Software for Balanced Lotto Wheels Based on Lexicographic Order, Indexes
By Ion Saliu, Founder of Lottery Wheeling Mathematics
Written on July 15, 2002; last update September 2011.
• Combinations ~ lotto software to generate universal combinations.
• LexicoWheels ~ lotto software to generate balanced lotto wheels based on lexicographical order (indexes).
• DrawIndex ~ lotto software to calculate the lexicographical ranks (indices) of every real lottery drawing.
• These reports were created by my lexicographical software DrawIndex. The program calculates the lexicographic order or index of lotto combinations in sets of numbers. You can see how disproportionate the indexes of the 163-line lotto wheel are. The 49-6 game has a total of 13,983,816 combinations. The 163-line wheel contains 86 of 163 combinations between the indexes 13,687,807 and 13,978,985!!! The 163-line lotto wheel contains 21 of 163 lines from the 1st million indexes!!!
I wrote in another article that the lottery drawings quite strongly tend to cluster in the FFG median area. That said, wouldn't it be far better to randomly generate combinations with indexes in the FFG median area? Even Kokostirk nods approvingly...
Dynamic versus Static in Lotto Analysis (combinations around the median and FFG median).
The 57-line group of 49 numbers consists of combinations symmetrically selected from the complete 13,983,816-combination set. I used a program similar to my Combinations lotto wheeling software. It generates combinations equally distanced (the step) and starting at an index that offers symmetry. Program name: LexicoWheels (menu #4 in the Bright 5, 6 software packages).
Lotto-6 Draw Lexicographic Order
File: WHEEL-49-163.IND
Line D R A W Lexicographical
no. Order
1: 1 2 3 7 11 15 2,963
2: 1 2 4 8 12 19 18,014
3: 1 2 5 9 16 20 32,177
4: 1 2 6 13 17 21 47,291
5: 1 2 10 14 18 22 89,077
6: 1 3 4 5 6 10 178,369
7: 1 3 8 9 13 14 229,735
...
157: 30 35 37 41 43 45 13,954,112
158: 30 36 41 44 46 47 13,955,312
159: 30 37 39 42 46 47 13,955,642
160: 31 34 39 40 41 49 13,961,927
161: 31 34 42 43 44 49 13,962,184
162: 33 36 39 44 45 46 13,974,292
163: 35 36 37 42 44 48 13,978,985
Total Hits: 0 4 117 2260
Lotto-6 Draw Lexicographical Order
File: SET-49-57.IND
Line D R A W Lexicographical
no. Order
1: 1 2 9 15 35 49 80,900
2: 1 3 24 29 40 45 327,720
3: 1 5 15 17 20 35 574,540
4: 1 7 17 19 26 46 821,360
5: 1 10 12 24 42 48 1,068,180
...
54: 18 22 30 33 45 46 13,162,360
55: 20 21 35 36 39 45 13,409,180
56: 22 27 29 33 37 48 13,656,000
57: 27 32 40 41 44 46 13,902,820
Total Hits: 0 2 33 771
~ Comparatively (line for line), the 163-line wheel should have:
Total Hits: 0 6 94 2205
worse better better
~ It appears I encounter this situation more often than not: the lotto wheels perform worse as far as the highest prizes are concerned! All that trouble to design the wheels, and to wheel the player's picks, only to expect a worse chance to hit the jackpot or the second prize! Given the extra effort, shouldn't the wheels ALWAYS show an advantage at all prize levels? Or, at least, show a clear advantage more often than not...
I do not recommend wheeling lotto numbers anymore. You still want to play lotto wheels from time to time? Or, you want to test if lotto wheeling works better than random play? Well, then, you can use my free lotto 5, 6, 7-wheels packages: SYSTEM6, WHEEL5, WHEEL7. The wheels are balanced. Keep in mind that they are also randomized — a keyword here. The randomized lotto wheels perform better than ordinary wheels.
The lexicographic indexes are very important. You may test this statement, or any other. The testing software is also free, plus other combinatorial software at this site. Testing will come at no cost to you; playing the wheels will cost you an arm and a leg, however. Read the article presenting the free lotto system packages:
"The best free lotto wheels, reduced lottery systems: balanced and randomized".
• LexicoWheels generates lotto wheels based on lexicographical indexes. The program does all the calculations automatically. Each lotto wheel guarantee (e.g. 4 of 6) has a specific step and a specific start index.
A lexicographic lotto wheel for 10 numbers with the 4 of 6 guarantee is equidistant from the start (index #1) and the end (index #210): combinations #15, 105, 195. Before you convert the wheel to your picks, you make sure your lotto picks are sorted in ascending order; e.g. 3, 7, 12, 19, 22, 23, 35, 38, 42, 49.
~ Superseded by the most powerful integrated packages
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