# 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.

## 1. Introductory Notes to Wheeling Last N Lotto Drawings

I say in one of my articles The Myth of 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! 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%.

## 2. The Best Software to Tackle Lotto Wheels and Lottery Wheeling

Let's use that unique piece of software, Super Formula, 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 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.

## 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 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

```

## Resources in Lottery, Software, Systems, Lotto Wheels, Strategies

Lists the main pages on the subject of lottery, software, lotto wheels, strategies, reduced lottery systems.

• Download Lottery Software Tools, Lotto Wheels, Reduced Systems:
• Wheel-632, Wheel-532, the best on-the-fly wheeling software; applies real lottery filtering. ~ Superseded by the most powerful integrated packages
• Pick-532, Pick-632 and, especially, the Bright / Ultimate software packages.
• Combinations, the universal combinations generator for any lotto, Keno, Powerball, Mega Millions, Euromillions;
• LexicoWheels, generator of lotto wheels based on lexicographical indexing; applies to any lotto, Keno, Powerball, Mega Millions, Euromillions or two-in-one lotto games.
• WheelCheck5, WheelCheck6, software to verify lotto wheels for missing combinations and generate lotto-5 and lotto6 systems.
• LottoWheeler, free wheeling software: Fill out lotto wheels with player lotto numbers. Supersedes the old-time favorite FillWheel (still offered). The two pieces of software replace the theoretical lotto numbers in the SYS/WHEEL files by your picks (the lotto numbers you want to play).
• Shuffle, SuperFormula to shuffle (randomize, randomly arrange) your lotto picks. Repeat the randomizing procedure several times. The randomized wheels can be used directly, without shuffling your lottery picks first.

• The Main Lotto, Lottery, Software, Strategy, Systems, Wheeling Page.
Presenting software to create free winning lotto, lottery strategies, systems based on mathematics. Get your lotto systems or wheels, the best lottery, lotto software, combinations, winning numbers.
• Lotto wheels for lottery games drawing 5 6 7 numbers.
The most advanced theory of lotto wheels or reduced lottery systems. Get also original lotto wheels for lotto games drawing 5, 6, or 7 numbers: Balanced, randomized, and free.

• Make Lotto Wheels: Manually, or in Lotto Wheeling Software.
• Lotto Wheeling Software, Lottery Winning Reports.
The best on-the-fly wheeling software; applies real lottery filtering.
• Free lottery software for players of lotto wheels: Fill out lotto wheels with player's picks (numbers to play).
• Software to verify lotto wheels for missing combinations and generate lotto 5, 6 abbreviated (reduced) systems.

• Balanced lotto wheels, lexicographic order, index, number set.
• Check lotto wheels for winners.

• Genuine Powerball wheels.
• Genuine Mega Millions wheels.
• Genuine Euromillions wheels.

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