1. Introductory Notes to the Myth of the Lotto Wheels
I say in one of my posts ("Comparative lotto software programs"): "The game of blackjack has its myth: Counting cards. The lottery has two myths: 'frequency reports' (cold/hot numbers!) and 'lotto wheels'."
Actually, the static (unbalanced) lotto wheels do more harm than good. The net results of the so-called abbreviated lotto systems or wheels: They accelerate the loss. (Well, isn't acceleration what the wheel is all about?) The so-called experts have always stressed the 'advantage' of wheeling the lotto numbers. (The stress always breaks the wheel, doesn't it?) Granted, many people honestly believe the lotto wheels create an advantage. But for a number of “experts” the lotto wheels really create an advantage: They sell wheels or wheeling software. (Nothing wrong with that: The wheel created big industries, such as wagon making, and tires, and Le Tour de France.)
2. Mathematical and Statistical Analysis of Lotto Wheels Performance
All of a sudden, the ol' good LotWon lottery software showed how damaging the lotto wheels can be. It struck me that the combination lexicographical order can be a tool in creating lottery wheels. I used COLORDER.EXE to create lotto wheels based on the official lottery odds. For example, the probability of getting '3 of 6' in a 6/49 lotto game is '1 in 57'. They say the “world record” for a 49-number wheel guaranteeing '3 of 6' is 163 combinations. I say to myself: ”Self, why not 57 combinations?” I ran my 'combination lexicographical order' lotto wheel against a real draw file (UK lottery, 642 draws). The 57-line wheel very closely followed the lotto odds. But why did I need to put all that effort in creating a wheel? Wasn't it easier to simply play 57 random combinations?
I put MDIEditor and Lotto WE to work. I generated several 57-combination sets. I checked all of them for winners against the same UK National Lottery draws file. The results were strikingly similar to the first case. Every 57-line set (wheel) very closely followed the lotto odds. Here is how the last random set fared:
Total Hits: 0 '6 of 6'; 0 '5 of 6'; 41 '4 in 6'; 666 '3 in 6'
Total Cost: 642 x 57 = 36,594 units
Total Winnings: (666 x 10) + (41 x 100) = 10,760 units
Net Loss: 25,834 units.
How about the "world champion", the 163-combination lotto wheel guaranteeing 100%+ '3 in 6'? Well, that wheel, too, followed closely the official lotto odds:
Total Hits: 0 '6 of 6'; 1 '5 of 6'; 104 '4 in 6'; 1872 '3 in 6'
Total Cost: 642 x 163 = 104,646 units
Total Winnings: (1872 x 10) + (104 x 100) + (1 * 3000) = 32,120 units
Net Loss: 72,526 units.
The bottom line is far more significant than any of the elements leading to it. 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 lottery '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'. The casinos LOVE when the players bet big, and then bigger. With one notable exception: The casino executives would love "to strangulate" the system players who bet big and bigger.
There is a plethora of terms describing the additional obstacle the players face. House advantage, house edge, percentage advantage, takeout, vigourish (?)… I think of a unified term, defined with more precision. The lottery commissions “take out” 50% of ticket sales, therefore distributing 50% to prizes. But the house edge is not necessarily 50%: It depends on a specific game and prize. The best term is player's disadvantage. For example, in a lotto 6/49 game, the odds of winning the lotto jackpot are 1 in 13,983,816; if the winner is paid $1,000,000 for a $1 winning ticket, the player's disadvantage is {1 – 1000000/13983816} = {1 – 0.0715) = 92.8%. At the double-zero roulette, the probability of winning a straight-up bet is 1 in 38. The casino plays $36 for a $1 winning bet. The player's disadvantage is {1 – 36/38} = {1 – 0.9474} = 5.26%.
The two reports (fragments) are at the end of this writing. You can replicate them for any data file (real lotto draws) and any wheel. Randomly generated or painfully designed. You can use great free lotto software to assist you. In addition to MDIEditor and Lotto WE, Winners.exe is a very helpful tool. It can check for winning numbers in just about any lottery game. Winners.exe also reports the wins in any lotto wheel, including for the latest games of Powerball, Mega Millions, and Euromillions.
3. Honest Opinion on Lotto Wheels and Number Wheeling
I put some trust in lotto wheeling. It happened quite some time ago, last millennium! I had at my fingertips a very serious wheeling book: Swedish Lotto Systems by Thomas H. Olsson. The book was first published in Sweden by Chavez Nyman Trading, 1985. It was published in the USA by Intergalactic Publishing Company in 1986. The book presented a variety of abbreviated systems for 6-number lotto games. It also showed the winning guarantees or percentages for several situations: N in 6, N in 5, N in 4. But then again, those lotto wheels have extra lines, compared to the odds of the lottery game.
I even improved on some of the wheels in Swedish Lotto Systems, while playing with COLORDER.EXE. The book had a 10-number system in 5 lines; I did it in 3 combinations (exactly the lotto odds!) The book had an 11-number lotto wheel in 11 lines; I did it in 5 combinations. I even created an 18-number system in 19 combinations. While it is not 100% guaranteed for a particular lottery drawing, it does follow the 6/18 odds for '4 of 6'. If successful 10 times, it will hit '4 of 6' around 10 times! Probably better than that!
Later, I have written specific lotto wheeling software based on lexicographical order or indexing: LexicoWheels.EXE.
• Forget about designed loto wheels! Better still, forget about lottery wheels altogether! The wheels only make money for those who sell lottery software. The lotto wheels and wheeling are the essence of all lottery software, except for LotWon. Some pushed the envelope so hard, that everything in lotto is now a...wheel! It is the only justification left for most lotto software packages. They say now full wheels. That's an oxymoron, a contradiction in terms. The lotto wheels are, in fact, reduced lotto systems. On the other hand, full is a reference to all the combinations of a lotto set. Wheeling lotto numbers is a way of reducing the number of combinations to play, instead of playing all lotto numbers in a set. They can't have it both ways: full and reduced!
•
LOTTO-6 Winning Number Checking Files: RAND57.649 (57) against UK-6 (642) Line Combinations 6 5 4 3 no. Checked Hits Hits Hits Hits 1 4 12 14 19 20 48 in draw # 8 1 4 12 14 19 20 48 in draw # 23 1 4 12 14 19 20 48 in draw # 72 1 4 12 14 19 20 48 in draw # 73 1 4 12 14 19 20 48 in draw # 79 1 4 12 14 19 20 48 in draw # 101 1 4 12 14 19 20 48 in draw # 322 1 4 12 14 19 20 48 in draw # 371 1 4 12 14 19 20 48 in draw # 488 1 4 12 14 19 20 48 in draw # 527 1 4 12 14 19 20 48 in draw # 573 ......... 56 7 22 37 39 43 46 in draw # 362 56 7 22 37 39 43 46 in draw # 404 56 7 22 37 39 43 46 in draw # 515 56 7 22 37 39 43 46 in draw # 631 57 17 18 20 26 27 35 in draw # 208 57 17 18 20 26 27 35 in draw # 384 57 17 18 20 26 27 35 in draw # 455 57 17 18 20 26 27 35 in draw # 480 57 17 18 20 26 27 35 in draw # 487 57 17 18 20 26 27 35 in draw # 558 Total Hits: 0 0 41 666 Total Cost: 642 x 57 = 36,594 units Total Winnings: (666 x 10) + (41 x 100) = 10,760 units Net Loss: 25,834 units LOTTO-6 Winning Number Checking Files: WHEEL-36.163 (163) against UK-6 (642) Line Combinations 6 5 4 3 no. Checked Hits Hits Hits Hits 1 1 2 3 4 5 49 in draw # 32 1 1 2 3 4 5 49 in draw # 60 1 1 2 3 4 5 49 in draw # 258 1 1 2 3 4 5 49 in draw # 288 1 1 2 3 4 5 49 in draw # 346 1 1 2 3 4 5 49 in draw # 350 1 1 2 3 4 5 49 in draw # 397 1 1 2 3 4 5 49 in draw # 425 1 1 2 3 4 5 49 in draw # 536 1 1 2 3 4 5 49 in draw # 583 1 1 2 3 4 5 49 in draw # 621 2 1 2 6 11 17 20 in draw # 11 2 1 2 6 11 17 20 in draw # 14 ......... 163 38 39 40 41 42 47 in draw # 66 163 38 39 40 41 42 47 in draw # 89 163 38 39 40 41 42 47 in draw # 154 163 38 39 40 41 42 47 in draw # 333 163 38 39 40 41 42 47 in draw # 370 163 38 39 40 41 42 47 in draw # 374 163 38 39 40 41 42 47 in draw # 513 163 38 39 40 41 42 47 in draw # 569 163 38 39 40 41 42 47 in draw # 580 Total Hits: 0 1 104 1872 Total Cost: 642 x 163 = 104,646 units Total Winnings: (1872 x 10) + (104 x 100) + (1 * 3000) = 32,120 units Net Loss: 72,526 units
4. Essential resources in lotto wheels and lottery wheeling
• 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.
• There is also another major factor: the lexicographical order or the index of the combinations in the set. A wheeled set such as the wheel “champion” has a horrendous configuration as far as the indexes are concerned. Half of its combinations have an index of over 13 million! That is, half of the wheel lines are from the bottom million of the 6/49 set! Read this page to see the wheel-163 indexes compared to a 57-line set with very symmetrical lexicographical order indexes: Software for Balanced Lotto Wheels Based on Lexicographic Order, Indexes.
I do not recommend wheeling lotto numbers anymore. You still want to play lotto wheels from time to time? You can also improve your lotto wheeling by running first Wheel6.exe. It is now option W = Wheel On-the-Fly (menu #2) in the most powerful suite of lotto software to date (2011): Bright6.exe. Generate as many wheeled lotto combinations as until the program seems to have stopped. Use the partially wheeled output file as … input to WheelCheck6.exe. It is option C = Check Systems in menu #4. The program will generate all combinations that are missing from the lotto wheel in order to assure the minimum guarantee.
The wheels are balanced. Keep in mind that they are also randomized — a keyword here. The randomized wheels perform better than ordinary wheels (static lotto wheels). The lexicographic indexes are very important. Read the article presenting the lotto system packages: Lotto Wheels for Lotto Games Drawing 5, 6, Or 7 Numbers. The systems and the software are free to run forever. Only downloading requires a reasonable one-time fee.
Check out:
Resources in Lotto, Lottery Software, Wheeling.
It lists the main pages on the subject of lottery, lotto, software, wheels and systems.