Rather than debunk any of these theories of lottery fraud or rigging, this article reveals the trends and patterns of winning lottery numbers for accepted scrutiny using basic material examination. It uses the results of the MegaMillions lottery and consists of the adjacent analyzes:
distribution of winning numbers over continuance behavioral stratification of numbers based on numerical position affair between mutually winning numbers bourgeois differences between winning numbers winning unit closeness
While such scrutiny has the plausible to yield favorable results, such as identifying the continuance or deficit of "higher quality numbers" to play, it is presented so as to beseech to those excited in amount patterns. MegaMillions Narration
Recently, MegaMillions drew the largest jackpot ever recorded at $370 million, exceeding the preceding draw up held by PowerBall.2 The prizes were not always so capacious, nor did the participants span the Usa. Inception heart in 1996, MegaMillions originally existed under a discrepant nomer: "The Burly Pastime." For two years this lottery was haggard weekly on Fridays until 1998, when a Tuesday delineation was added. Over the foregone eleven years, the character of participating states has doubled from one six to twelve. Although there are babe interstate variations regarding how jackpots are paid to winners, the basic merriment play remains the identical.3
A unmarried dollar in MegaMillions purchases a 1 in 175,711,536 chance of transplanting the jackpot. A player may suffrage for a "QuickPick" establish of numbers generated automatically by a pc or they may choose to choose their own numbers. Owing to 2005, MegaMillions allows players to select five numbers between 1 and 56 plus a sixth symbol, the MegaBall, between 1 and 46. This, but, was not always the choice pool. When the "Capacious Pastime" was conceived, players were prone a pool of numbers 1 buttoned up 50 to select for their anterior five balls and numbers 1 wound up 25 for their sixth. Day one in 1999, players were offered the numbers 1 wound up 50 for the five usual balls and 1 wrapped up 36 for the sixth. When the merriment became MegaMillions in 2002, players selected numbers between 1 and 52 for both the five universal balls and the MegaBall.4
As a headmost transaction, it was de rigueur to pay for a party of MegaMillions’ lottery numbers. Happily, the Au courant Jersey Lottery website has an archive of all winning numbers on account of Sept 6, 1996.5 As an added bonus, the archive of numbers exists in both HTML format for a boss mesh presentation and as a delimited folder which is conducive for importing into a database. For the purposes of this argument, the winning lottery numbers were imported into Microsoft SQL Server Especial for processing queries. Subsequent graphs were then created with Microsoft Excel to imagine the trends and behaviour.6
The delimited folder of winning lottery numbers contained the results for 1078 drawings and provides the adjacent fields:
Year – formatted as YYYY Month – formatted as MM Date – formatted as DD Age of Week – formatted as Tuesday and Friday Ball 1, 2, 3, 4, 5 – as an integer MegaBall – as an integer Passion Payout – when display, formatted as a decimal payment Period – formatted as YYYYMMDD Distribution of Winning Numbers Over Clock
The basic trend analysed was if or not the numbers happen with an still distribution. Balls 1, 2, 3, 4 and 5 were consolidated into a unmarried data to analyse their overall closeness of occurence. Everyone seperate narration of the lottery – two editions of BigGame and two editions of MegaMillions – were analysed independently to distinguish any outlying lifetime. Thereupon, a collateral classification was performed to decide the distribution of the MegaBall symbol. The adjacent charts feature the amount of times everyone digit was selected over the progression of the the filled span of MegaMillion’s drawings.
When the BigGame debuted, players were allowed to select numbers between 1 and 50 with a MegaBall ranging from 1 to 25. Everyone quantity has been stressed at least eight times as compared with the most frequent winners that occurred twenty-seven times. Overall, the numbers chalk up been stressed around seventeen times everyone. The most frequent symbol, 35, exceeds the rapacious by 2.76 deviations as compared with the least occurring cipher, 49, which lagged the penny-pinching by -2.46 deviations. The cardinal chronicle of the BigGame is the solitary delineation with a descending trend border that when combined with the deviations finger the distribution as slightly abnormal. The MegaBall amount 17 appeared fifteen times while 23 occurred isolated once. The morals MegaBall was strained seven times.
The BigGame was changed on January 13, 1999 to exaggeration the digit of available MegaBalls from pool of 25 to 36. The important represantation pool remained the duplicate, ranging between 1 and 50. Everyone quantity has been stressed at least twenty-one times while the most often taut symbol has appeared forty-six times. Overall, all numbers accept been pinched roughly thirty-four times. One one digit, 4, exceeds two deviations from the greedy at 2.11 deviations. 19 was -2.29 deviations from the greedy, the peerless character to seem less than two deviations from customary. The moment anecdote of the BigGame has the flattest trend border that when combined with the deviations button down the distribution as habitual. The numbers 2 and 3 were pinched the most as MegaBalls at fifteen times apiece while 11 was strained the fewest at four times. On principles, everyone MegaBall appeared ten times.
On May 15, 2002 the MegaMillions delineation expanded the pool of numbers available to players to gamut from 1 finished 52. Everyone figure has been tense at least twenty times while the most often stressed unit has appeared forty-five times. Overall, all numbers accept been tense roughly thirty-one times. The two most taut numbers, 32 and 10, are the alone two numbers to deviate from the close by a influence larger than two; 2.59 and 2.41 respectively. The least pinched numeral, 33, is onliest -2.04 deviations from the penurious. Although the linear trend borderline rises modestly, the influential numbers hog a relatively yet distribution over extent. The MegaBall ranges from 1 terminated 52. The amount 34 was stressed the most on 14 occasions while 51 appeared by oneself once. Overall, everyone MegaBall has appeared an guideline of six times.
Players retain had the choice of picture numbers between 1 and 56 thanks to June 22, 2005. Every digit has been tense at least ten times while the most often pinched cipher has appeared thirty times. Overall, everyone unit has appeared an customary of twenty times. In spite of activity pinched the most, both 7 and 53 are sole 2.17 deviations from the beggarly. Yet the least strained amount, 47, is -2.17 deviations from the penurious. Overall, the valuable numbers get a relatively still distribution over era. The MegaBall ranges from 1 on ice 46. 4 and 42 ability the most stressed position with nine wins while lousy with numbers round up the low limitation with one two wins. Overall, everyone MegaBall has appeared an standard of five times.
Behavioral Stratification of Numbers Based on Numerical Position
After looking at the behaviour of the numbers in aggregate, the adventure of numbers respective to their position was analysed. Unfortunately, the lottery does not store the numbers in the classification they were tense. Rather, the news data saves the winning lottery numbers in ascending computation.7 As such, positional discussion focused on how the numbers are stratified within their obsessed position.
Each of the six graphs betoken the top fifteen numbers per position:
Leafy bars emblematize the ongoing narration of MegaMillions where players choose from numbers 1 fini 56 and a MegaBall digit of 1 completed 46. Melancholy bars exemplify the weighted organization of a unit’s winning percentage from all MegaMillions picture variations because 1996. The bloodshot limit represents a five variable polynomial trend border to the winning percentage of the contemporary MegaMillions illustration pool.
Ignoring the account differences in quantity pooling across the lottery’s growth, the anterior ball has ranged between 1 and 37 with an sample winning quantity of 8. Looking at the ongoing anecdote of MegaMillions, the antecedent ball shows a steeper trend curve with almost twice the drawings on winning numbers as any other ball. MegaMillions winning numbers ranged from 1 finished 37 with an guideline winning ball of 17 in that 2002. The numbers 7, 5, 1, 2 and 3 act for 39.91% of the winning numbers on the cardinal ball.
Ignoring the narration differences in symbol pooling across the lottery’s vitality, the moment ball has ranged between 2 and 46 with an guideline winning digit of 17. Looking at the ongoing anecdote of MegaMillions, the moment ball shows a shallower trend curve. MegaMillions winning numbers ranged from 2 complete 43 with an principles winning ball of 22 on account of 2002. The numbers 13, 12, 17, 25, 10, 18, 20, 14 and 21 appear as 40.77% of the winning numbers on the moment ball.
Ignoring the novel differences in digit pooling across the lottery’s being, the third ball has ranged between 5 and 54 with an customary winning amount of 29. Looking at the contemporary history of MegaMillions, the third ball shows the shallowest trend curve. MegaMillions winning numbers ranged from 3 over 54 with an criterion winning ball of 26 because 2002. The numbers 20, 35, 31, 25, 37, 26, 32, 24, 23 and 38 act for 39.06% of the winning numbers on the third ball.
Ignoring the story differences in digit pooling across the lottery’s existence, the fourth ball has ranged between 5 and 55 with an criterion winning symbol of 35. Looking at the now novel of MegaMillions, the fourth ball’s trend curve begins to steepen. MegaMillions winning numbers ranged from 7 wrapped up 55 with an criterion winning ball of 35 because 2002. The numbers 51, 42, 46, 36, 48, 40, 38, 39 and 49 equal 40.77% of the winning numbers on the fourth ball.
Ignoring the legend differences in amount pooling across the lottery’s career, the fifth ball has ranged between 13 and 56 with an guideline winning digit of 44. Looking at the happening narration of MegaMillions, the fifth ball’s trend curve steepens sharply. MegaMillions winning numbers ranged from 26 complete 56 with an guideline winning ball of 41 by reason of 2002. The numbers 53, 54, 56, 52 and 55 body 42.92% of the winning numbers on the fifth ball.
Ignoring the anecdote differences in character pooling across the lottery’s existence, the MegaBall has ranged between 1 and 52 with an standard winning unit of 20. Looking at the happening account of MegaMillions, the MegaBall’s trend curve is relatively apartment lodgings. MegaBall winning numbers ranged from 1 fini 46 with an principles winning ball of 23 because 2002. The numbers on the graph act for 44.64% of the winning numbers on the MegaBall.
Additionally, an dialogue was performed to impel which numbers "triumph calm." After all, a player does not want to pick all six numbers in plan to achievement bread from MegaMillions. Thence, all credible combinations of balls 1, 2, 3, 4 and 5 were formed to analyse the occurence of ball relationships.
There are ten combinations of ball pairs: [1 2], [1 3], [1 4], [1 5], [2 3], [2 4], [2 5], [3 4], [3 5], & [4 5]. Using the MegaMillions facts, there are 10,780 potential pairs of which 1503 are uncommon over the lottery’s activity. In the now legend of MegaMillions, there are 2330 potential pairs of which 1202 are rare. Pairs of numbers develop wholly often; 1426 pairs gain occurred 10,703 times throughout the lottery’s vitality compared with 692 pairs that chalk up appeared 1820 times in on account of the fourth novel of MegaMillions began.
The graph at ethical shows that in the happening novel of MegaMillions, pairs of numbers triumph repeatedly wholly frequently. Over the lottery’s career, specific pairs keep won extremely regularly.
There are ten combinations of ball triples: [1 2 3], [1 2 4], [1 2 5], [1 3 4], [1 3 5], [1 4 5], [2 3 4], [2 3 5], [2 4 5], & [3 4 5]. There are 10,780 feasible triples of which 8675 are rare over the lottery’s duration. Within the bygone narration of MegaMillions, there are 2330 imaginable triples of which 2245 are particular. 1789 sets of triplets corner repeated 3894 times in the activity of the lottery. Five sets of triplets bear occurred five times and two sets of triplets include occurred six times. In the foregone year, on the other hand, one shot twenty-three sets of three balls admit repeated twice.
In the graph to the fly, there annex been multifarious repeat winning combinations of three numbers in the activity of the lottery, although it is a less frequent phenomenon in the happening chronicle. Quadruples
There are five combinations of ball quadruples: [1 2 3 4], [1 2 3 5], [1 2 4 5], [1 3 4 5], & [2 3 4 5]. There are 5390 credible quadruplets of which 5328 are single over the lottery’s vitality. In that June 22, 2005 there are 1165 solo combinations of feasible quadruplets. Sixty-two sets of four numbers keep repeated twice because MegaMillions began. There annex been naught sets of quadruplets winning deeper than once in the now chronicle of MegaMillions.
There is single one combination of ball quintuples: [1 2 3 4 5]. Apart one place of five numbers has ever repeated twice in the narration of MegaMillions: (11, 14, 18, 33, 48).
A constant extent of analysing numeral groups was to determine the trends by which numbers differ from one another. For instance, while probability gives the numbers 20, 21, 22, 23 and 24 the equivalent chance of appearing as any other combination, is it feasible? The numbers for the most original story of MegaMillions were scrutinized to arbitrate whether there is a average contrast between everyone ball.
The graph depicts the alteration between the 1st/2nd position, 2nd/3rd position, 3rd/4th position and 4th/5th position. Overall, everyone split differs by an principles of nine (indicated by intersecting love). 70% of the discongruity distribution aspersion between 1 and 20. While it is unlikely for the adequate series to possess peculiar (tight or mere broad) differences, it is not necessarily an scarce locus. Thanks to 2005, there retain been twenty-six occasions where two subsequent numbers include differed by extra than 30.
Analyzing the distribution of numbers over interval individual if half the picture in terms of any liable symbol’s propensity in relation to winning. Another angle to assent to was the secular closeness by which a character wins. For instance, a amount may keep won on thirty occasions, on the contrary possibly they were all two years ago. To scan this behaviour, the chronology delta between everyone symbol’s appearance was cataloged to set up statistics for all numbers and for everyone digit across the vitality of the fourth chronicle of MegaMillions. Then, the dialogue was repeated using solitary the most modern six months of news to discern the cross shorten of numbers that score often consistently and which numbers are just a now brilliance in the pan.
This graph depicts the numbers with the shortest, principles bit between appearance on account of legend four of MegaMillions began in 2005. Simply having a low standard, on the other hand, is not a acceptable indicator that a quantity occurs often. The dispirited column depicts the ratio of wins that occurred with a age delta below principles. Numbers with a ratio above 50% are indicative of winning ofttimes in “clumps” whereas numbers below 50% emblematize a wider spread of bombshell closeness. It should be famous, on the contrary, that low closeness “clumping” further comes with a in agreement dearth of appearance.
The six month graph replicates the logic get going above on the vitality graph, peerless this allotment restricted to winning numbers over the ended six months. The intersecting cross reduce of often winning numbers enact those that not isolated conquest over date on the contrary those that annex demonstrated a virgin propensity for appearing usually. Over six months, there is a span of numbers that obtain both a low delta of days between appearance ’’and’’ a elevated ratio of occurrences on a amassed frequent justification than criterion. Equally, a handful of the new numbers acquire low ratios, indicating their principles is skewed by bursts of low delta wins counterbalance by diverse frequent gaps of knowing length.
Interesting as these trends may be, they testament not boost in manufacture the odds of winning the MegaMillions lottery any greater whether the step is de facto objective and adventitious. Nevertheless, in the calamity there is some peculiar thing skewing the ball choice such that any of these trends last, a player stands a mildly exceptional chance of winning a limited affection ended the choice of weighted numbers.
1 "The Lottery is Rigged." Uncoverer. Accessed Oct 2007 from http://www.uncoveror.com/lottery.htm.
2 Roland, Neil. "Mega Millions Lottery Jackpot Forthwith List $370 Million." Bloomberg. Accessed Oct 2007 from http://www.bloomberg.com/apps/news?pid=20601103&sid=afUgc0t0u3hg&refer=us.
3 "How to Play: Play the pastime." MegaMillions.com_. Accessed Oct 2007 from http://megamillions.com/howtoplay/play_game.aspgame.asp.
4 "Approximately Us: Pastime Account." MegaMillions.com_. Accessed Oct 2007 from http://megamillions.com/aboutus/game_history.asphistory.asp.
5 Just out Jersey Lottery. Accessed Sept 2007 from http://www.state.nj.us/lottery/data/big.dat.
6 Microsoft SQL Server Certain. Accessed Sep 2007 from http://www.microsoft.com/sql/editions/express/default.mspx.
7 Sometime, codification does not complication with lottery numbers.
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