Written by Ion Saliu on January 3, 2003 (3 WE).
• CheckHits.exe, version 1.0, January 3, 2003.
1. Introductory notes to wheeling last N lotto drawings
I say in one of my posts ("Comparative lottery, lotto software programs, systems + strategies 101"):
“The game of blackjack has its myth: CARD COUNTING. The lottery has two myths: 'frequency reports' (cold/hot numbers!) and 'lotto wheels'.”
(The article also discusses the thin-ice foundation of Gail Howard's lotto system. Her lotto system has some statistical validity, but it has no mathematical clue! Read how to generate automatically much more powerful lotto, lottery, Powerball, gambling systems based on the mathematics of SKIPS.)
I say in another post "The myth of lottery, lotto wheels or abbreviated lotto systems":
“Actually, the lotto wheels do more harm than good. The net results of the so-called abbreviated lotto systems or wheels: They accelerate the loss ... They say: 'The more you play, the higher the winning probability.' Well, think again! In most situations, the more you play, the more you lose! That's because the 'house advantage' or the 'house edge' is applied to higher quantities. 'The more you play, the higher the winning probability' is valid only in rare situations. It is the case of mathematically founded strategies. The player must overcome not only the odds, but also the 'percentage advantage'.”
I say also that lotto wheeling has become a brain-frying activity for many. I showed that it is more sensical money-wise to just play a number of random combinations equal to the odds for the respective prize. For example, the odds of hitting '3 of 6' in a 6/49 game are '1 in 57'. Playing 57 random combinations loses significantly less money than playing a so-called record lotto wheel of 163 lines.
I say also elsewhere at this 1000+-page website that lotto, lottery, all gambling games are ruled by the mighty 'Fundamental Formula of Gambling' (FFG). In a nutshell, all events of chance tend to repeat more often after an interval of trials less than or equal to the FFG median. Every event has an exact FFG or probability median calculated by FFG for a degree of certainty DC equal to 50%.
2. The best software (freeware!) to tackle lotto wheels and wheeling
Let's use that unique piece of software, FORMULA.EXE, option F: 'Fundamental Formula of Gambling'. Let's work with the 6/49 game and a real draw file: the UK National Lottery. Again, the probability of winning '3 of 6' is 1 in 57. FFG calculates the median for p=1/57 as 39.16, rounded up to 40 for DC=50%.
How close is that figure (40) to reality in the UK 6/49 history file? The file I've been using for this analysis has 737 draws (contains a few so-called 'extra' draws). The file has 733 regular draws from the beginning of the game to the draw of January 1, 2003. The median for the '3 of 6' case is around 38. That's within 1 standard deviation from the expected (theoretical) value. Use again FORMULA.EXE, option S: 'Standard Deviation'. An event of probability p=1/57 has a binomial standard deviation BDF=3.56 in a range of 737 trials. There is no data file (unadulterated, of course) that will not comply with the 'Fundamental Formula of Gambling'! Therefore, in our example, a '3 of 6' number group will tend to repeat within 40 draws since last hit.
We was seeing clearly that playing a 163-line 6/49 lotto wheel is a no-no. What if we was playing plainly and simply the last 40 or the last 57 draws? Checking it manually would be virtually impossible without serious errors. And thus it was my duty to write specific software. I came up with this new 32-bit DOS program:
CheckHits.exe
The workhorse performs the job in mere seconds for even the largest of the lotto draw files. The application takes two primary parameters:
1) how many past draws to simulate playing;
2) check all possible draws in a history file.
The UK 6/49 lotto has 737 draws on my PC. Let's suppose I played the last 57 draws. The program can check a maximum range of 737 – 57 = 680 past draws. If I play the last 40 draws, than the maximum analysis range is 737 – 40 = 697 past draws.
Both cases show better results than random expectation. Of course, the financial show is far superior to a 163-combination wheel. The 40-draw case is, however, clearly better than the 57-draw play.
1) The 57-draw case registered 685 '3 of 6' wins. The random expectation is very close to that figure. 57 draws played 680 times = 38,760 combinations. Random expectation yields 680 '3 of 6' hits. The 57-combination “wheel” offered a 0.7% improvement.
2) The 40-draw case registered 506 '3 of 6' wins. The random expectation is now farther from that figure. 40 draws played 697 times =27,880 combinations. Random expectation yields 27,880 / 57 = 489 '3 of 6' hits. The 40-combination “wheel” offered a 3.5% improvement.
And now, a bombshell! The wheels are optimized for their specific guarantees, but perform poorly for higher prizes! Even if the 40-past-draw “wheel” is superior to a larger wheel (e.g. 163 lines), it still works best for the '3 of 6' prizes. But, it performs worse than random expectation for higher prizes. In our example, the 40-past-draw wheel registered 21 '4 of 6' wins. Random play yields 27,880 / 1032 = 27 hits!
The lottery player should look for situations that increase the winning percentages for higher prizes, even if the lower prizes would go down. When I presented the 'wonder grid' I said also that, by contrast, strategies based on pairings strongly favor the higher prizes, especially the jackpot! The wheels give the player a disadvantage even before the game starts!
Trying higher-prize wheels based on the last draws becomes impractical above the '3 of 6' level. The '4 of 6' case would require a 6/49 history file of 1032 draws, and then some 200 more for a meaningful analysis.
3. Mathematical and statistical analysis of lotto wheels performance
Here are the reports. They can also show to the keen-eyed analyst-player that the winning situations also follow FFG. You'll notice that the winning situations are consecutive. If the skip is 2 or more, it's better not to play!
LOTTO-6 Winning Number Checking
When Playing Last N Past Draws
Data File: C:\LOTTO\UK-6
Last 40 draws played 697 draws
Date: 01-04-2003
---------------------------------------------------------------------------
Line Combinations 6 5 4 3
no. Checked Hits Hits Hits Hits
---------------------------------------------------------------------------
26 15 16 18 36 37 49 in draw # 2
16 4 5 8 19 31 37 in draw # 3
37 4 7 9 17 36 46 in draw # 3
28 2 9 10 11 13 16 in draw # 7
44 6 11 19 35 36 44 in draw # 8
35 2 23 28 33 45 47 in draw # 9
38 4 17 26 28 38 46 in draw # 9
31 4 7 12 29 37 42 in draw # 10
41 1 6 8 20 29 38 in draw # 10
44 6 11 19 35 36 44 in draw # 11
22 12 30 43 44 45 47 in draw # 12
24 16 18 35 36 39 48 in draw # 13
19 10 21 26 31 48 49 in draw # 14
43 10 22 23 30 33 42 in draw # 14
48 7 10 16 34 47 48 in draw # 14
32 8 14 24 27 29 32 in draw # 15
39 5 14 19 32 34 42 in draw # 18
44 6 11 19 35 36 44 in draw # 21
. . . .
698 5 8 23 24 28 48 in draw # 681
692 10 11 29 32 33 40 in draw # 682
722 11 12 17 26 36 42 in draw # 682
708 12 15 26 44 46 49 in draw # 683
711 15 16 17 28 32 46 in draw # 683
686 7 10 23 28 30 48 in draw # 684
711 15 16 17 28 32 46 in draw # 684
691 10 22 28 30 36 37 in draw # 686
698 5 8 23 24 28 48 in draw # 686
709 1 21 29 31 32 40 in draw # 692
---------------------------------------------------------------------------
Total Hits: 0 0 21 506
---------------------------------------------------------------------------
LOTTO-6 Winning Number Checking
When Playing Last N Past Draws
Data File: C:\LOTTO\UK-6
Last 57 draws played 680 draws
Date: 01-04-2003
---------------------------------------------------------------------------
Line Combinations 6 5 4 3
no. Checked Hits Hits Hits Hits
---------------------------------------------------------------------------
53 2 4 5 22 27 29 in draw # 1
26 15 16 18 36 37 49 in draw # 2
56 14 17 18 22 32 37 in draw # 2
57 18 21 32 36 39 41 in draw # 2
16 4 5 8 19 31 37 in draw # 3
37 4 7 9 17 36 46 in draw # 3
28 2 9 10 11 13 16 in draw # 7
48 7 10 16 34 47 48 in draw # 7
44 6 11 19 35 36 44 in draw # 8
35 2 23 28 33 45 47 in draw # 9
38 4 17 26 28 38 46 in draw # 9
31 4 7 12 29 37 42 in draw # 10
41 1 6 8 20 29 38 in draw # 10
44 6 11 19 35 36 44 in draw # 11
54 4 25 28 36 42 49 in draw # 11
22 12 30 43 44 45 47 in draw # 12
24 16 18 35 36 39 48 in draw # 13
19 10 21 26 31 48 49 in draw # 14
43 10 22 23 30 33 42 in draw # 14
48 7 10 16 34 47 48 in draw # 14
. . . .
729 7 17 23 32 38 42 in draw # 675
690 4 5 9 25 30 47 in draw # 676
709 1 21 29 31 32 40 in draw # 677
714 9 15 22 31 34 48 in draw # 677
719 4 17 41 42 44 49 in draw # 678
732 2 3 27 29 39 44 in draw # 678
706 5 15 21 42 43 45 in draw # 679
699 11 25 28 33 34 47 in draw # 680
---------------------------------------------------------------------------
Total Hits: 0 0 30 685
---------------------------------------------------------------------------
• Data analyses show beyond doubt that the lotto wheels are beaten by random play. The wheels are optimized for their specific guarantees. That is, a '4 of 6' lotto wheel performs well as far as the '4 of 6' prize is concerned. At the same time, the wheel performs worse at hitting higher prizes (5 of 6, for example). But if one has a strategy that picks the best to play 18 numbers, one is better served if playing random combinations consisting of the 18 numbers. If the 18-number wheel consisted of 19 combinations (the odds of getting exactly '4 of 6' for 18 lotto-6 numbers), it will hit the '4 of 6' prize according to the odds. The player improves the chance of hitting '5 of 6', even '6 of 6' if playing 19 random combinations of the same 18 numbers. A short explanation for this assessment founded on thorough data analysis: Lotto is random; wheeling is less random, since the combinations are hand-built. Randomization is the key explanation.
My lotto freeware can be easily set to play only certain numbers. The numbers to be eliminated from the field can be written at the top of the 'LEAST' files. In MDIEditor and Lotto the numbers NOT to be played can be typed directly in the filter input form.
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.EXE, WHEEL5.EXE, WHEEL7.EXE. The wheels are balanced. Keep in mind that they are also randomized—a keyword here. The randomized 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 freeware 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 5, lotto 6, lotto 7 lottery wheels, reduced systems: balanced and randomized".
4. Essential resources in lotto, lottery wheeling and wheels
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