The Fundamental Formula of Lotto Wheeling:
Play the Last N Lottery Drawings
Written by Ion Saliu on January 3, 2003 (3 WE); later updates.
CheckHits, version 2.0, 2011.
"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! It is undeniable mathematics, if you play without mathematical-founded strategies. The average loss is calculated as total cost multiplied by the house edge (at best 50% in lottery).
I say also that lotto wheeling has become a brain-frying activity for many. I showed that it makes more sense money-wise to just play a number of random lotto combinations equal to the odds for the respective prize. For example, the odds of hitting 3 of 6 in a 6/49 lotto game are 1 in 57. Playing 57 random combinations loses significantly less money than playing a so-called best-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%.
How close is that figure (40) to reality in the UK Lottery 6/49 history file? The file I've been using for this analysis has 737 drawings (contains a few so-called 'extra' draws). The file has 733 regular lotto drawings from the beginning of the game to the draw of January 1, 2003. The median for the 3 of 6 lotto case is around 38. That's within 1 standard deviation from the expected (theoretical) value. Use again SuperFORMULA, 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 lotto drawings since last hit.
We are 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 lotto draws? Checking it manually would be virtually impossible without serious errors. And thus it was my duty to write specific lotto software. I came up with this new 32-bit Command Prompt program:
CheckHits: 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 lottery drawings.
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 lotto 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 lotto "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 lotto 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 lottery wonder grid I said also that, by contrast, strategies based on pairings strongly favor the higher prizes, especially the jackpot! The lotto wheels give the player a disadvantage even before the game starts!
Trying higher-prize lotto 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 drawings, and then some 200 more for a meaningful analysis.
LOTTO-6 Winning Number Checking
When Playing Last N Lottery Drawings
Data File: C:\LOTTO\UK-6-49
Last 40 draws played
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
. . . .
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 Lottery Drawings
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
. . . .
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
Total Hits: 0 0 30 685
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