Written by Ion Saliu on July 11, 2002.
• The wonder grid is not surrounded by noise, but definitely is surrounded by interest. Maybe people keep quiet about it for a good reason. The “Search” page of my web site shows 'wonder grid' or 'wonder-grid' among the top keywords. I also receive emails with requests to detail the concept, and do so on an individual basis! Instead of emailing 100 on-an-individual-basis strategies, I decided to write software to check the wonder grid automatically. The wonder grid is a very complex matter. It would take days and big headaches to check the 'magical wheel' manually and for dozens of past draws.
The new lotto software (freeware!) is entitled:
GridCheck632.EXE, version 1.00, July 2002 - 32bit character mode (command prompt) application.
GridCheck632.EXE checks the past performance of the GRID6 files for various draw ranges. The program starts a number of draws back in the DATA-6 file and creates 3 GRID6 files: for N*1, N*2, N*3 draws. N represents the biggest number in the game. By default, the program checks how the GRID6 files performed in the previous 100 draws (the span). Your data file must have at least {SPAN + (N*3)} draws. If your lotto-6 game has 49 numbers and SPAN=100 (check the previous 100 draws), then your files must have at least 100+49*3=247 draws. The program will let you know what to do to overcome the error.
The program creates three GRID6 files in the background. The first one is a range equal to the biggest number in your lotto game (e.g. 49); the second file is created for a range equal to N*2 (the biggest lotto number times 2); the third file is created for a range equal to N*3 (the biggest lotto number times 3).
The GRID6 checking reports will be saved to 3 disk files. Defaults: ChkGrid6.N1, ChkGrid6.N2, ChkGrid6.N3. They show how many hits (if any!) the corresponding grid had for a particular drawing. Here is a more clarifying example, with data for Pennsylvania 6/69 lotto game.
1) The program started at draw #2 and created a grid file for a range of 69*2=118 draws. Therefore, the program created the first wonder grid: the best 69 pairings in the range 2-120 past draws. The program stopped at draw #120 in the PA-6 data file. Next, the program created a winning report for draw #1. Important fact: the program does not create a wonder grid for the current draw. It would be a case of 'curve fitting': the wonder grid would hit the jackpot every ten draws or so! But such case would not take place in reality! We must exclude the current draw from the range that creates the wonder grid. The winning report (almost the same as in UTIL632.EXE or WINNERS.EXE) checks for “future” draws. In this first step, the “future” consists of one draw only: #1. The winning report check for '6 of 6' winners, '5 of 6' winners and '4 of 6' winners. I excluded the '3 of 6' prize from the reports. There are way too many lines! The reports would be too large and slower! Right now, it takes around one minute to generate the wonder grid checking reports. Usually, there are no hits at position #1.
2) The second step. The program continues at draw #3 and creates a grid file for a range of 69*2=118 draws. Therefore, the program created the second wonder grid: the best 69 pairings in the range 3-121 past draws. The program stopped at draw #121 in the PA-6 data file. Next, the program created a winning report for draws #1 to #2. In this second step, the “future” consists of two draws: #1 and #2.
Usually, the wonder grid starts hitting after 5-6 draws ('4 of 6'). Higher prizes require a wider gap between hits. In the case above, draw #38 registered one '5 of 6' hit. The streak continued uninterrupted to draw #53. Had I decided to play just before draw #38, I would have hit 5 winners after 6 draws. That is, draw #32 would have given me one ticket with 5 winners (also one ticket with 4 winners). Had I decided to play just before draw #53, I would have hit 5 winners after 53-32=21 draws. That is, draw #32 would have given me one ticket with 5 winners (also one ticket with 4 winners). A good strategy would be to wait for 5 draws, then start playing for the next up to 35 draws (N/2). The skips are different from game to game. That's why the three grid reports are so useful.
•• How to figure out the validity and strength of various strategies? The most common rule is to compare a strategy to random play. The benchmark is the 'normal probability rule':
I touched the subject in a previous message, after I updated FORMULA.EXE to calculate the binomial standard deviation. (See "New FORMULA.EXE 3.1, the standard deviation, politics”.)
Also previously, I presented a static strategy that beats random selection by far more than 3 standard deviations. (See "FFG Median, Filtering, Probability, Jackpot”.)
The normal probability rule applied to the '6 of 6' case is summarized by FORMULA.EXE as follows:
The wonder grid consists of 69 combinations for a lotto 6/69 game. The wonder grid is expected to hit '5 of 6' within 69/2 = 35 draws. In this case, number of trials is 69 x 35 = 2,415.
Resources in Lotto, Lottery Software, Wheeling.
GRID6.N2 Winning Number Checking - 07-10-2002
=============================================
~ Draw # 37 > 2 4 8 11 16 53
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 37 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
16 16 2 3 40 49 32 in draw # 11
-----------------------------------------------------------------------------
Total Hits: 0 0 1
-----------------------------------------------------------------------------
~ Draw # 38 > 1 9 31 45 55 59
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 38 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
1 1 10 31 26 11 22 in draw # 32
16 16 2 3 40 49 32 in draw # 11
22 22 1 31 32 41 59 in draw # 32
-----------------------------------------------------------------------------
Total Hits: 0 1 2
-----------------------------------------------------------------------------
~ Draw # 39 > 18 21 23 25 43 53
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 39 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
1 1 10 31 26 11 22 in draw # 32
16 16 2 3 40 49 32 in draw # 11
22 22 1 31 32 41 59 in draw # 32
-----------------------------------------------------------------------------
Total Hits: 0 1 2
-----------------------------------------------------------------------------
~ Draw # 40 > 7 8 19 36 40 45
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 40 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
1 1 10 31 26 11 22 in draw # 32
16 16 2 3 40 49 32 in draw # 11
22 22 1 31 32 41 59 in draw # 32
-----------------------------------------------------------------------------
Total Hits: 0 1 2
-----------------------------------------------------------------------------
~ Draw # 41 > 30 41 62 64 65 67
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 41 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
1 1 10 31 26 11 22 in draw # 32
16 16 2 3 40 49 32 in draw # 11
22 22 1 31 32 41 59 in draw # 32
-----------------------------------------------------------------------------
Total Hits: 0 1 2
-----------------------------------------------------------------------------
~ Draw # 42 > 16 29 42 45 50 58
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 42 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
1 1 10 31 26 11 22 in draw # 32
16 16 2 3 40 49 32 in draw # 11
22 22 1 31 32 41 59 in draw # 32
-----------------------------------------------------------------------------
Total Hits: 0 1 2
-----------------------------------------------------------------------------
~ Draw # 43 > 6 13 44 46 62 63
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 43 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
1 1 10 31 26 11 22 in draw # 32
16 16 2 3 40 49 32 in draw # 11
22 22 1 31 32 41 59 in draw # 32
-----------------------------------------------------------------------------
Total Hits: 0 1 2
-----------------------------------------------------------------------------
~ Draw # 44 > 20 21 23 30 42 44
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 44 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
1 1 10 31 26 11 22 in draw # 32
16 16 2 3 40 49 32 in draw # 11
22 22 1 31 32 41 59 in draw # 32
-----------------------------------------------------------------------------
Total Hits: 0 1 2
-----------------------------------------------------------------------------
~ Draw # 45 > 8 20 24 32 51 68
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 45 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
1 1 10 31 26 11 22 in draw # 32
16 16 2 3 40 49 32 in draw # 11
22 22 1 31 32 41 59 in draw # 32
-----------------------------------------------------------------------------
Total Hits: 0 1 2
-----------------------------------------------------------------------------
~ Draw # 46 > 2 20 22 34 43 47
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 46 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
1 1 10 31 26 11 22 in draw # 32
16 16 2 3 40 49 32 in draw # 11
22 22 1 31 32 41 59 in draw # 32
-----------------------------------------------------------------------------
Total Hits: 0 1 2
-----------------------------------------------------------------------------
~ Draw # 47 > 24 43 45 48 62 63
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 47 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
1 1 10 31 26 11 22 in draw # 32
16 16 2 3 40 49 32 in draw # 11
22 22 1 31 32 41 59 in draw # 32
-----------------------------------------------------------------------------
Total Hits: 0 1 2
-----------------------------------------------------------------------------
~ Draw # 48 > 9 30 43 44 62 63
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 48 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
1 1 10 31 26 11 22 in draw # 32
16 16 2 3 40 49 32 in draw # 11
22 22 1 31 32 41 59 in draw # 32
-----------------------------------------------------------------------------
Total Hits: 0 1 2
-----------------------------------------------------------------------------
~ Draw # 49 > 7 16 23 32 63 64
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 49 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
1 1 10 31 26 11 22 in draw # 32
16 16 2 3 40 49 41 in draw # 11
22 22 1 31 32 41 59 in draw # 32
-----------------------------------------------------------------------------
Total Hits: 0 1 2
-----------------------------------------------------------------------------
~ Draw # 50 > 2 16 40 46 53 68
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 50 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
1 1 10 31 26 11 22 in draw # 32
16 16 3 49 33 40 41 in draw # 11
22 22 1 31 32 41 59 in draw # 32
-----------------------------------------------------------------------------
Total Hits: 0 1 2
-----------------------------------------------------------------------------
~ Draw # 51 > 2 10 27 33 45 55
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 51 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
1 1 10 31 26 11 22 in draw # 32
16 16 3 49 33 40 41 in draw # 11
22 22 1 31 32 41 59 in draw # 32
-----------------------------------------------------------------------------
Total Hits: 0 1 2
-----------------------------------------------------------------------------
~ Draw # 52 > 11 17 32 54 65 69
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 52 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
1 1 10 31 26 11 22 in draw # 32
16 16 3 49 26 33 34 in draw # 11
22 22 1 31 32 41 59 in draw # 32
-----------------------------------------------------------------------------
Total Hits: 0 1 2
-----------------------------------------------------------------------------
~ Draw # 53 > 17 21 40 41 53 69
~ Files: GRID6.N2 ( 69 ) against > PA-6 ( 53 )
-----------------------------------------------------------------------------
Line Combinations 6 5 4
no. Checked Hits Hits Hits
-----------------------------------------------------------------------------
1 1 10 31 26 11 22 in draw # 32
16 16 3 49 26 33 34 in draw # 11
22 22 1 31 32 41 59 in draw # 32
-----------------------------------------------------------------------------
Total Hits: 0 1 2
-----------------------------------------------------------------------------
The draw range or the span of analysis is a most important element. We was not sure about the optimal value of the range. First, I said it was N*3; then I said it must be N. It appears that the best range is N*2. The range N*1 is also a good value. As of three-times-the-biggest-number, it probably creates an outdated grid file. A range beyond N*3 is useless. You can look at the three reports and see which one(s) fared the best in your lotto-6 game. Again, I'm (almost) convinced that the best ranges are N*2 followed by N*1.
The case above is the report for an N*2 grid file.
99.7% of the successes will fall within 3 standard deviations from the expected (theoretical) number of successes.
If a strategy beats the random expectation by more than 3 standard deviations, it surely has a solid foundation. The margin of error is less than 0.3%.
The game analyzed was Pennsylvania 6/69. The probability of hitting '6 of 6' is 1 in 119877472. The probability of winning '5 of 6' is 1 in 317136. I generated 10,000 combinations around the FFG median. I checked 350 real draws in the 6/69 lotto game. Therefore the number of trials was 350 * 10000=3,500,000.
The standard deviation for an event of probability
p = .00000001 (1 in 119877472)
in 3500000 binomial experiments is:
BSD = .17
The expected (theoretical) number of successes is: 0.29
Based on the Normal Probability Rule:
• 68.2% of the successes will fall within 1 Standard Deviation
from 0.29 - i.e., between 0.12 - 0.46
•• 95.4% of the successes will fall within 2 Standard Deviations
from 0.29 - i.e., between 0 - 0.63
••• 99.7% of the successes will fall within 3 Standard Deviations
from 0.29 - i.e., between 0 - 0.80
The strategy I presented had one '6 of 6' winner. It clearly beat the random expectation by one extra standard deviation!
The '5 of 6' case:
The standard deviation for an event of probability
p = .00000315 (1 in 317136)
in 3500000 binomial experiments is:
BSD = 3.32
The expected (theoretical) number of successes is: 11
Based on the Normal Probability Rule:
• 68.2% of the successes will fall within 1 Standard Deviation
from 11 - i.e., between 8 - 14
•• 95.4% of the successes will fall within 2 Standard Deviations
from 11 - i.e., between 5 - 17
••• 99.7% of the successes will fall within 3 Standard Deviations
from 11 - i.e., between 2 - 20
The strategy I presented had 75 '5 of 6' winners. It beat the random expectation handily: by 16 extra standard deviations! (75 – 11 = 64; 64 / 3.32 = 19.27 standard deviations. 19.27 – 3 = 16.27 standard deviations beyond the level-3 required by the normal probability rule.)
The standard deviation for an event of probability
p = .00000315 (1 in 317136)
in 2415 binomial experiments is:
BSD = 0.09
The expected (theoretical) number of successes is: 0.008
Based on the Normal Probability Rule:
• 68.2% of the successes will fall within 1 Standard Deviation
from 0.008 - i.e., between 0 - 0.098
•• 95.4% of the successes will fall within 2 Standard Deviations
from 0.008 - i.e., between 0 - 0.188
••• 99.7% of the successes will fall within 3 Standard Deviations
from 0.008 - i.e., between 0 - 0.278
The wonder grid also beat random expectation: by 8 extra standard deviations! (1 success – 0.008 = 0.992; 0.992 / 0.09 = 11 standard deviations. 11 – 3 = 8 standard deviations beyond the level-3 required by the normal probability rule.)
The advantage of the wonder grid is its much lower COW (cost of winning).
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