think is cheating by the team or at worst gross negligence by the casino.

I didn't mean to ridicule you, just AP.

Sorry for the confusion - I apologize for any confusion on my part...

To summarize my view of AP:

It's just more Voodoo that can't be substantiated in the slightest except by folks who sell $29.99 AP systems or Roulette wheels; same thing with "reading random numbers".

My suggestion to those who want to spend thousands of hours traveling down the AP highway:

1) Get a mechanical Roulette wheel, like the air-ball ones the casinos use, and do your own version of Myth Busters - let the thing run for a year and let it release the ball in the same area and document the effects of humidity, static electricity, ball release speed, slowing of the wheel, etc - get the data and then publish a paper. Try to be a little scientific and move out of the Voodoo cellar.

2) If you want to program in super fancy equations that's fine but simulation software using Heuristic programming, is just simpler - it watches input and output over millions of observations and it will build a model for you without any programming. It has no idea what's going on but it models the real world and the basis for most simulation software. Just like Monte Carlo simulation can accurately calculate the area or volume of things without knowing any calculus so can Heuristic modeling reproduce and simulate physical things.

PM me if you have something earthshaking - I can't wait.

Best of luck to you all......

Read Eudaemonic Pie for the full story.

Quote:MauiSunsetTo all you AP Roulette gamblers out there:

You believe that you can get an advantage over the casino by studying the physics and math behind a spinning wheel and spinning ball - I'm happy for you.

Maybe under strict controlled environments that's possible - but the casino is the real world and all your wonderful theories make no sense at all:

>That wheel is constantly slowing down, the spin last time was made at a faster rate than this one.

>And then the dealer spins the wheel faster to start the cycle all over again.

>The ball is let go at different speeds and the dealer does not look at the wheel to release it in the general area of the last spin.

>The pit boss can switch out white balls and you have brand new characteristics in play.

>The wheel used today may have been not the wheel at the same table yesterday - maintenance replaced it for some reason.

>The dealers take a break every hour and his/her 15 minute replacement spins the ball totally different.

You guys know all this stuff and always drag out mysterious people, formulas, computers, and processes and imply that they compensate for all the above.

BS - Roulette can't be beaten by mathematicians, physicists, engineers, or PhDs.

No matter how smart you are you can't beat Roulette - that's the sad truth. Einstein said it best:

"You cannot beat a roulette table unless you steal money from it"

No one has ever proven Einstein wrong on this subject - no one.....

P.S.

All I'm asking for is verifiable proof that AP has "beaten Roulette" in this post - certainly there should be proof somewhere.

Einstein has never studied the game of roulette as it should be done.

No real AP would tell how to achieve it. And it took hard work to accomplish

AP business is for very few people.

this is often asked around a Roulette table (heard it yesterday actually)Quote:MauiSunsetSo how many spins are needed for all 38 numbers to show up?

38 numbers (160.7 being the average number of spins - still no guarantee)

spins | prob all 38#s show at least 1 time |
---|---|

38 | 4.86120346021012e-16 |

100 | 0.046602998 |

150 | 0.482251976 |

161 | 0.583797212 |

200 | 0.830154284 |

250 | 0.952596867 |

300 | 0.987321779 |

380 | 0.998491899 |

37 numbers (155.5 being the average number of spins)

spins | prob all 37#s show at least 1 time |
---|---|

37 | 1.303986462408241e-15 |

100 | 0.0640028 |

150 | 0.530644148 |

156 | 0.585913854 |

200 | 0.855284399 |

250 | 0.961401657 |

300 | 0.990074217 |

370 | 0.998536958 |

data from R code (uses Markov chain) found here: https://sites.google.com/view/krapstuff/roulette

different from: https://wizardofvegas.com/member/nope27/blog/#post153

ROULETTE 00 WHEEL "AT LEAST 1" NUMBER NOT HITTING