For the Pick 6, Pool 49 Lotto game there are 13,983,816 possibilities for the winning number. For any set you play the prize groups can be calculated which includes getting nothing and their percentage likelihood for each of those 13,983,816 possibilities.

Now, I realize and have pointed out before that for 13,983,816 draws there is no guarantee all the possibilities will be represented and it is certain there will be duplicates. However, an interesting exercise is to compare the results over say 100 simulated draws where the prizes are proportional to their representation. The following table gives the results for eight 163 line Lotto Designs with the method of construction in brackets and the covering percentage for 3 if 6: -

THE NOTION THAT COVERAGE ALONE IS AN INDICATOR OF THE BEST YIELD IN A LOTTO DESIGN IS PROVED FALSE AND GENERALLY INTRODUCING DISTORTION INTO THE PRIZE GROUP DISTRIBUTION REDUCES THE YIELD. FURTHER, AS THE LINES YOU PLAY PER DRAW INCREASE SO SHOULD A HIGHER PRIZE BE COVERAGE TARGETTED IN ACCORDANCE WITH THE ODDS.

Below is a comparison between the Cover C(49,6,3,6)=163 and the first 163 lines taken from my 365 line Cover with all integers included, no duplicate Threes and Coverage obtained by simply selecting for each line the next best play for 3if6 which does better than the 163 line Cover by 7% and to rub in the salt even random selections is marginally better. The Unique 3's™ Covers at any number of lines give good coverage and give a better yield than an optimized full or partial distorted prize distribution cover and other than the full pool for the Lotto game.

Colin Fairbrother

This article first published on the web 25/2/2010 and has been viewed 56587 times. The author may be contacted at fairbros@bigpond.com. To generate sets of Lotto numbers to play for most Lotto games around the world go to LottoToWin ^{®} where for a US$5.00 annual subscription you can store the numbers as well, to check later for wins. The numbers produced have no duplicate subset combinations of two integers (if applicable) or three integers, use all the integers for the particular Lotto game and maximize the coverage of the potential winning main number. The articles on this site have been selected from the many at the forum LottoPoster