Posted by nope27
Mar 10, 2011

## Last words

From the end of my last post at:
http://wizardofvegas.com/forum/off-topic/general/4688-odds-on-6-7-8/

Back to your regularly scheduled program.
Not bad English for a Spaniard.

My Mother passed away last month, my Father this past Saturday, looks like it is my turn.
Turn, turn, turn

Enjoy the math of gambling everyone
Thank you Wizard for allowing me a personal Blog on your site.

Ayecarumba Mar 10, 2011

Wizard Mar 10, 2011

You're welcome.

I'm also sorry about your double loss. Take some time with that; you're welcome back any time. I take it your closing is a reference to Ecclesiastes chapter 3. This is your time to mourn and weep. There is also a time to laugh and dance. Don't forget that.

odiousgambit Mar 11, 2011

so often when one goes, the other goes soon after.

Condolences.

Posted by nope27
Sep 26, 2010

## Roulette 00 Wheel "at least 1" number NOT hitting

The below table is for the probability of NOT hitting "at least 1" number in x spins.
question #2 at WoO.

Wizards' Example: for "at least 1" number NOT hitting in 200 spins
Sum i=1 to 37 [(-1)^(i+1) × combin(38,i) × ((38-i)/38)^38] = 16.9845715651245%
Prob of "at least 1"  Prob of "at least 1"expected
spinsNot Hitting spinsNot Hitting# of spins
500.999999975489 2000.1698461177.5
550.999999272776 2050.1501051365.7
600.999990736518 2100.1324941585.0
650.999933186420 2150.1168221840.4
700.999678962024 2200.1029072137.9
750.998859296229 2250.0905742484.2
800.996782096871 2300.0796612887.2
850.992419788336 2350.0700193356.2
900.984526581332 2400.0615103901.8
950.971855305521 2450.0540094536.3
1000.953397 2500.0474035273.9
1050.928566 2550.0415906131.3
1100.897287 2600.0364787127.7
1150.859979 2650.0319858285.2
1200.817465 2700.0280399629.6
1250.770840 2750.02457411190.6
1300.721334 2800.02153413002.9
1350.670186 2850.01886615106.3
1400.618557 2900.01652717547.0
1450.567464 2950.01447620378.5
1500.517748 3000.01267823662.6
1510.508031 3050.01110327471.0
1520.498401 3100.00972231886.3
1530.488861 3150.00851337004.2
1540.479415 3200.00745342935.5
1550.470067 3250.00652549808.0
1600.424903 3300.00571257769.6
1650.382575 3350.00500166991.2
1700.343269 3400.00437777670.3
1750.307056 3450.00383290035.1
1800.273919 3500.003354104349.3
1850.243775 3550.002936120917.4
1900.216494 3600.002570140091.3
1950.191911 3650.002249162277.1
3700.001969187944.2
3750.001723217634.2
3800.001508251972.6
3850.001320291681.5
3900.001155337594.3
3950.001011390673.0
4000.000885452027.8

Posted by nope27
Sep 22, 2010

## Roulette Probability single 0 wheel

Roulette Probability Table for 1/37 (single 0 wheel)
Roulette probability1/37at least
SpinsSingle # chanceSplit bet (2 numbers)Street bet (3 # chance)corner bet (4 # chance)5#sLine Bet (6 # chance)Dozen bet (12 # chance)Even Money 18 numbersSpins
00.000% 0.000%0.000%0.000%0.000%0.000%0.000%0
12.703%5.405%8.108%10.811%13.514%16.216%32.432%48.649%1
25.332%10.519%15.559%20.453%25.201%29.803%54.346%73.630%2
37.891%15.355%22.405%29.053%35.309%41.186%69.153%86.459%3
410.380%19.931%28.697%36.723%44.051%50.723%79.157%93.046%4
512.803%24.259%34.478%43.563%51.612%58.714%85.917%96.429%5
615.159%28.353%39.791%49.665%58.151%65.409%90.485%98.166%6
717.452%32.226%44.673%55.106%63.806%71.019%93.571%99.058%7
819.683%35.889%49.159%59.960%68.697%75.718%95.656%99.516%8
921.854%39.355%53.281%64.288%72.927%79.656%97.065%99.752%9
1023.966%42.633%57.069%68.149%76.586%82.955%98.017%99.872%10
1126.021%45.734%60.550%71.592%79.750%85.719%98.660%99.935%11
1228.020%48.667%63.748%74.664%82.486%88.035%99.095%99.966%12
1329.966%51.442%66.688%77.403%84.853%89.975%99.388%99.983%13
1431.859%54.067%69.389%79.846%86.900%91.601%99.587%99.991%14
1533.700%56.549%71.871%82.024%88.670%92.963%99.721%99.995%15
1635.492%58.898%74.152%83.968%90.201%94.104%99.811% 16
1737.236%61.120%76.247%85.701%91.525%95.060%99.872% 17
1838.932%63.222%78.173%87.247%92.671%95.861%99.914% 18
1940.582%65.210%79.943%88.626%93.661%96.532%99.942% 19
2042.188%67.090%81.569%89.855%94.518%97.095%99.961% 20
2143.751%68.869%83.064%90.952%95.259%97.566%99.973% 21
2245.271%70.552%84.437%91.930%95.899%97.961%99.982% 22
2346.750%72.144%85.699%92.803%96.453%98.291%99.988% 23
2448.189%73.649%86.858%93.581%96.933%98.568%99.992% 24
2549.590%75.074%87.924%94.275%97.347%98.801%99.994% 25
2650.952%76.421%88.903%94.894%97.706%98.995%99.996% 26
2752.278%77.696%89.803%95.446%98.016%99.158%  27
2853.568%78.901%90.630%95.938%98.284%99.295%  28
2954.822%80.042%91.389%96.377%98.516%99.409%  29
3056.043%81.121%92.087%96.769%98.716%99.505%  30
3157.231%82.141%92.729%97.118%98.890%99.585%  31
3258.387%83.106%93.319%97.430%99.040%99.652%  32
3359.512%84.020%93.860%97.708%99.170%99.709%  33
3460.606%84.883%94.358%97.955%99.282%99.756%  34
3561.671%85.700%94.816%98.176%99.379%99.796%  35
3662.707%86.473%95.236%98.374%99.463%99.829%  36
3763.715%87.205%95.622%98.549%99.535%99.856%  37
3864.696%87.896%95.977%98.706%99.598%99.880%  38
3965.650%88.551%96.303%98.846%99.652%99.899%  39
4066.578%89.169%96.603%98.971%99.699%99.916%  40
4167.481%89.755%96.878%99.082%99.740%99.929%  41
4268.360%90.309%97.132%99.181%99.775%99.941%  42
4369.215%90.832%97.364%99.270%99.806%99.950%  43
4470.047%91.328%97.578%99.349%99.832%99.958%  44
4570.857%91.797%97.774%99.419%99.855%99.965%  45
4671.645%92.240%97.955%99.482%99.874%99.971%  46
4772.411%92.660%98.121%99.538%99.891%99.976%  47
4873.157%93.056%98.273%99.588%99.906%99.980%  48
4973.882%93.432%98.413%99.632%99.919%99.983%  49
5074.588%93.787%98.542%99.672%99.930%99.986%  50
5175.275%94.123%98.660%99.708%99.939%99.988%  51
5275.943%94.440%98.769%99.739%99.947%99.990%  52
5376.593%94.741%98.868%99.767%99.954%99.992%  53
5477.226%95.025%98.960%99.793%99.961%99.993%  54
5577.841%95.294%99.044%99.815%99.966%99.994%  55
5678.440%95.548%99.122%99.835%99.971%99.995%  56
5779.023%95.789%99.193%99.853%99.975%   57
5879.590%96.017%99.259%99.869%99.978%   58
5980.142%96.232%99.319%99.883%99.981%   59
6080.678%96.436%99.374%99.896%99.984%   60
6181.200%96.628%99.425%99.907%99.986%   61
6281.709%96.811%99.471%99.917%99.988%   62
6382.203%96.983%99.514%99.926%99.989%   63
6482.684%97.146%99.554%99.934%99.991%   64
6583.152%97.300%99.590%99.941%99.992%   65
6683.607%97.446%99.623%99.947%99.993%   66
6784.050%97.584%99.654%99.953%99.994%   67
6884.481%97.715%99.682%99.958%99.995%   68
6984.901%97.838%99.707%99.963%99.996%   69
7085.309%97.955%99.731%99.967%99.996%   70
7185.706%98.066%99.753%99.970%99.997%   71
7286.092%98.170%99.773%99.974%99.997%   72
7386.468%98.269%99.791%99.976%99.998%   73
7486.834%98.363%99.808%99.979%99.998%   74
7587.190%98.451%99.824%99.981%99.998%   75
7687.536%98.535%99.838%99.983%99.998%   76
7787.873%98.614%99.851%99.985%99.999%   77
7888.201%98.689%99.863%99.987%99.999%   78
7988.519%98.760%99.874%99.988%99.999%   79
8088.830%98.827%99.885%99.989%99.999%   80
8189.132%98.890%99.894%99.991%    81
8289.425%98.950%99.903%99.992%    82
8389.711%99.007%99.910%99.992%    83
8489.989%99.061%99.918%99.993%    84
8590.260%99.112%99.924%99.994%    85
8690.523%99.160%99.931%99.995%    86
8790.779%99.205%99.936%99.995%    87
8891.028%99.248%99.941%99.996%    88
8991.271%99.289%99.946%99.996%    89
9091.507%99.327%99.950%99.997%    90
9191.736%99.363%99.954%99.997%    91
9291.960%99.398%99.958%99.997%    92
9392.177%99.430%99.962%99.998%    93
9492.388%99.461%99.965%99.998%    94
9592.594%99.490%99.968%99.998%    95
9692.794%99.518%99.970%99.998%    96
9792.989%99.544%99.973%99.998%    97
9893.179%99.569%99.975%     98
9993.363%99.592%99.977%     99
10093.542%99.614%99.979%     100
10193.717%99.635%99.980%     101
10293.887%99.655%99.982%     102
10394.052%99.673%99.983%     103
10494.213%99.691%99.985%     104
10594.369%99.708%99.986%     105
10694.521%99.723%99.987%     106
10794.669%99.738%99.988%     107
10894.813%99.753%99.989%     108
10994.954%99.766%99.990%     109
11095.090%99.779%99.991%     110
11195.223%99.791%99.992%     111
11295.352%99.802%99.992%     112
11395.477%99.813%99.993%     113
11495.600%99.823%99.993%     114
11595.719%99.832%99.994%     115
11695.834%99.841%99.995%     116
11795.947%99.850%99.995%     117
11896.056%99.858%99.995%     118
11996.163%99.866%      119
12096.267%99.873%      120
12196.368%99.880%      121
12296.466%99.886%      122
12396.561%99.892%      123
12496.654%99.898%      124
12596.745%99.904%      125
12696.833%99.909%      126
12796.918%99.914%      127
12897.002%99.919%      128
12997.083%99.923%      129
13097.161%99.927%      130
13197.238%99.931%      131
13297.313%99.935%      132
13397.385%99.938%      133
13497.456%99.942%      134
13597.525%99.945%      135
13697.592%99.948%      136
13797.657%99.951%      137
13897.720%99.953%      138
13997.782%99.956%      139
14097.842%99.958%      140
14197.900%99.960%      141
14297.957%99.963%      142
14398.012%99.965%      143
14498.066%99.967%      144
14598.118%99.968%      145
14698.169%99.970%      146
14798.218%99.972%      147
14898.267%99.973%      148
14998.313%99.975%      149
15098.359%99.976%      150
15198.403%99.977%      151
15298.446%99.979%      152
15398.488%99.980%      153
15498.529%99.981%      154
15598.569%99.982%      155
15699.102%99.983%      156
15799.126%99.984%      157
15898.682%99.985%      158
15998.718%99.985%      159
16098.752%99.986%      160
16198.786%99.987%      161
16298.819%99.988%      162
16398.851%99.988%      163
16498.882%99.989%      164
16598.912%99.990%      165
16698.941%99.990%      166
16798.970%99.991%      167
16898.998%99.991%      168
16999.025%99.992%      169
17099.051%99.992%      170
17199.077%99.993%      171
17299.102%99.993%      172
17399.126%99.993%      173
17499.150%99.994%      174
17599.173%99.994%      175
17699.195%99.994%      176
17799.217%99.995%      177
17899.238%99.995%      178
17999.259%99.995%      179
18099.279%       180
18199.298%       181
18299.317%       182
18399.336%       183
18499.354%       184
18599.371%       185
18699.388%       186
18799.405%       187
18899.421%       188
18999.436%       189
19099.452%       190
19199.466%       191
19299.481%       192
19399.495%       193
19499.508%       194
19599.522%       195
19699.535%       196
19799.547%       197
19899.559%       198
19999.571%       199
20099.583%       200

mrjjj Sep 26, 2010

No problem, take your time and have a safe flight. Thanks for the info. Ken

mrjjj Sep 26, 2010

I wonder why my post jumped all the way to the top? Ken

Posted by nope27
Sep 22, 2010

## Roulette Probability 00 wheel

I like the idea of putting tables in one place. here are a few of mine for Roulette. 00 wheel.
I play Roulette and I am asked "what is the chance of" many times. Now I can direct one here.

These are "at least 1" tables or a cumulative frequency table.(So one has the chance of hitting at least 1 or more)
Formulas are:
Formula for a 00 wheel is: 1-((1-(p/38))^n) where n=# of spins and p=# of numbers
Formula for a 0 wheel is: 1-((1-(p/37))^n) where n=# of spins and p=# of numbers

Roulette Probability Table for 1/38 (00 wheel)
Roulette probability1/38
SpinsSingle # chanceSplit bet (2 numbers)Street bet (3 # chance)corner bet (4 # chance)5#sLine Bet (6 # chance)Dozen bet (12 # chance)Even Money 18 numbersSpins
12.632%5.263%7.895%10.526%13.158%15.789%31.579%47.368%1
25.194%10.249%15.166%19.945%24.584%29.086%53.186%72.299%2
37.689%14.973%21.864%28.371%34.508%40.283%67.969%85.421%3
410.118%19.448%28.032%35.911%43.125%49.712%78.084%92.327%4
512.483%23.688%33.714%42.658%50.609%57.652%85.005%95.961%5
614.786%27.704%38.947%48.694%57.107%64.339%89.740%97.874%6
717.029%31.509%43.767%54.094%62.751%69.969%92.980%98.881%7
819.212%35.114%48.206%58.926%67.652%74.711%95.197%99.411%8
921.338%38.529%52.295%63.250%71.909%78.704%96.714%99.690%9
1023.408%41.764%56.062%67.118%75.605%82.067%97.751%99.837%10
1125.424%44.829%59.530%70.580%78.815%84.898%98.462%99.914%11
1227.386%47.733%62.725%73.676%81.602%87.283%98.947%99.955%12
1329.297%50.484%65.668%76.447%84.023%89.291%99.280%99.976%13
1431.158%53.090%68.379%78.927%86.125%90.982%99.507%99.987%14
1532.970%55.559%70.875%81.145%87.951%92.406%99.663%99.993%15
1634.734%57.898%73.174%83.130%89.536%93.605%99.769% 16
1736.451%60.114%75.292%84.905%90.913%94.614%99.842% 17
1838.123%62.213%77.243%86.494%92.109%95.465%99.892% 18
1939.752%64.202%79.039%87.916%93.147%96.181%99.926% 19
2041.337%66.086%80.694%89.188%94.049%96.784%99.949% 20
2142.881%67.871%82.218%90.326%94.832%97.292%99.965% 21
2244.384%69.562%83.622%91.344%95.512%97.719%99.976% 22
2345.848%71.164%84.915%92.256%96.102%98.079%99.984% 23
2447.273%72.682%86.106%93.071%96.615%98.383%99.989% 24
2548.660%74.120%87.203%93.800%97.061%98.638%99.992% 25
2650.011%75.482%88.213%94.453%97.447%98.853%99.995% 26
2751.327%76.772%89.144%95.037%97.783%99.034%  27
2852.608%77.995%90.001%95.559%98.075%99.187%  28
2953.855%79.153%90.790%96.027%98.328%99.315%  29
3055.069%80.250%91.517%96.445%98.548%99.423%  30
3156.252%81.289%92.187%96.819%98.739%99.514%  31
3257.403%82.274%92.804%97.154%98.905%99.591%  32
3358.524%83.207%93.372%97.453%99.049%99.656%  33
3459.615%84.091%93.895%97.722%99.174%99.710%  34
3560.678%84.928%94.377%97.961%99.283%99.756%  35
3661.713%85.722%94.821%98.176%99.377%99.794%  36
3762.720%86.473%95.230%98.368%99.459%99.827%  37
3863.701%87.185%95.607%98.540%99.530%99.854%  38
3964.657%87.859%95.953%98.693%99.592%99.877%  39
4065.587%88.498%96.273%98.831%99.646%99.897%  40
4166.492%89.104%96.567%98.954%99.692%99.913%  41
4267.374%89.677%96.838%99.064%99.733%99.927%  42
4368.233%90.221%97.088%99.163%99.768%99.938%  43
4469.069%90.735%97.318%99.251%99.799%99.948%  44
4569.883%91.223%97.529%99.330%99.825%99.956%  45
4670.675%91.685%97.724%99.400%99.848%99.963%  46
4771.447%92.122%97.904%99.463%99.868%99.969%  47
4872.198%92.537%98.070%99.520%99.885%99.974%  48
4972.930%92.930%98.222%99.570%99.901%99.978%  49
5073.642%93.302%98.362%99.616%99.914%99.981%  50
5174.336%93.655%98.492%99.656%99.925%99.984%  51
5275.011%93.988%98.611%99.692%99.935%99.987%  52
5375.669%94.305%98.720%99.725%99.943%99.989%  53
5476.309%94.605%98.821%99.754%99.951%99.991%  54
5576.933%94.889%98.914%99.780%99.957%99.992%  55
5677.540%95.158%99.000%99.803%99.963%99.993%  56
5778.131%95.412%99.079%99.824%99.968%   57
5878.706%95.654%99.152%99.842%99.972%   58
5979.267%95.883%99.219%99.859%99.976%   59
6079.812%96.099%99.280%99.874%99.979%   60
6180.344%96.305%99.337%99.887%99.982%   61
6280.861%96.499%99.390%99.899%99.984%   62
6381.364%96.683%99.438%99.909%99.986%   63
6481.855%96.858%99.482%99.919%99.988%   64
6582.332%97.023%99.523%99.928%99.990%   65
6682.797%97.180%99.561%99.935%99.991%   66
6783.250%97.328%99.595%99.942%99.992%   67
6883.691%97.469%99.627%99.948%99.993%   68
6984.120%97.602%99.657%99.954%99.994%   69
7084.538%97.728%99.684%99.958%99.995%   70
7184.945%97.848%99.709%99.963%99.996%   71
7285.341%97.961%99.732%99.967%99.996%   72
7385.727%98.069%99.753%99.970%99.997%   73
7486.102%98.170%99.772%99.973%99.997%   74
7586.468%98.267%99.790%99.976%99.997%   75
7686.824%98.358%99.807%99.979%99.998%   76
7787.171%98.444%99.822%99.981%99.998%   77
7887.509%98.526%99.836%99.983%99.998%   78
7987.837%98.604%99.849%99.985%99.999%   79
8088.157%98.677%99.861%99.986%99.999%   80
8188.469%98.747%99.872%99.988%    81
8288.772%98.813%99.882%99.989%    82
8389.068%98.875%99.891%99.990%    83
8489.356%98.934%99.900%99.991%    84
8589.636%98.990%99.908%99.992%    85
8689.908%99.044%99.915%99.993%    86
8790.174%99.094%99.922%99.994%    87
8890.433%99.142%99.928%99.994%    88
8990.684%99.187%99.934%99.995%    89
9090.929%99.230%99.939%99.996%    90
9191.168%99.270%99.944%99.996%    91
9291.401%99.309%99.948%99.996%    92
9391.627%99.345%99.952%99.997%    93
9491.847%99.379%99.956%99.997%    94
9592.062%99.412%99.960%99.997%    95
9692.271%99.443%99.963%99.998%    96
9792.474%99.472%99.966%99.998%    97
9892.672%99.500%99.968%     98
9992.865%99.526%99.971%     99
10093.053%99.551%99.973%     100
10193.236%99.575%99.975%     101
10293.414%99.597%99.977%     102
10393.587%99.619%99.979%     103
10493.756%99.639%99.981%     104
10593.920%99.658%99.982%     105
10694.080%99.676%99.984%     106
10794.236%99.693%99.985%     107
10894.387%99.709%99.986%     108
10994.535%99.724%99.987%     109
11094.679%99.739%99.988%     110
11194.819%99.752%99.989%     111
11294.955%99.766%99.990%     112
11395.088%99.778%99.991%     113
11495.217%99.790%99.992%     114
11595.343%99.801%99.992%     115
11695.466%99.811%99.993%     116
11795.585%99.821%99.993%     117
11895.701%99.830%99.994%     118
11995.814%99.839%      119
12095.925%99.848%      120
12196.032%99.856%      121
12296.136%99.863%      122
12396.238%99.871%      123
12496.337%99.877%      124
12596.433%99.884%      125
12696.527%99.890%      126
12796.619%99.896%      127
12896.708%99.901%      128
12996.794%99.906%      129
13096.879%99.911%      130
13196.961%99.916%      131
13297.041%99.920%      132
13397.119%99.925%      133
13497.194%99.929%      134
13597.268%99.932%      135
13697.340%99.936%      136
13797.410%99.939%      137
13897.478%99.943%      138
13997.545%99.946%      139
14097.609%99.948%      140
14197.672%99.951%      141
14297.733%99.954%      142
14397.793%99.956%      143
14497.851%99.958%      144
14597.908%99.961%      145
14697.963%99.963%      146
14798.016%99.965%      147
14898.069%99.967%      148
14998.119%99.968%      149
15098.169%99.970%      150
15198.217%99.972%      151
15298.264%99.973%      152
15398.310%99.974%      153
15498.354%99.976%      154
15598.397%99.977%      155
15698.982%99.978%      156
15799.008%99.979%      157
15898.521%99.981%      158
15998.560%99.982%      159
16098.598%99.983%      160
16198.634%99.983%      161
16298.670%99.984%      162
16398.705%99.985%      163
16498.739%99.986%      164
16598.773%99.987%      165
16698.805%99.987%      166
16798.836%99.988%      167
16898.867%99.989%      168
16998.897%99.989%      169
17098.926%99.990%      170
17198.954%99.990%      171
17298.982%99.991%      172
17399.008%99.991%      173
17499.034%99.992%      174
17599.060%99.992%      175
17699.085%99.993%      176
17799.109%99.993%      177
17899.132%99.993%      178
17999.155%99.994%      179
18099.177%       180
18199.199%       181
18299.220%       182
18399.241%       183
18499.261%       184
18599.280%       185
18699.299%       186
18799.317%       187
18899.335%       188
18999.353%       189
19099.370%       190
19199.386%       191
19299.403%       192
19399.418%       193
19499.434%       194
19599.449%       195
19699.463%       196
19799.477%       197
19899.491%       198
19999.504%       199
20099.517%       200

mrjjj Sep 23, 2010

I have a question on this because I got into a HUGE debate regarding this around a year ago at another board.

(00 wheel).... I'll use for example, 1 number bet. Are you saying on the 11th spin, I have a 25.424% chance (use whatever term you want) of my number hitting? Ken

nope27 Sep 23, 2010

I have a question on this because I got into a HUGE debate regarding this around a year ago at another board.

(00 wheel).... I'll use for example, 1 number bet. Are you saying on the 11th spin, I have a 25.424% chance (use whatever term you want) of my number hitting? Ken

Yes, Ken you are correct.

(And, because this is a distribution table, one can also say that 25.42% of "all" 1 number bets HIT within 11 spins.

Actual data on a relative/cumulative table proves the last statement is correct. Of course, not perfectly correct, for the shout run, we must still apply the normal distribution with its standard deviations to set its ranges. But this would need another blog to explain and show.)

This is an "at least 1 only" table or cumulative frequency table.

your example above, you have 25.42% chance of "at least 1" hit. you could have 2 or more.

one can expand the table.

In 11 spins:

74.58% results in NO Hits

25.42%/1 or more hits

3.25%/2 or more hits

0.26%/3 or more hits

0.01%/4 or more hits

an expanded table can be easily made in a spreadsheet like excel using the "binodist" function.

(I'm currently on vacation and not at my regular computer)

I plan on adding a blog showing how to make a complete binomial distribution frequency table, showing the 3 outcomes.

1.exact probability column

2.at least (or more) column

3.or less (at most) column

mrjjj Sep 23, 2010

You realize there are a ton of people that would disagree with this? Many will say, every spin will still be a 1/38 chance of a number hitting regardless of the past. Myself? I'm kind of in the middle on this subject and I HATE not taking a side, I really dont know. I wish I could find an old thread from VLS regarding this subject. Ken

nope27 Sep 23, 2010

Yes, I agree with you. many people can not get away from the probability of one trial vs. the probability of a series of trials are different.

The math is correct. Many may disagree with my conclusions.

The above table IS theoretical. ALL math.

Actual roulette spins and rng spins (empirical data) verify the above table to be correct as long as one can calculate the standard deviation for each type of bet per n spins.

The mean average for a "1 number hit" in 1000 spins is 26.32 with a 5.06 SD.

I know 99 out of 100 people that read the above sentence do not understand those numbers.

(I assume that you do. You seem to know what you are talking about.

You know that in 25 spins, 3 is the average of numbers with 2 hits. Im sure only a few people actually know and believe that is true. Now, either you know how to do the math, and I do, and/or you found that out empirically.)

getting back to my example:

6.9 of those 26 hits, will happen within 11 spins, theoretically.

All one has to do is count the absolute frequencies to arrive at the total. But not always. The SD would be 2.2 rounded. That gives a range of 1 SD(68%)between 4.7 to 9.1. That is a big range! We are working with a prob of 1/38.

I see no value for myself in "proving anything" to anyone. But I do enjoy learning, and asking questions is part of that learning.

nope27 Sep 23, 2010

edit my last comment.

The SD to my last example of 2.2 should be 1.1 and the range would be 5.8 to 8.0

I did not see how to correct my comment

mrjjj Sep 25, 2010

I'll post a quick story. A while back I use to play a certain method. I get to the casino and start crossing off every number that hit until only one was left. In the beginning, this takes around 3 hours. I then start my progression on that LAST number, 1-95 progression. While I'm betting, continue to write down numbers for future use. I would leave the casino with some very nice winning days!! I had two losing days (\$3,500 per loss) and have not played this method in a while but as of NOW, its not off my list quite yet.

Anyways, the average 'looking back' at the last time the number hit was around 245 spins PLUS the 95 spins for betting = 340 spins. WOW! Think about it, 340 spins without a number hitting?? Yep and your chart only goes up to 200. How many 99% in a row are there? ALOT but I still lost (twice). Like I said, I'm on the fence for this topic. I do believe that numbers can be 'due' but sometimes I think the opposite, I do NOT know. Ken

nope27 Sep 25, 2010

Ken, I understand how it can be sometimes confusing, the math that is, based off of actual experience.

I currently play almost the type of way you explained as one of my methods of play in Roulette.

I start crossing off numbers that have hit and when 6 are left un-hit I start betting on those remaining 6. I never go after just having one left because of how far it can go before hitting.

you need to take the complement of the event, meaning the chances of the opposite to happen.

example:200 spins at least 1 will hit in 200 spins

1 will NOT hit 0.483% or 1 in 207.1

300 spins:99.966% will hit at least 1 time/0.034% will NOT hit 1 time/ or 1 in 2982.3

350 spins:99.991% will hit at least 1 time/0.009% will NOT hit 1 time/ or 1 in 11315. These are not very large numbers.

519 spins:99.9999025% will hit at least 1 time/0.0000975% will NOT hit 1 time/ or 1 in 1025632 (1 in a million)Now 1 million IS a large number compared to 11,000 or 3,000.

I recently ran a million spin simulation 1000 times and every number had disappeared well over 500 spins at least once and over half the numbers twice.

It is the reason I never go for that "last one" to hit. Because it can disappear for quite some time.

That is why I love to run simulations. A theoretical table like the one above can sometimes not be intuitively correct, but simulations prove do other wise.

Good Luck

nope27 Sep 26, 2010

Ken, not to add any more confusion. The last example I gave was for 1 number exactly, as if you selected it before hand.

350 spins:99.991% will hit at least 1 time/0.009% will NOT hit 1 time/ or 1 in 11315. These are not very large numbers.

The probability is different for any 1 number. Exactly the way you have played you would have to multiply 0.009% by 38 to have .342% or a 1 in 292 chance of not hitting. Im at an airport in Chicago waiting for a flight back to CA and I will add the simulation that goes with the latest #s. Im tired.

7craps Sep 26, 2010

nice work.

Data Tables can give wrong answers if we do not read them correctly.

We need to make sure we are always comparing apples to apples or we can come up with bad conclusions from the data table.I have made many mistakes, many times, glad to have found The Wizard.

The Wizards' formula took me awhile to duplicate in Excel, but it works and my table looks just like yours.

mrjjj Sep 29, 2010

You might be interested? >>> http://vlsroulette.com/grabb/

goatcabin Oct 25, 2010

"I have a question on this because I got into a HUGE debate regarding this around a year ago at another board.

(00 wheel).... I'll use for example, 1 number bet. Are you saying on the 11th spin, I have a 25.424% chance (use whatever term you want) of my number hitting? Ken"

Whoa! These figures are not for any specific spin, but for, in this case, all 11 spins. If you have gone 10 spins without your number hitting, on the 11th spin the probability of it hitting is .0263, just like it is on every spin. There is no "maturity of chances". Note how the probability at every step for one number is

( ( (37/38)^n) -1)

where n is the number of spins. Each time a spin goes by without your number hitting, the probabiilties table "shifts up" by one row. For example, after three spins without your number hitting, the probability of hitting it within 11 spins (from the beginning of the experiment) is not .254, but .192, because now you have only 8 spins left of the original 11.

(37/38)^8 - 1 = .192

The other side of this coin is that, if you hit the number on the 3rd spin, the probability of getting it within those first 11 spins is now 1.0, i.e. certainty.

Cheers,

Alan Shank

(member goatcabin)