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# Power Mega Balls with Three Sum Math

Topic closed. 167 replies. Last post 2 months ago by Sunglasses.

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The Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
3675 Posts
Offline
 Posted: May 17, 2015, 1:08 pm - IP Logged

We've been working on applying the concept of Sums to other lottery types and in a different way.

The Sum is a math process that adds the numbers in a lottery game like Pick 3 to come up with a total or sum of the numbers.

As an example, if the following are some Pick 3 combinations:

 Draw A B C 1 0 5 9 2 7 9 1 3 8 8 8 4 2 3 1

then their sums are as follows:

 Draw A + B + C = Sum 1 0 + 5 + 9 = 14 2 7 + 9 + 1 = 17 3 8 + 8 + 8 = 24 4 2 + 3 + 1 = 6

Now, that's pretty simple and it's what we would call an Inline Sum; meaning it is inline with the combination.

The Inline Sum is in this direction:

 Draw A → B → C → Sum 1 0 → 5 → 9 → 14 2 7 → 9 → 1 → 17 3 8 → 8 → 8 → 24 4 2 → 3 → 1 → 6

There is another way to sum these numbers and it is what we call Insequence; meaning it sums the numbers in a column of the combination as they are drawn.

The Insequence Sum is in this direction:

 Draw A B C 1 0 5 9 ↓ ↓ ↓ ↓ 2 7 9 1 ↓ ↓ ↓ ↓ 3 8 8 8 ↓ ↓ ↓ ↓ Sum 15 22 18

Then moving down the draws the next Insequence Sum is:

 Draw A B C 2 7 9 1 ↓ ↓ ↓ ↓ 3 8 8 8 ↓ ↓ ↓ ↓ 4 2 3 1 ↓ ↓ ↓ ↓ Sum 17 20 10

This Insequence Sum of the Pick 3 numbers follows the same distribution of sums as the Inline Sum.

Below the range of sums and the total count for each sum is shown:

 Sum Count 0 1 1 3 2 6 3 10 4 15 5 21 6 28 7 36 8 45 9 55 10 63 11 69 12 73 13 75 14 75 15 73 16 69 17 63 18 55 19 45 20 36 21 28 22 21 23 15 24 10 25 6 26 3 27 1

We're only going over the introduction of concept of Insequnce Sums right now.

Next we will get into the application to games like Powerball and Mega Millions.

Continues...

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
3675 Posts
Offline
 Posted: May 17, 2015, 1:43 pm - IP Logged

We began to think about an application of the Insequence Sums to the Powerball and Mega Millions games.

This will have an interesting way of helping to pick the next set of numbers using only 2 previous draws.

First, let's look at the Insequence Sums for Mega Millions.

The last 3 draws as of 2015-05-17 are below:

 Year Month Day A B C D E MB 2015 5 8 9 21 25 66 72 7 2015 5 12 14 30 33 36 44 2 2015 5 15 11 17 21 36 74 15

We can use the Insequence Sum to get a sum for each column.

 Year Month Day A B C D E MB 2015 5 8 9 21 25 66 72 7 2015 5 12 14 30 33 36 44 2 2015 5 15 11 17 21 36 74 15 - - Sum 34 68 79 138 190 24

This is just one example of an Insequence Sum.

Like the Insequence Sum for Pick 3, there is a Sum and Count or Frequency Distribution of the sums in each column.

Below are the Insequence Sum Distributions for just the Powerball and Mega Ball numbers.

 Powerball Mega Ball Sum Count Sum Count 3 1 3 1 4 3 4 3 5 6 5 6 6 10 6 10 7 15 7 15 8 21 8 21 9 28 9 28 10 36 10 36 11 45 11 45 12 55 12 55 13 66 13 66 14 78 14 78 15 91 15 91 16 105 16 105 17 120 17 120 18 136 18 133 19 153 19 144 20 171 20 153 21 190 21 160 22 210 22 165 23 231 23 168 24 253 24 169 25 276 25 168 26 300 26 165 27 325 27 160 28 351 28 153 29 378 29 144 30 406 30 133 31 435 31 120 32 465 32 105 33 496 33 91 34 528 34 78 35 561 35 66 36 595 36 55 37 630 37 45 38 663 38 36 39 694 39 28 40 723 40 21 41 750 41 15 42 775 42 10 43 798 43 6 44 819 44 3 45 838 45 1 46 855 - - 47 870 - - 48 883 - - 49 894 - - 50 903 - - 51 910 - - 52 915 - - 53 918 - - 54 919 - - 55 918 - - 56 915 - - 57 910 - - 58 903 - - 59 894 - - 60 883 - - 61 870 - - 62 855 - - 63 838 - - 64 819 - - 65 798 - - 66 775 - - 67 750 - - 68 723 - - 69 694 - - 70 663 - - 71 630 - - 72 595 - - 73 561 - - 74 528 - - 75 496 - - 76 465 - - 77 435 - - 78 406 - - 79 378 - - 80 351 - - 81 325 - - 82 300 - - 83 276 - - 84 253 - - 85 231 - - 86 210 - - 87 190 - - 88 171 - - 89 153 - - 90 136 - - 91 120 - - 92 105 - - 93 91 - - 94 78 - - 95 66 - - 96 55 - - 97 45 - - 98 36 - - 99 28 - - 100 21 - - 101 15 - - 102 10 - - 103 6 - - 104 3 - - 105 1 - -

Continues...

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
3675 Posts
Offline
 Posted: May 17, 2015, 2:22 pm - IP Logged

Next we found the distribution of the Insequence Sums for the individual columns A to E for both Powerball and Mega Millions.

These counts are huge and later we will look at a different way of looking at this huge set of counts.

Below are the Insequence Sums for Powerball:

 Powerball Sum A B C D E 3 76370735308483000 - - - - 4 213311364137487000 - - - - 5 396942381177804000 - - - - 6 615136159234327000 25050878776000 - - - 7 857359101540873000 142394468832000 - - - 8 1114524765212210000 471949336782000 - - - 9 1378857345152210000 1191270066940800 3652264000 - - 10 1643764935530890000 2535988382904900 31696434000 - - 11 1903722012701900000 4796633746119600 152780928300 - - 12 2154160609186790000 8312628678683510 539896261575 166375 - 13 2391369673133680000 13464159524383900 1560559327470 1960200 - 14 2612402131495640000 20662536258785200 3908221788240 12507990 - 15 2814989198097260000 30339574874399500 8781248296806 57294096 1 16 2997461489794500000 42936462405091100 18114327990765 210861615 15 17 3158676535111260000 58892497435234600 34865441667720 662130720 120 18 3297952280082490000 78634037599464700 63359593434640 1840672280 680 19 3415006215574880000 102563929768750000 109688506166880 4643268480 3060 20 3509899769117610000 131051648003151000 182163442685418 10816755138 11628 21 3582987622282150000 164424318610227000 291816308678460 23573806160 38760 22 3634871631926710000 202958770473589000 452942270718480 48543237180 116280 23 3666359050190350000 246874711914814000 683675327556540 95185722720 319770 24 3678424754007950000 296329102442962000 1006586642619030 178839579930 817190 25 3672177210142570000 351411758560998000 1449294011259340 323599394976 1961256 26 3648827916317860000 412142207081281000 2045069622806400 566272553400 4457400 27 3609664073001400000 478467776908622000 2833432304214700 961704851200 9657700 28 3556024253762060000 550262900746147000 3860709713411630 1589815843425 20058300 29 3489276854918940000 627329581444530000 5180555495756250 2564736831000 40116600 30 3410801117438180000 709398963537774000 6854406231490560 4046498658210 77558760 31 3321970525734240000 796133938687795000 8951863086796050 6255771922800 145422675 32 3224138399213770000 887132704104880000 11550983433529300 9492217787025 265182525 33 3118625503081040000 981933185340390000 14738468317052400 14157062193600 471435600 34 3006709515121420000 1080018228990330000 18609732518968800 20780558686800 818809200 35 2889616194910870000 1180821466640790000 23268845070519800 30055053853440 1391975640 36 2768512111181850000 1283733748674940000 28828329409029700 42874413162900 2319959400 37 2644498791925130000 1388110045201140000 35408813918153400 60380602135200 3796297200 38 2518608170238790000 1493276711214520000 43138525335037900 84018246651000 6107086800 39 2391799206966430000 1598539014042520000 52152619424555600 115598015112640 9669554100 40 2264955578808210000 1703188823024230000 62592345391931700 157369672284516 15084504396 41 2138884327860310000 1806512364121670000 74604042708729900 212105648149440 23206929840 42 2014315375448780000 1907797945649370000 88337971340830200 283195943146320 35240152720 43 1891901809691620000 2006343565437080000 103946978767663000 374755151815680 52860229080 44 1772220862457530000 2101464314413980000 121585009646082000 491742328282155 78378960360 45 1655775497306680000 2192499496735120000 141405466476229000 640094337269288 114955808528 46 1542996535608120000 2278819392077940000 163559432146754000 826873231624110 166871334960 47 1434245253345060000 2359831591544850000 188193767749433000 1060428069827280 239877544005 48 1329816386151380000 2434986844644250000 215449101535085000 1350571432945000 341643774795 49 1229941484885500000 2503784361023950000 245457727311140000 1708770718291680 482320623240 50 1134792568548590000 2565776516935410000 278341432933916000 2148354075170860 675248872536 51 1044486025607010000 2620572922761180000 314209281804197000 2684730605020800 937845656300 52 959086718791041000 2667843814289620000 353155372412475000 3335624172828150 1292706174900 53 878612252226235000 2707322736724620000 395256602980481000 4121319867663600 1768966344600 54 803037363317546000 2738808496631570000 440570470089862000 5064921806696500 2403979904200 55 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36117296946942300 47855699958816 66 230259820236280000 2508142911405650000 1221199975798180000 42155694033828600 60992558771040 67 204677147999149000 2445968929266010000 1301491217011420000 49030581294097900 77413632286320 68 181559317656689000 2379148120590830000 1382892983999450000 56830938225162300 97862516286480 69 160718186144583000 2308200323317880000 1465032098255940000 65651443981140600 123234279768160 70 141973576298856000 2233653276466680000 1547512118268160000 75592327917521800 154603004161950 71 125153859791252000 2156037129430600000 1629916299256560000 86759129545006800 193253741792475 72 110096356189099000 2075879263576050000 1711810902465770000 99262359175613300 240719500649075 73 96647573267503300 1993699472515260000 1792748813299970000 113217051306954000 298823922856200 74 84663311309128100 1910005537254960000 1872273422750340000 128742203768860000 369730384322250 75 74008651903069600 1825289223084690000 1949922722666540000 145960096836640000 455998301634582 76 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942088098708486000 2555715915860050000 482284463330879000 3791483751055650 87 12452107244102400 874103234979003000 2578714017632480000 529072646985275000 4525457806113080 88 10580116432984100 809009393366510000 2595257264381430000 578907860728085000 5388532442546180 89 8969042880201690 746894556794328000 2605229868673860000 631820163495445000 6400975349082600 90 7585796284746970 687819653091168000 2608561870605670000 687819653091169000 7585796284746970 91 6400975349082600 631820163495445000 2605229868673860000 746894556794328000 8969042880201690 92 5388532442546180 578907860728084000 2595257264381430000 809009393366510000 10580116432984100 93 4525457806113080 529072646985275000 2578714017632490000 874103234979003000 12452107244102400 94 3791483751055650 482284463330880000 2555715915860050000 942088098708486000 14622148694417700 95 3168809001723840 438495243334619000 2526423365686700000 1012847498108930000 17131788859618200 96 2641843073410440 397640885376502000 2491039721685640000 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29078984349975 26222890492138800 990321073090806000 2661825911525440000 323779395132871000 118 22512762077400 22217684088742600 917657119338718000 2700576638501080000 361229056056119000 119 17345898649800 18750389209471800 847545301821741000 2732405642794690000 402166759737852000 120 13298522298180 15760252849662500 780180090550310000 2756964486914650000 446802051415040000 121 10142940735900 13191740454009600 715723702125498000 2773953386508450000 495340513142165000 122 7694644696200 10994309071792200 654306488277471000 2783126024653670000 547980454764492000 123 5804731963800 9122158780072800 596027668066398000 2784293659805010000 604909054476297000 124 4353548972850 7533968365504350 540956367714921000 2777328505382130000 666297888407820000 125 3245372870670 6192620598316320 489132931859620000 2762166363106920000 732298405160661000 126 2403979904200 5064921806696500 440570470089863000 2738808496631570000 803037363317547000 127 1768966344600 4121319867663600 395256602980481000 2707322736724620000 878612252226235000 128 1292706174900 3335624172828150 353155372412475000 2667843814289620000 959086718791041000 129 937845656300 2684730605020800 314209281804197000 2620572922761180000 1044486025607010000 130 675248872536 2148354075170860 278341432933916000 2565776516935410000 1134792568548590000 131 482320623240 1708770718291680 245457727311140000 2503784361023950000 1229941484885500000 132 341643774795 1350571432945000 215449101535085000 2434986844644260000 1329816386151380000 133 239877544005 1060428069827280 188193767749433000 2359831591544850000 1434245253345050000 134 166871334960 826873231624110 163559432146754000 2278819392077950000 1542996535608120000 135 114955808528 640094337269288 141405466476229000 2192499496735120000 1655775497306670000 136 78378960360 491742328282155 121585009646082000 2101464314413980000 1772220862457530000 137 52860229080 374755151815680 103946978767663000 2006343565437080000 1891901809691620000 138 35240152720 283195943146320 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3321970525734240000 150 77558760 4046498658210 6854406231490560 709398963537774000 3410801117438180000 151 40116600 2564736831000 5180555495756250 627329581444530000 3489276854918940000 152 20058300 1589815843425 3860709713411630 550262900746147000 3556024253762060000 153 9657700 961704851200 2833432304214700 478467776908622000 3609664073001400000 154 4457400 566272553400 2045069622806400 412142207081281000 3648827916317860000 155 1961256 323599394976 1449294011259340 351411758560998000 3672177210142570000 156 817190 178839579930 1006586642619030 296329102442962000 3678424754007950000 157 319770 95185722720 683675327556540 246874711914814000 3666359050190350000 158 116280 48543237180 452942270718480 202958770473589000 3634871631926710000 159 38760 23573806160 291816308678460 164424318610227000 3582987622282150000 160 11628 10816755138 182163442685418 131051648003151000 3509899769117610000 161 3060 4643268480 109688506166880 102563929768750000 3415006215574880000 162 680 1840672280 63359593434640 78634037599464700 3297952280082490000 163 120 662130720 34865441667720 58892497435234600 3158676535111260000 164 15 210861615 18114327990765 42936462405091100 2997461489794500000 165 1 57294096 8781248296806 30339574874399500 2814989198097260000 166 - 12507990 3908221788240 20662536258785200 2612402131495640000 167 - 1960200 1560559327470 13464159524383900 2391369673133680000 168 - 166375 539896261575 8312628678683510 2154160609186790000 169 - - 152780928300 4796633746119600 1903722012701900000 170 - - 31696434000 2535988382904900 1643764935530890000 171 - - 3652264000 1191270066940800 1378857345152210000 172 - - - 471949336782000 1114524765212210000 173 - - - 142394468832000 857359101540873000 174 - - - 25050878776000 615136159234327000 175 - - - - 396942381177804000 176 - - - - 213311364137487000 177 - - - - 76370735308483000

Now Mega Millions:

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Continues...

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
3675 Posts
Offline
 Posted: May 17, 2015, 2:53 pm - IP Logged

When we graph these, we can see the Power Ball and Mega Ball Insequence Sums look a lot like the Pick 3 sums.

Continues...

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
3675 Posts
Offline
 Posted: May 17, 2015, 2:59 pm - IP Logged

The individual Insequence Sums of the columns are a bit different.

We can see columns A, B, D, and E are a little lopsided; one way and the other.

Also, column A is symmetrical with E; meaning it's the mirror image of each.

In addition, B is symmertrical with D, and C is what as known as self symmetric or a mirror image of itself.

Continues...

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
3675 Posts
Offline
 Posted: May 17, 2015, 3:27 pm - IP Logged

With those huge numbers, we like to reduce them down to a Probability table.

This make it easy to see what sum is more likely to happen and it make it more even between columns and the extra ball numbers.

The following table shows all Insequence Sum Probabilities for both Powerball and Mega Millions.

 Insequence Sum Probability Table Powerball Mega Millions Sum A B C D E PB Sum A B C D E MB 3 0.0609% 0.0000% 0.0000% 0.0000% 0.0000% 0.0023% 3 0.0296% 0.0000% 0.0000% 0.0000% 0.0000% 0.0296% 4 0.1700% 0.0000% 0.0000% 0.0000% 0.0000% 0.0070% 4 0.0841% 0.0000% 0.0000% 0.0000% 0.0000% 0.0889% 5 0.3163% 0.0000% 0.0000% 0.0000% 0.0000% 0.0140% 5 0.1590% 0.0000% 0.0000% 0.0000% 0.0000% 0.1778% 6 0.4902% 0.0000% 0.0000% 0.0000% 0.0000% 0.0233% 6 0.2505% 0.0000% 0.0000% 0.0000% 0.0000% 0.2963% 7 0.6833% 0.0001% 0.0000% 0.0000% 0.0000% 0.0350% 7 0.3550% 0.0000% 0.0000% 0.0000% 0.0000% 0.4444% 8 0.8882% 0.0004% 0.0000% 0.0000% 0.0000% 0.0490% 8 0.4694% 0.0001% 0.0000% 0.0000% 0.0000% 0.6222% 9 1.0989% 0.0009% 0.0000% 0.0000% 0.0000% 0.0653% 9 0.5908% 0.0002% 0.0000% 0.0000% 0.0000% 0.8296% 10 1.3100% 0.0020% 0.0000% 0.0000% 0.0000% 0.0840% 10 0.7168% 0.0005% 0.0000% 0.0000% 0.0000% 1.0667% 11 1.5172% 0.0038% 0.0000% 0.0000% 0.0000% 0.1050% 11 0.8452% 0.0010% 0.0000% 0.0000% 0.0000% 1.3333% 12 1.7167% 0.0066% 0.0000% 0.0000% 0.0000% 0.1283% 12 0.9739% 0.0017% 0.0000% 0.0000% 0.0000% 1.6296% 13 1.9058% 0.0107% 0.0000% 0.0000% 0.0000% 0.1539% 13 1.1013% 0.0027% 0.0000% 0.0000% 0.0000% 1.9556% 14 2.0819% 0.0165% 0.0000% 0.0000% 0.0000% 0.1819% 14 1.2260% 0.0043% 0.0000% 0.0000% 0.0000% 2.3111% 15 2.2434% 0.0242% 0.0000% 0.0000% 0.0000% 0.2122% 15 1.3467% 0.0064% 0.0000% 0.0000% 0.0000% 2.6963% 16 2.3888% 0.0342% 0.0000% 0.0000% 0.0000% 0.2449% 16 1.4623% 0.0091% 0.0000% 0.0000% 0.0000% 3.1111% 17 2.5173% 0.0469% 0.0000% 0.0000% 0.0000% 0.2799% 17 1.5720% 0.0127% 0.0000% 0.0000% 0.0000% 3.5556% 18 2.6283% 0.0627% 0.0001% 0.0000% 0.0000% 0.3172% 18 1.6750% 0.0172% 0.0000% 0.0000% 0.0000% 3.9407% 19 2.7216% 0.0817% 0.0001% 0.0000% 0.0000% 0.3569% 19 1.7707% 0.0228% 0.0000% 0.0000% 0.0000% 4.2667% 20 2.7972% 0.1044% 0.0001% 0.0000% 0.0000% 0.3988% 20 1.8587% 0.0295% 0.0000% 0.0000% 0.0000% 4.5333% 21 2.8554% 0.1310% 0.0002% 0.0000% 0.0000% 0.4431% 21 1.9387% 0.0376% 0.0000% 0.0000% 0.0000% 4.7407% 22 2.8968% 0.1617% 0.0004% 0.0000% 0.0000% 0.4898% 22 2.0104% 0.0471% 0.0000% 0.0000% 0.0000% 4.8889% 23 2.9219% 0.1967% 0.0005% 0.0000% 0.0000% 0.5388% 23 2.0737% 0.0582% 0.0001% 0.0000% 0.0000% 4.9778% 24 2.9315% 0.2362% 0.0008% 0.0000% 0.0000% 0.5901% 24 2.1286% 0.0709% 0.0001% 0.0000% 0.0000% 5.0074% 25 2.9265% 0.2801% 0.0012% 0.0000% 0.0000% 0.6437% 25 2.1751% 0.0855% 0.0001% 0.0000% 0.0000% 4.9778% 26 2.9079% 0.3285% 0.0016% 0.0000% 0.0000% 0.6997% 26 2.2133% 0.1019% 0.0002% 0.0000% 0.0000% 4.8889% 27 2.8767% 0.3813% 0.0023% 0.0000% 0.0000% 0.7580% 27 2.2433% 0.1202% 0.0003% 0.0000% 0.0000% 4.7407% 28 2.8339% 0.4385% 0.0031% 0.0000% 0.0000% 0.8187% 28 2.2655% 0.1406% 0.0004% 0.0000% 0.0000% 4.5333% 29 2.7808% 0.4999% 0.0041% 0.0000% 0.0000% 0.8816% 29 2.2800% 0.1631% 0.0006% 0.0000% 0.0000% 4.2667% 30 2.7182% 0.5654% 0.0055% 0.0000% 0.0000% 0.9469% 30 2.2871% 0.1876% 0.0007% 0.0000% 0.0000% 3.9407% 31 2.6474% 0.6345% 0.0071% 0.0000% 0.0000% 1.0146% 31 2.2872% 0.2143% 0.0010% 0.0000% 0.0000% 3.5556% 32 2.5695% 0.7070% 0.0092% 0.0000% 0.0000% 1.0845% 32 2.2805% 0.2432% 0.0013% 0.0000% 0.0000% 3.1111% 33 2.4854% 0.7825% 0.0117% 0.0000% 0.0000% 1.1569% 33 2.2676% 0.2741% 0.0017% 0.0000% 0.0000% 2.6963% 34 2.3962% 0.8607% 0.0148% 0.0000% 0.0000% 1.2315% 34 2.2486% 0.3072% 0.0021% 0.0000% 0.0000% 2.3111% 35 2.3029% 0.9410% 0.0185% 0.0000% 0.0000% 1.3085% 35 2.2242% 0.3423% 0.0027% 0.0000% 0.0000% 1.9556% 36 2.2063% 1.0231% 0.0230% 0.0000% 0.0000% 1.3878% 36 2.1946% 0.3795% 0.0034% 0.0000% 0.0000% 1.6296% 37 2.1075% 1.1062% 0.0282% 0.0000% 0.0000% 1.4694% 37 2.1602% 0.4185% 0.0042% 0.0000% 0.0000% 1.3333% 38 2.0072% 1.1901% 0.0344% 0.0001% 0.0000% 1.5464% 38 2.1215% 0.4594% 0.0051% 0.0000% 0.0000% 1.0667% 39 1.9061% 1.2739% 0.0416% 0.0001% 0.0000% 1.6187% 39 2.0789% 0.5020% 0.0063% 0.0000% 0.0000% 0.8296% 40 1.8050% 1.3573% 0.0499% 0.0001% 0.0000% 1.6863% 40 2.0328% 0.5462% 0.0077% 0.0000% 0.0000% 0.6222% 41 1.7046% 1.4397% 0.0595% 0.0002% 0.0000% 1.7493% 41 1.9836% 0.5918% 0.0092% 0.0000% 0.0000% 0.4444% 42 1.6053% 1.5204% 0.0704% 0.0002% 0.0000% 1.8076% 42 1.9315% 0.6388% 0.0111% 0.0000% 0.0000% 0.2963% 43 1.5077% 1.5989% 0.0828% 0.0003% 0.0000% 1.8612% 43 1.8772% 0.6869% 0.0132% 0.0000% 0.0000% 0.1778% 44 1.4124% 1.6747% 0.0969% 0.0004% 0.0000% 1.9102% 44 1.8208% 0.7360% 0.0157% 0.0000% 0.0000% 0.0889% 45 1.3196% 1.7473% 0.1127% 0.0005% 0.0000% 1.9545% 45 1.7628% 0.7859% 0.0185% 0.0000% 0.0000% 0.0296% 46 1.2297% 1.8161% 0.1303% 0.0007% 0.0000% 1.9942% 46 1.7034% 0.8363% 0.0217% 0.0000% 0.0000% - 47 1.1430% 1.8807% 0.1500% 0.0008% 0.0000% 2.0292% 47 1.6430% 0.8872% 0.0254% 0.0001% 0.0000% - 48 1.0598% 1.9405% 0.1717% 0.0011% 0.0000% 2.0595% 48 1.5820% 0.9383% 0.0295% 0.0001% 0.0000% - 49 0.9802% 1.9954% 0.1956% 0.0014% 0.0000% 2.0851% 49 1.5205% 0.9894% 0.0341% 0.0001% 0.0000% - 50 0.9044% 2.0448% 0.2218% 0.0017% 0.0000% 2.1061% 50 1.4589% 1.0403% 0.0393% 0.0001% 0.0000% - 51 0.8324% 2.0884% 0.2504% 0.0021% 0.0000% 2.1224% 51 1.3974% 1.0908% 0.0451% 0.0001% 0.0000% - 52 0.7643% 2.1261% 0.2814% 0.0027% 0.0000% 2.1341% 52 1.3362% 1.1406% 0.0515% 0.0002% 0.0000% - 53 0.7002% 2.1576% 0.3150% 0.0033% 0.0000% 2.1411% 53 1.2755% 1.1896% 0.0586% 0.0002% 0.0000% - 54 0.6400% 2.1827% 0.3511% 0.0040% 0.0000% 2.1434% 54 1.2156% 1.2375% 0.0665% 0.0003% 0.0000% - 55 0.5836% 2.2013% 0.3898% 0.0049% 0.0000% 2.1411% 55 1.1567% 1.2842% 0.0751% 0.0003% 0.0000% - 56 0.5310% 2.2134% 0.4311% 0.0060% 0.0000% 2.1341% 56 1.0988% 1.3294% 0.0846% 0.0004% 0.0000% - 57 0.4821% 2.2189% 0.4750% 0.0073% 0.0000% 2.1224% 57 1.0422% 1.3730% 0.0949% 0.0005% 0.0000% - 58 0.4367% 2.2180% 0.5214% 0.0088% 0.0000% 2.1061% 58 0.9869% 1.4148% 0.1061% 0.0006% 0.0000% - 59 0.3948% 2.2107% 0.5704% 0.0105% 0.0000% 2.0851% 59 0.9331% 1.4545% 0.1183% 0.0007% 0.0000% - 60 0.3561% 2.1971% 0.6218% 0.0126% 0.0000% 2.0595% 60 0.8809% 1.4921% 0.1315% 0.0009% 0.0000% - 61 0.3205% 2.1776% 0.6754% 0.0149% 0.0000% 2.0292% 61 0.8303% 1.5274% 0.1457% 0.0011% 0.0000% - 62 0.2879% 2.1522% 0.7313% 0.0177% 0.0000% 1.9942% 62 0.7815% 1.5602% 0.1610% 0.0013% 0.0000% - 63 0.2580% 2.1213% 0.7892% 0.0209% 0.0000% 1.9545% 63 0.7344% 1.5904% 0.1774% 0.0015% 0.0000% - 64 0.2308% 2.0852% 0.8490% 0.0246% 0.0000% 1.9102% 64 0.6891% 1.6179% 0.1949% 0.0018% 0.0000% - 65 0.2060% 2.0443% 0.9104% 0.0288% 0.0000% 1.8612% 65 0.6457% 1.6426% 0.2136% 0.0021% 0.0000% - 66 0.1835% 1.9988% 0.9732% 0.0336% 0.0000% 1.8076% 66 0.6042% 1.6645% 0.2335% 0.0025% 0.0000% - 67 0.1631% 1.9493% 1.0372% 0.0391% 0.0001% 1.7493% 67 0.5645% 1.6833% 0.2546% 0.0029% 0.0000% - 68 0.1447% 1.8960% 1.1021% 0.0453% 0.0001% 1.6863% 68 0.5267% 1.6991% 0.2770% 0.0034% 0.0000% - 69 0.1281% 1.8395% 1.1675% 0.0523% 0.0001% 1.6187% 69 0.4907% 1.7119% 0.3005% 0.0040% 0.0000% - 70 0.1131% 1.7801% 1.2333% 0.0602% 0.0001% 1.5464% 70 0.4566% 1.7215% 0.3253% 0.0047% 0.0000% - 71 0.0997% 1.7182% 1.2989% 0.0691% 0.0002% 1.4694% 71 0.4242% 1.7280% 0.3513% 0.0055% 0.0000% - 72 0.0877% 1.6544% 1.3642% 0.0791% 0.0002% 1.3878% 72 0.3936% 1.7315% 0.3786% 0.0063% 0.0000% - 73 0.0770% 1.5889% 1.4287% 0.0902% 0.0002% 1.3085% 73 0.3648% 1.7318% 0.4070% 0.0073% 0.0000% - 74 0.0675% 1.5222% 1.4921% 0.1026% 0.0003% 1.2315% 74 0.3376% 1.7291% 0.4367% 0.0084% 0.0000% - 75 0.0590% 1.4547% 1.5540% 0.1163% 0.0004% 1.1569% 75 0.3120% 1.7234% 0.4675% 0.0096% 0.0000% - 76 0.0514% 1.3867% 1.6140% 0.1315% 0.0004% 1.0845% 76 0.2880% 1.7147% 0.4994% 0.0111% 0.0000% - 77 0.0448% 1.3187% 1.6718% 0.1482% 0.0005% 1.0146% 77 0.2655% 1.7032% 0.5324% 0.0126% 0.0000% - 78 0.0389% 1.2509% 1.7270% 0.1666% 0.0007% 0.9469% 78 0.2444% 1.6889% 0.5665% 0.0144% 0.0000% - 79 0.0337% 1.1837% 1.7792% 0.1867% 0.0008% 0.8816% 79 0.2247% 1.6719% 0.6015% 0.0164% 0.0000% - 80 0.0292% 1.1174% 1.8282% 0.2087% 0.0010% 0.8187% 80 0.2064% 1.6524% 0.6374% 0.0186% 0.0000% - 81 0.0252% 1.0522% 1.8736% 0.2326% 0.0012% 0.7580% 81 0.1893% 1.6303% 0.6742% 0.0211% 0.0000% - 82 0.0217% 0.9883% 1.9151% 0.2585% 0.0015% 0.6997% 82 0.1733% 1.6060% 0.7117% 0.0238% 0.0000% - 83 0.0186% 0.9261% 1.9524% 0.2866% 0.0018% 0.6437% 83 0.1586% 1.5795% 0.7499% 0.0268% 0.0000% - 84 0.0160% 0.8657% 1.9852% 0.3169% 0.0021% 0.5901% 84 0.1449% 1.5509% 0.7887% 0.0302% 0.0001% - 85 0.0137% 0.8072% 2.0134% 0.3495% 0.0025% 0.5388% 85 0.1322% 1.5204% 0.8280% 0.0339% 0.0001% - 86 0.0117% 0.7508% 2.0368% 0.3844% 0.0030% 0.4898% 86 0.1205% 1.4881% 0.8676% 0.0380% 0.0001% - 87 0.0099% 0.6966% 2.0551% 0.4216% 0.0036% 0.4431% 87 0.1097% 1.4543% 0.9075% 0.0424% 0.0001% - 88 0.0084% 0.6447% 2.0683% 0.4614% 0.0043% 0.3988% 88 0.0997% 1.4190% 0.9475% 0.0474% 0.0001% - 89 0.0071% 0.5952% 2.0762% 0.5035% 0.0051% 0.3569% 89 0.0905% 1.3824% 0.9876% 0.0528% 0.0001% - 90 0.0060% 0.5482% 2.0789% 0.5482% 0.0060% 0.3172% 90 0.0821% 1.3446% 1.0275% 0.0586% 0.0001% - 91 0.0051% 0.5035% 2.0762% 0.5952% 0.0071% 0.2799% 91 0.0743% 1.3059% 1.0672% 0.0650% 0.0002% - 92 0.0043% 0.4614% 2.0683% 0.6447% 0.0084% 0.2449% 92 0.0672% 1.2664% 1.1065% 0.0720% 0.0002% - 93 0.0036% 0.4216% 2.0551% 0.6966% 0.0099% 0.2122% 93 0.0607% 1.2262% 1.1453% 0.0796% 0.0002% - 94 0.0030% 0.3844% 2.0368% 0.7508% 0.0117% 0.1819% 94 0.0548% 1.1855% 1.1835% 0.0878% 0.0003% - 95 0.0025% 0.3495% 2.0134% 0.8072% 0.0137% 0.1539% 95 0.0493% 1.1444% 1.2209% 0.0967% 0.0003% - 96 0.0021% 0.3169% 1.9852% 0.8657% 0.0160% 0.1283% 96 0.0444% 1.1030% 1.2574% 0.1064% 0.0004% - 97 0.0018% 0.2866% 1.9524% 0.9261% 0.0186% 0.1050% 97 0.0399% 1.0616% 1.2928% 0.1167% 0.0005% - 98 0.0015% 0.2585% 1.9151% 0.9883% 0.0217% 0.0840% 98 0.0358% 1.0202% 1.3271% 0.1279% 0.0005% - 99 0.0012% 0.2326% 1.8736% 1.0522% 0.0252% 0.0653% 99 0.0321% 0.9789% 1.3600% 0.1398% 0.0006% - 100 0.0010% 0.2087% 1.8282% 1.1174% 0.0292% 0.0490% 100 0.0287% 0.9379% 1.3915% 0.1527% 0.0007% - 101 0.0008% 0.1867% 1.7792% 1.1837% 0.0337% 0.0350% 101 0.0257% 0.8973% 1.4214% 0.1664% 0.0009% - 102 0.0007% 0.1666% 1.7270% 1.2509% 0.0389% 0.0233% 102 0.0229% 0.8571% 1.4496% 0.1811% 0.0010% - 103 0.0005% 0.1482% 1.6718% 1.3187% 0.0448% 0.0140% 103 0.0204% 0.8175% 1.4760% 0.1967% 0.0012% - 104 0.0004% 0.1315% 1.6140% 1.3867% 0.0514% 0.0070% 104 0.0182% 0.7786% 1.5005% 0.2134% 0.0013% - 105 0.0004% 0.1163% 1.5540% 1.4547% 0.0590% 0.0023% 105 0.0162% 0.7405% 1.5230% 0.2310% 0.0015% - 106 0.0003% 0.1026% 1.4921% 1.5222% 0.0675% - 106 0.0144% 0.7031% 1.5434% 0.2498% 0.0018% - 107 0.0002% 0.0902% 1.4287% 1.5889% 0.0770% - 107 0.0127% 0.6666% 1.5616% 0.2696% 0.0021% - 108 0.0002% 0.0791% 1.3642% 1.6544% 0.0877% - 108 0.0113% 0.6311% 1.5775% 0.2905% 0.0024% - 109 0.0002% 0.0691% 1.2989% 1.7182% 0.0997% - 109 0.0100% 0.5966% 1.5911% 0.3126% 0.0027% - 110 0.0001% 0.0602% 1.2333% 1.7801% 0.1131% - 110 0.0088% 0.5631% 1.6023% 0.3358% 0.0031% - 111 0.0001% 0.0523% 1.1675% 1.8395% 0.1281% - 111 0.0078% 0.5307% 1.6111% 0.3601% 0.0036% - 112 0.0001% 0.0453% 1.1021% 1.8960% 0.1447% - 112 0.0069% 0.4994% 1.6174% 0.3856% 0.0041% - 113 0.0001% 0.0391% 1.0372% 1.9493% 0.1631% - 113 0.0060% 0.4692% 1.6212% 0.4123% 0.0046% - 114 0.0000% 0.0336% 0.9732% 1.9988% 0.1835% - 114 0.0053% 0.4402% 1.6224% 0.4402% 0.0053% - 115 0.0000% 0.0288% 0.9104% 2.0443% 0.2060% - 115 0.0046% 0.4123% 1.6212% 0.4692% 0.0060% - 116 0.0000% 0.0246% 0.8490% 2.0852% 0.2308% - 116 0.0041% 0.3856% 1.6174% 0.4994% 0.0069% - 117 0.0000% 0.0209% 0.7892% 2.1213% 0.2580% - 117 0.0036% 0.3601% 1.6111% 0.5307% 0.0078% - 118 0.0000% 0.0177% 0.7313% 2.1522% 0.2879% - 118 0.0031% 0.3358% 1.6023% 0.5631% 0.0088% - 119 0.0000% 0.0149% 0.6754% 2.1776% 0.3205% - 119 0.0027% 0.3126% 1.5911% 0.5966% 0.0100% - 120 0.0000% 0.0126% 0.6218% 2.1971% 0.3561% - 120 0.0024% 0.2905% 1.5775% 0.6311% 0.0113% - 121 0.0000% 0.0105% 0.5704% 2.2107% 0.3948% - 121 0.0021% 0.2696% 1.5616% 0.6666% 0.0127% - 122 0.0000% 0.0088% 0.5214% 2.2180% 0.4367% - 122 0.0018% 0.2498% 1.5434% 0.7031% 0.0144% - 123 0.0000% 0.0073% 0.4750% 2.2189% 0.4821% - 123 0.0015% 0.2310% 1.5230% 0.7405% 0.0162% - 124 0.0000% 0.0060% 0.4311% 2.2134% 0.5310% - 124 0.0013% 0.2134% 1.5005% 0.7786% 0.0182% - 125 0.0000% 0.0049% 0.3898% 2.2013% 0.5836% - 125 0.0012% 0.1967% 1.4760% 0.8175% 0.0204% - 126 0.0000% 0.0040% 0.3511% 2.1827% 0.6400% - 126 0.0010% 0.1811% 1.4496% 0.8571% 0.0229% - 127 0.0000% 0.0033% 0.3150% 2.1576% 0.7002% - 127 0.0009% 0.1664% 1.4214% 0.8973% 0.0257% - 128 0.0000% 0.0027% 0.2814% 2.1261% 0.7643% - 128 0.0007% 0.1527% 1.3915% 0.9379% 0.0287% - 129 0.0000% 0.0021% 0.2504% 2.0884% 0.8324% - 129 0.0006% 0.1398% 1.3600% 0.9789% 0.0321% - 130 0.0000% 0.0017% 0.2218% 2.0448% 0.9044% - 130 0.0005% 0.1279% 1.3271% 1.0202% 0.0358% - 131 0.0000% 0.0014% 0.1956% 1.9954% 0.9802% - 131 0.0005% 0.1167% 1.2928% 1.0616% 0.0399% - 132 0.0000% 0.0011% 0.1717% 1.9405% 1.0598% - 132 0.0004% 0.1064% 1.2574% 1.1030% 0.0444% - 133 0.0000% 0.0008% 0.1500% 1.8807% 1.1430% - 133 0.0003% 0.0967% 1.2209% 1.1444% 0.0493% - 134 0.0000% 0.0007% 0.1303% 1.8161% 1.2297% - 134 0.0003% 0.0878% 1.1835% 1.1855% 0.0548% - 135 0.0000% 0.0005% 0.1127% 1.7473% 1.3196% - 135 0.0002% 0.0796% 1.1453% 1.2262% 0.0607% - 136 0.0000% 0.0004% 0.0969% 1.6747% 1.4124% - 136 0.0002% 0.0720% 1.1065% 1.2664% 0.0672% - 137 0.0000% 0.0003% 0.0828% 1.5989% 1.5077% - 137 0.0002% 0.0650% 1.0672% 1.3059% 0.0743% - 138 0.0000% 0.0002% 0.0704% 1.5204% 1.6053% - 138 0.0001% 0.0586% 1.0275% 1.3446% 0.0821% - 139 0.0000% 0.0002% 0.0595% 1.4397% 1.7046% - 139 0.0001% 0.0528% 0.9876% 1.3824% 0.0905% - 140 0.0000% 0.0001% 0.0499% 1.3573% 1.8050% - 140 0.0001% 0.0474% 0.9475% 1.4190% 0.0997% - 141 0.0000% 0.0001% 0.0416% 1.2739% 1.9061% - 141 0.0001% 0.0424% 0.9075% 1.4543% 0.1097% - 142 0.0000% 0.0001% 0.0344% 1.1901% 2.0072% - 142 0.0001% 0.0380% 0.8676% 1.4881% 0.1205% - 143 0.0000% 0.0000% 0.0282% 1.1062% 2.1075% - 143 0.0001% 0.0339% 0.8280% 1.5204% 0.1322% - 144 0.0000% 0.0000% 0.0230% 1.0231% 2.2063% - 144 0.0001% 0.0302% 0.7887% 1.5509% 0.1449% - 145 0.0000% 0.0000% 0.0185% 0.9410% 2.3029% - 145 0.0000% 0.0268% 0.7499% 1.5795% 0.1586% - 146 0.0000% 0.0000% 0.0148% 0.8607% 2.3962% - 146 0.0000% 0.0238% 0.7117% 1.6060% 0.1733% - 147 0.0000% 0.0000% 0.0117% 0.7825% 2.4854% - 147 0.0000% 0.0211% 0.6742% 1.6303% 0.1893% - 148 0.0000% 0.0000% 0.0092% 0.7070% 2.5695% - 148 0.0000% 0.0186% 0.6374% 1.6524% 0.2064% - 149 0.0000% 0.0000% 0.0071% 0.6345% 2.6474% - 149 0.0000% 0.0164% 0.6015% 1.6719% 0.2247% - 150 0.0000% 0.0000% 0.0055% 0.5654% 2.7182% - 150 0.0000% 0.0144% 0.5665% 1.6889% 0.2444% - 151 0.0000% 0.0000% 0.0041% 0.4999% 2.7808% - 151 0.0000% 0.0126% 0.5324% 1.7032% 0.2655% - 152 0.0000% 0.0000% 0.0031% 0.4385% 2.8339% - 152 0.0000% 0.0111% 0.4994% 1.7147% 0.2880% - 153 0.0000% 0.0000% 0.0023% 0.3813% 2.8767% - 153 0.0000% 0.0096% 0.4675% 1.7234% 0.3120% - 154 0.0000% 0.0000% 0.0016% 0.3285% 2.9079% - 154 0.0000% 0.0084% 0.4367% 1.7291% 0.3376% - 155 0.0000% 0.0000% 0.0012% 0.2801% 2.9265% - 155 0.0000% 0.0073% 0.4070% 1.7318% 0.3648% - 156 0.0000% 0.0000% 0.0008% 0.2362% 2.9315% - 156 0.0000% 0.0063% 0.3786% 1.7315% 0.3936% - 157 0.0000% 0.0000% 0.0005% 0.1967% 2.9219% - 157 0.0000% 0.0055% 0.3513% 1.7280% 0.4242% - 158 0.0000% 0.0000% 0.0004% 0.1617% 2.8968% - 158 0.0000% 0.0047% 0.3253% 1.7215% 0.4566% - 159 0.0000% 0.0000% 0.0002% 0.1310% 2.8554% - 159 0.0000% 0.0040% 0.3005% 1.7119% 0.4907% - 160 0.0000% 0.0000% 0.0001% 0.1044% 2.7972% - 160 0.0000% 0.0034% 0.2770% 1.6991% 0.5267% - 161 0.0000% 0.0000% 0.0001% 0.0817% 2.7216% - 161 0.0000% 0.0029% 0.2546% 1.6833% 0.5645% - 162 0.0000% 0.0000% 0.0001% 0.0627% 2.6283% - 162 0.0000% 0.0025% 0.2335% 1.6645% 0.6042% - 163 0.0000% 0.0000% 0.0000% 0.0469% 2.5173% - 163 0.0000% 0.0021% 0.2136% 1.6426% 0.6457% - 164 0.0000% 0.0000% 0.0000% 0.0342% 2.3888% - 164 0.0000% 0.0018% 0.1949% 1.6179% 0.6891% - 165 0.0000% 0.0000% 0.0000% 0.0242% 2.2434% - 165 0.0000% 0.0015% 0.1774% 1.5904% 0.7344% - 166 0.0000% 0.0000% 0.0000% 0.0165% 2.0819% - 166 0.0000% 0.0013% 0.1610% 1.5602% 0.7815% - 167 0.0000% 0.0000% 0.0000% 0.0107% 1.9058% - 167 0.0000% 0.0011% 0.1457% 1.5274% 0.8303% - 168 0.0000% 0.0000% 0.0000% 0.0066% 1.7167% - 168 0.0000% 0.0009% 0.1315% 1.4921% 0.8809% - 169 0.0000% 0.0000% 0.0000% 0.0038% 1.5172% - 169 0.0000% 0.0007% 0.1183% 1.4545% 0.9331% - 170 0.0000% 0.0000% 0.0000% 0.0020% 1.3100% - 170 0.0000% 0.0006% 0.1061% 1.4148% 0.9869% - 171 0.0000% 0.0000% 0.0000% 0.0009% 1.0989% - 171 0.0000% 0.0005% 0.0949% 1.3730% 1.0422% - 172 0.0000% 0.0000% 0.0000% 0.0004% 0.8882% - 172 0.0000% 0.0004% 0.0846% 1.3294% 1.0988% - 173 0.0000% 0.0000% 0.0000% 0.0001% 0.6833% - 173 0.0000% 0.0003% 0.0751% 1.2842% 1.1567% - 174 0.0000% 0.0000% 0.0000% 0.0000% 0.4902% - 174 0.0000% 0.0003% 0.0665% 1.2375% 1.2156% - 175 0.0000% 0.0000% 0.0000% 0.0000% 0.3163% - 175 0.0000% 0.0002% 0.0586% 1.1896% 1.2755% - 176 0.0000% 0.0000% 0.0000% 0.0000% 0.1700% - 176 0.0000% 0.0002% 0.0515% 1.1406% 1.3362% - 177 0.0000% 0.0000% 0.0000% 0.0000% 0.0609% - 177 0.0000% 0.0001% 0.0451% 1.0908% 1.3974% - - - - - - - - 178 0.0000% 0.0001% 0.0393% 1.0403% 1.4589% - - - - - - - - 179 0.0000% 0.0001% 0.0341% 0.9894% 1.5205% - - - - - - - - 180 0.0000% 0.0001% 0.0295% 0.9383% 1.5820% - - - - - - - - 181 0.0000% 0.0001% 0.0254% 0.8872% 1.6430% - - - - - - - - 182 0.0000% 0.0000% 0.0217% 0.8363% 1.7034% - - - - - - - - 183 0.0000% 0.0000% 0.0185% 0.7859% 1.7628% - - - - - - - - 184 0.0000% 0.0000% 0.0157% 0.7360% 1.8208% - - - - - - - - 185 0.0000% 0.0000% 0.0132% 0.6869% 1.8772% - - - - - - - - 186 0.0000% 0.0000% 0.0111% 0.6388% 1.9315% - - - - - - - - 187 0.0000% 0.0000% 0.0092% 0.5918% 1.9836% - - - - - - - - 188 0.0000% 0.0000% 0.0077% 0.5462% 2.0328% - - - - - - - - 189 0.0000% 0.0000% 0.0063% 0.5020% 2.0789% - - - - - - - - 190 0.0000% 0.0000% 0.0051% 0.4594% 2.1215% - - - - - - - - 191 0.0000% 0.0000% 0.0042% 0.4185% 2.1602% - - - - - - - - 192 0.0000% 0.0000% 0.0034% 0.3795% 2.1946% - - - - - - - - 193 0.0000% 0.0000% 0.0027% 0.3423% 2.2242% - - - - - - - - 194 0.0000% 0.0000% 0.0021% 0.3072% 2.2486% - - - - - - - - 195 0.0000% 0.0000% 0.0017% 0.2741% 2.2676% - - - - - - - - 196 0.0000% 0.0000% 0.0013% 0.2432% 2.2805% - - - - - - - - 197 0.0000% 0.0000% 0.0010% 0.2143% 2.2872% - - - - - - - - 198 0.0000% 0.0000% 0.0007% 0.1876% 2.2871% - - - - - - - - 199 0.0000% 0.0000% 0.0006% 0.1631% 2.2800% - - - - - - - - 200 0.0000% 0.0000% 0.0004% 0.1406% 2.2655% - - - - - - - - 201 0.0000% 0.0000% 0.0003% 0.1202% 2.2433% - - - - - - - - 202 0.0000% 0.0000% 0.0002% 0.1019% 2.2133% - - - - - - - - 203 0.0000% 0.0000% 0.0001% 0.0855% 2.1751% - - - - - - - - 204 0.0000% 0.0000% 0.0001% 0.0709% 2.1286% - - - - - - - - 205 0.0000% 0.0000% 0.0001% 0.0582% 2.0737% - - - - - - - - 206 0.0000% 0.0000% 0.0000% 0.0471% 2.0104% - - - - - - - - 207 0.0000% 0.0000% 0.0000% 0.0376% 1.9387% - - - - - - - - 208 0.0000% 0.0000% 0.0000% 0.0295% 1.8587% - - - - - - - - 209 0.0000% 0.0000% 0.0000% 0.0228% 1.7707% - - - - - - - - 210 0.0000% 0.0000% 0.0000% 0.0172% 1.6750% - - - - - - - - 211 0.0000% 0.0000% 0.0000% 0.0127% 1.5720% - - - - - - - - 212 0.0000% 0.0000% 0.0000% 0.0091% 1.4623% - - - - - - - - 213 0.0000% 0.0000% 0.0000% 0.0064% 1.3467% - - - - - - - - 214 0.0000% 0.0000% 0.0000% 0.0043% 1.2260% - - - - - - - - 215 0.0000% 0.0000% 0.0000% 0.0027% 1.1013% - - - - - - - - 216 0.0000% 0.0000% 0.0000% 0.0017% 0.9739% - - - - - - - - 217 0.0000% 0.0000% 0.0000% 0.0010% 0.8452% - - - - - - - - 218 0.0000% 0.0000% 0.0000% 0.0005% 0.7168% - - - - - - - - 219 0.0000% 0.0000% 0.0000% 0.0002% 0.5908% - - - - - - - - 220 0.0000% 0.0000% 0.0000% 0.0001% 0.4694% - - - - - - - - 221 0.0000% 0.0000% 0.0000% 0.0000% 0.3550% - - - - - - - - 222 0.0000% 0.0000% 0.0000% 0.0000% 0.2505% - - - - - - - - 223 0.0000% 0.0000% 0.0000% 0.0000% 0.1590% - - - - - - - - 224 0.0000% 0.0000% 0.0000% 0.0000% 0.0841% - - - - - - - - 225 0.0000% 0.0000% 0.0000% 0.0000% 0.0296% -

Continues...

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

Economy class
Belgium
Member #123700
February 27, 2012
4035 Posts
Offline
 Posted: May 17, 2015, 3:39 pm - IP Logged

We've been working on applying the concept of Sums to other lottery types and in a different way.

The Sum is a math process that adds the numbers in a lottery game like Pick 3 to come up with a total or sum of the numbers.

As an example, if the following are some Pick 3 combinations:

 Draw A B C 1 0 5 9 2 7 9 1 3 8 8 8 4 2 3 1

then their sums are as follows:

 Draw A + B + C = Sum 1 0 + 5 + 9 = 14 2 7 + 9 + 1 = 17 3 8 + 8 + 8 = 24 4 2 + 3 + 1 = 6

Now, that's pretty simple and it's what we would call an Inline Sum; meaning it is inline with the combination.

The Inline Sum is in this direction:

 Draw A → B → C → Sum 1 0 → 5 → 9 → 14 2 7 → 9 → 1 → 17 3 8 → 8 → 8 → 24 4 2 → 3 → 1 → 6

There is another way to sum these numbers and it is what we call Insequence; meaning it sums the numbers in a column of the combination as they are drawn.

The Insequence Sum is in this direction:

 Draw A B C 1 0 5 9 ↓ ↓ ↓ ↓ 2 7 9 1 ↓ ↓ ↓ ↓ 3 8 8 8 ↓ ↓ ↓ ↓ Sum 15 22 18

Then moving down the draws the next Insequence Sum is:

 Draw A B C 2 7 9 1 ↓ ↓ ↓ ↓ 3 8 8 8 ↓ ↓ ↓ ↓ 4 2 3 1 ↓ ↓ ↓ ↓ Sum 17 20 10

This Insequence Sum of the Pick 3 numbers follows the same distribution of sums as the Inline Sum.

Below the range of sums and the total count for each sum is shown:

 Sum Count 0 1 1 3 2 6 3 10 4 15 5 21 6 28 7 36 8 45 9 55 10 63 11 69 12 73 13 75 14 75 15 73 16 69 17 63 18 55 19 45 20 36 21 28 22 21 23 15 24 10 25 6 26 3 27 1

We're only going over the introduction of concept of Insequnce Sums right now.

Next we will get into the application to games like Powerball and Mega Millions.

Continues...

 0 0 0 0 1 3 2 3 2 7 6 4 3 7 9 7 4 10 9 16 5 16 34 17 6 32 36 32 7 44 46 43 8 60 60 63 9 67 93 85 10 83 100 123 11 131 123 129 12 131 176 157 13 170 186 181 14 164 215 225 15 216 208 214 16 267 229 229 17 231 260 252 18 254 238 250 19 242 255 213 20 253 236 228 21 229 262 235 22 214 207 196 23 210 172 195 24 178 138 166 25 132 120 118 26 118 94 104 27 93 83 84 28 58 50 51 29 54 30 42 30 32 30 36 31 26 23 15 32 12 9 17 33 6 8 14 34 4 5 5 35 1 2 5 36 0 1 1

Is there a reason why you picked 4 drawings for the vertical sum?

That sum can range from 0 to 36.

What did you find in it that is worth a bet?

Local vertical sums for four drawings are above.

The Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
3675 Posts
Offline
 Posted: May 17, 2015, 3:44 pm - IP Logged

Using the Mega Millions we can look up the probabilities a particular Insequence Sum was likely to occur.

 Year Month Day A B C D E MB 2015 5 8 9 21 25 66 72 7 2015 5 12 14 30 33 36 44 2 2015 5 15 11 17 21 36 74 15 - - Sum 34 68 79 138 190 24

Looking a the Mega Ball (MB) to start, we can see the Insequence Sum is 24.

In the Mega Millions probability chart we find there was a 5.0074% probability of a sum 24 happening.

 Mega Millions Sum A B C D E MB 24 2.1286% 0.0709% 0.0001% 0.0000% 0.0000% 5.0074%

Also, this just happens to be the most frequent Insequence Sum for the Mega Ball.

Continues...

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
3675 Posts
Offline
 Posted: May 17, 2015, 4:09 pm - IP Logged
 0 0 0 0 1 3 2 3 2 7 6 4 3 7 9 7 4 10 9 16 5 16 34 17 6 32 36 32 7 44 46 43 8 60 60 63 9 67 93 85 10 83 100 123 11 131 123 129 12 131 176 157 13 170 186 181 14 164 215 225 15 216 208 214 16 267 229 229 17 231 260 252 18 254 238 250 19 242 255 213 20 253 236 228 21 229 262 235 22 214 207 196 23 210 172 195 24 178 138 166 25 132 120 118 26 118 94 104 27 93 83 84 28 58 50 51 29 54 30 42 30 32 30 36 31 26 23 15 32 12 9 17 33 6 8 14 34 4 5 5 35 1 2 5 36 0 1 1

Is there a reason why you picked 4 drawings for the vertical sum?

That sum can range from 0 to 36.

What did you find in it that is worth a bet?

Local vertical sums for four drawings are above.

We used 4 draws to show the Insequence Sums move down the draw sequence.

It's just a sum of only 3 numbers as shown below.

 Draw A B C 1 0 5 9 ↓ ↓ ↓ ↓ 2 7 9 1 ↓ ↓ ↓ ↓ 3 8 8 8 ↓ ↓ ↓ ↓ Sum 15 22 18

the next three sum in our example draws is:

 Draw A B C 2 7 9 1 ↓ ↓ ↓ ↓ 3 8 8 8 ↓ ↓ ↓ ↓ 4 2 3 1 ↓ ↓ ↓ ↓ Sum 17 20 10

note the three sums has moved down the draws.

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
3675 Posts
Offline
 Posted: May 17, 2015, 4:28 pm - IP Logged

Using the Mega Millions we can look up the probabilities a particular Insequence Sum was likely to occur.

 Year Month Day A B C D E MB 2015 5 8 9 21 25 66 72 7 2015 5 12 14 30 33 36 44 2 2015 5 15 11 17 21 36 74 15 - - Sum 34 68 79 138 190 24

Looking a the Mega Ball (MB) to start, we can see the Insequence Sum is 24.

In the Mega Millions probability chart we find there was a 5.0074% probability of a sum 24 happening.

 Mega Millions Sum A B C D E MB 24 2.1286% 0.0709% 0.0001% 0.0000% 0.0000% 5.0074%

Also, this just happens to be the most frequent Insequence Sum for the Mega Ball.

Continues...

Moving on we can see what the probabilies were for each of the columns.

 Year Month Day A B C D E MB 2015 5 8 9 21 25 66 72 7 2015 5 12 14 30 33 36 44 2 2015 5 15 11 17 21 36 74 15 - - Sum 34 68 79 138 190 24

The probabilities for each Insequence Sum.

 / Mega Millions A B C D E MB Sum 34 68 79 138 190 24 Proability 2.2486% 1.6991% 0.6015% 1.3446% 2.1215% 5.0074%

Continues...

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

South Carolina
United States
Member #18322
July 9, 2005
1704 Posts
Offline
 Posted: May 17, 2015, 4:42 pm - IP Logged

How do you use any of this analysis to figure out what numbers to play for the next PB/MM game ???

The Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
3675 Posts
Offline
 Posted: May 17, 2015, 4:50 pm - IP Logged

How do you use any of this analysis to figure out what numbers to play for the next PB/MM game ???

We will be getting to that in a bit.

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 #59354
March 13, 2008
3962 Posts
Offline
 Posted: May 17, 2015, 5:17 pm - IP Logged

I like the way you think, gona automate my wheels

RL

Working on my Ph.D.  "University of hard Knocks"

I will consider the opinion that my winnings are a product of chance if you are willing to consider

they are not.  Many great discoveries come while searching for something else

Trump / 2016 & 2020

The Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
3675 Posts
Offline
 Posted: May 17, 2015, 7:03 pm - IP Logged

We use the Insequence Sums and Probability tables to select numbers for the next drawing.

Below are the last two Mega Millions draws as of 2015-05-17.

 Year Month Day A B C D E MB 2015 5 12 14 30 33 36 44 2 2015 5 15 11 17 21 36 74 15

From this the next draw is unknown.

 Year Month Day A B C D E MB 2015 5 12 14 30 33 36 44 2 2015 5 15 11 17 21 36 74 15 2015 5 19 ?? ?? ?? ?? ?? ??

However, we do know the Insequence Sums.

This becomes a matter of 'What comes next?' based on what we know about the previous two draws and the Insequence Sums.

We will look at the Mega Ball (MB) to start.

The last two MB numbers were 2 and 15.

This can be setup as an equation like this: 2 + 15 + ?? = Sum

The Sum is already known and we know the probabilities of each Sum.

Now, we can guess the next MB ?? by subtracting 2 and 15 from the Sum like so: ?? = Sum - 2 - 17

Continues...

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
3675 Posts
Offline
 Posted: May 17, 2015, 7:52 pm - IP Logged

We use the Insequence Sums and Probability tables to select numbers for the next drawing.

Below are the last two Mega Millions draws as of 2015-05-17.

 Year Month Day A B C D E MB 2015 5 12 14 30 33 36 44 2 2015 5 15 11 17 21 36 74 15

From this the next draw is unknown.

 Year Month Day A B C D E MB 2015 5 12 14 30 33 36 44 2 2015 5 15 11 17 21 36 74 15 2015 5 19 ?? ?? ?? ?? ?? ??

However, we do know the Insequence Sums.

This becomes a matter of 'What comes next?' based on what we know about the previous two draws and the Insequence Sums.

We will look at the Mega Ball (MB) to start.

The last two MB numbers were 2 and 15.

This can be setup as an equation like this: 2 + 15 + ?? = Sum

The Sum is already known and we know the probabilities of each Sum.

Now, we can guess the next MB ?? by subtracting 2 and 15 from the Sum like so: ?? = Sum - 2 - 17

Continues...

typo in the last post.

The equation should be ?? = Sum - 2 - 15.

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