
Written by Ion Saliu on Febrero 02, 2002.
• I received a strange request from a...school student! The teacher (?) gave the class a programming assignment. “Determine exactly how many combinations can add up to a certain sum-total.” The question was exemplified for a particular lotto game! Let's say, a 6/49 game. The sum-totals of the combinations range between 1+2+3+4+5+6=21 and 44+45+46+47+48+49=279. How many combinations are there for the sum-total 150? How many for the sum-total 49?
Child or parent, there is a tendency to look for so-called patterns in lotto games. One of the most sought-after patterns is 'sum-totals'. That is, most combinations will total an amount situated in the middle of the sum ranges. Such aurea mediocritas can be calculated as {(1+N)/2] * 6; i.e. in loto 6/49: 1+49=50; 50/2=25; 25 * 6 = 150. Indeed, that's the mid point of the 6/49 sum range. The sum-total equal to 150 has the largest amount of combinations in a lotto 6/49 game. In a pick-3 game, there are two such ranges: 13 and 14. Since the 13/14 ranges contain the most combinations, they will, in general, come out more frequently. Some jump to the conclusion that there is a strong bias in favor of sum-total 13! Or, others conclude that the lottery drawings are “fixed”! Get it? Isn't '13' a number with a special meaning?!
I've seen in newsgroups numerous posts on some mysterious patterns in lotto games. I saw ads for a potential lotto syndicate. The objective is to play ... 300,000+ combinations! The author claims he discovered magical patterns in a lotto game! Actually, I smell the author wants to play all the combinations that add up to a couple of mid-point sum ranges. For example, the “richest” sum-total in lotto 6/49 is 150. It consists of 165,772 combinations. Probably one more sum range and there will be over 315,000 combinations to play! The author, however, has no clue of another important factor: the skip. The 315,000 combinations can encounter skips of several draws, sometimes 20 or more! The players have no clue how the skips (losing streaks) have evolved in recent past. Besides, there is no technology to print that amount of tickets in a few days. Further, what lottery outlet would have the technology, the time, and the personnel to process such a huge amount of play slips? Only when lottery commissions will allow online playing things may change…
This is a form of filters that my software avoids. I call them 'inner filters' because they have no relation to past draws. The inner filters are always constant. If one plays the 'sum-total=150 inner filter' the result is always 165,772 combinations. If one plays the '3_odd+3_even inner filter' the result is always the same. My software uses the 'sum', but as an external filter. It 'purges' combinations based on past results. The pick-3 and pick-4 modules in LotWon use some inner filters. In pick-3: odd/even digits, under_4/over_5 digits, under_13/over_14 sum-totals. If playing the following configuration of the odd/even + low/high filters:
E-E-E;L-L-L generates 27 combinations consisting of the digits 0, 2, 4. Sometimes, a different structure of E/L leads to 8 combinations (having double digits, such as 2-2-3). I noticed it is more difficult to track the skips of the inner filters. LotWon is the only software that tracks the skips for any type of filters.
In any event, I made a child's wish come true! I wrote SUMS.EXE, which can be downloaded from my free downloads site. The 32-bit application can generate all the combinations for any sum-total, in any lottery game: Pick-3, pick-4, lotto-5, lotto-6, lotto-7, Powerball/Mega Millions, and Euromillions.
The application is extraordinarily powerful. It calculates meaningful statistics for a lotto/lottery data file: Sum, Root Sum (Fadic Addition), Average, Standard Deviation, Average Deviation from Mean Average, Average of Deltas. At the end of the report, SUMS.EXE calculates the medians of the above statistical parameters.
Here is a sample report for a statistically large data file in the Pennsylvania lotto-5 game.
Apparently, there were problems with my 16-bit freeware SHUFFLE.EXE. Some informed me in the lines: And, of course, I may be nice sometimes. But I won't be a free consultant and/or a no-fee programmer for everybody. Kids should remind their fathers of such reality. Fathers, then, will “consult” the market in search of the best consultants/programmers and the fees. Best of luck!
Statistics For File: C:\LOTTERY\LOTTO-5
Total Lines: 3768
================================================================================
Drawings Sum Root Average StdDev AvgDev AvgDel
================================================================================
1 16 19 22 26 84 3 16.80 8.57 6.64 6.25
9 11 13 22 38 93 3 18.60 10.67 9.12 7.25
8 14 23 28 29 102 3 20.40 8.16 7.52 5.25
19 22 27 31 38 137 2 27.40 6.71 5.68 4.75
....
================================================================================
Medians: 100 5 20.00 10.03 8.64 6.75
================================================================================
The combinations can also be saved to text files. Depending on a PC performance, a user can create text files for each sum-total in a lotto game in days. The program also plots a chart of all the sums in a game. The chart looks like a Gauss (normal distribution) bell (or curve).
“This remind me of my problem now with your software (Shuffle.Exe) when loading, it return's this 'Error 9 at pgm-ctr : 1423' . How ever I have no way of knowing the Error Code, or perhaps my files are too large?”
Most likely, the file size was the problem. 16-bit DOS can only handle files up to 640KB. I re-wrote SHUFFLE.EXE as 32-bit software that runs under DOS 7+ (Win95/98/Me/NT4/2000+). Better to run it at the command prompt, in full-screen mode. I haven't met a file size limit yet. Who knows. If you met such a limit, buy more memory. Otherwise, keep in mind that 32-bit software has size limits, too. Around two gigabytes, mind you!
For the “children of computer-impaired father figures and computer-idiot educators” want also programs to put together all inner filters: sum-totals, odds/evens, low/high, decades, etc. Plus how their skips move! Well, we know who they are!
Ion Saliu




Copyright ©1997-2007, Ion Saliu. All rights reserved worldwide. Reproduction, in any form, of the contents of this site is strictly prohibited. Read important copyright information regarding web site www.saliu.com