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 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! 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 lotto 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, Super 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 drawingss (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' lotto 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 lotto drawings 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 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 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 draws, and then some 200 more for a meaningful analysis.