Lottery Sums, Root Sum — Pick Daily, Pick 5 (formerly Quinto), Lotto 5, 6, Powerball, Mega Millions, Euromillions
By Ion Saliu, Founder of Lottery Mathematics
First captured by the WayBack Machine (web.archive.org) on October 23, 2007.
A lot of lottery players have a keen interest in a topic such as the title of this document: sums of lottery games. Furthermore, if you land in lottery communities (forums, newsgroups, blogs), you will come across quite a few requests to show charts of sum-totals or sums of various lotto and lottery games.
The surprise for you and me has to do with this scarcity: There is only one piece of software that accurately creates such statistical charts! Just one lottery program, fittingly named Sums . Yes, it’s me who wrote it! But I am not writing this to brag about that piece of incredulously great lotto software – or am I? NOT!
Sums has always plotted charts for the sums in just about any kind of lottery and lotto games (since 1990s). And, for sure, no other program has ever done it. They lie when they claim they created the lottery some charts in Excel spreadsheets. A spreadsheet cannot handle millions and millions of lotto combinations, especially games like Powerball and Mega Millions. I’ve seen code by others to only generate lotto combinations for one sum-total at a time, not for an entire game in one run.
This piece of special software does a whole lot more mathematically than just plotting sum tables. For starters, the application generates all the combinations for a given sum-total. You can’t do that in an Excel spreadsheet. Moreover, the Sums lottery software performs comprehensive statistical analyses of lottery data (results) files. The statistics of a lotto data file show the sums, and then sum. I mean some. mean averages, medians, standard deviation, average deviations, deltas.
This lottery program came to life by request from. a school student! A computer science teacher gave the class a programming assignment:
- “Determine exactly how many lotto combinations can add up to a certain sum-total.”
Deltas, anyone? Well, that sounds like a fancy word. It is for the alphabet letter D of the Classical Greek language (the one that educated humans in creating the Modern Civilization). D is the mnemonic for difference. Lottery deltas are differences between adjacent lottery numbers. For example, delta_1 represents the difference between the number one and the 2nd number in a lotto combination. The delta is expressed as an absolute number, not a signed number. Lotto number_1 = 1; lotto number_2 = 7; delta = 7 – 1 = 6 (it is never minus 6).
Let us show here for everybody to see and use — for their personal usage only — never for commercial use! (Other sites will never tell you what lottery software they are using to plot the charts of any possible lotto game. for such software has been mine-only in the 20th and 21st centuries!)
Following are links to sum-total, root sums charts for a wide variety of lottery and lotto games all over the world. Each game has its own Web page for the best possible viewing. The sum-total/root sums charts show the percentages as well. The percentages are directly related to the theoretical lottery probabilities.
SuperLotto-Plus Sums, Root Sum Chart; current game format: 5 of 47 AND 1 of 27
The screenshot below shows an analysis of a data (drawings) file for the Powerball, Mega Millions lotto game.
- Function S = Sum-up lottery-drawings files. Here is the most sophisticated statistical analysis of lottery drawings — sum-totals, root sums, average, standard deviation, deltas, medians. You won’t find it anywhere else; unless they use my software Sums legitimately. (I doubt it. I’ve never given anybody permission to make public the results of my software. because nobody ever asked me!)
Axiomatic one, the statistical parameters of the bottom line (Medians) are virtually identical to what mathematics calculates for the respective parameters. By the way – StdDev means standard deviation, while Del refers to lotto deltas – or the absolute difference between two neighboring numbers. The statistical parameters for the most common lotto game (6/49) are mathematically equivalent (the real data is for the Pennsylvania Lottery Match 6, 864 drawings analyzed):
How about that controversial lotto-6 combination that a million lottery players worldwide play every week. 1 2 3 4 5 6 Lotto Combination Probability, Odds?
Well, indelibly axiomatic colleague of mine, look no further than the bottom line. The (in)famous combonation above has a sum of 21; mathematically and practically, that sum-total should be close to 150 (anyway, not that far away as sum 21 is). The average delta of 1 2 3 4 5 6 is a mere 1; mathematically and practically, that delta average should be close to 7.40. The average is a very low 3.5. The standard deviation is the most convincing tell-tale fact: 1.71. It is 7.5 times lower than the norm of 12.90!
As we can see now, a combination like 1 2 3 4 5 6 is statistically very far away from the mathematical norms.
Resources in Lottery Software, Lotto Wheeling, Lottery Sums
Introduction to Lottery Mathematics: Probabilities, Appearance, Repeat, Affinity or Number Affiliation, Wheels, Systems, Strategies.
Presenting software to create free winning lotto, lottery strategies, systems based on mathematics. Get your lotto systems or wheels, the best lottery, lotto software, combinations, winning numbers.
Read a genuine analysis of Excel spreadsheets applied to lottery and lotto developing of software, systems, and strategies. Combining Excel analysis with powerful lottery and lotto software programmed by this author, Parpaluck.
Also applicable to LotWon lottery, lotto software; plus Powerball, Mega Millions, Euromillions. Visual Tutorial, Book, Manual: Lottery Software, Lotto Apps, Programs.Special lottery software charts show the sums or sum-totals of many lotto, lottery games: pick digit lotteries, lotto, Powerball, Mega Millions, Euromillions.
Lottery sum chart
This can be used as a continuation of Edge18 SUM ROOTS and BASE ROOTS or on its own.
To start with look at the sums chart found in the Foundation section (and below)
Track only the 10 to 18 SUMs (highlighted in green) Close to 90% of all your number hit in this area, so its mainly a time saver not having to keep track of the others.
Now using your history file, track the sums and Mark off each of those SUMs when they hit (represented below using the gray boxes)
At the bottom of the tracking sheet count the number of times each of the SUM totals hit. In the chart above you will notice that SUM 15, SUM 16 & SUM 18 all only hit once. Having more numbers then SUM 18, SUM 15&16 are favored more likely to hit. Then the fact that SUM 15 is more due (last hit farther back then SUM 16) makes SUM 15 the HOTTEST SUM TO TRACK.
Now using your favorite method, simply eliminate all of the options that do not have a 15 SUM. Or if you feel the 15 SUM is going to hit, play all the options.
6- Way Box
069 078 159 168 249 258 267 348 357 456
177 339 366 447
Using the History file, SUM 15 hit 2 days later.
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