Active Topics Memberlist Search Help  
Register Login 
Covers or Wheels with Guarantees and Unique 3's  
LottoPoster Forums : NUMBER SETS TO PLAY FROM DIFFERENT METHODS : Covers or Wheels with Guarantees and Unique 3's 
Topic: Cover or Wheel with Guarantee C(49,6,3,6,1)=163.  
Author  Message  
Colin F
Lotto Systems Tester Creator & Analyst To dream the impossible dream ... Joined: September 30 2004 Location: Australia Online Status: Offline Posts: 678 
Topic: Cover or Wheel with Guarantee C(49,6,3,6,1)=163. Posted: January 20 2007 at 8:49pm 

For those familiar with Covers as applicable to Lotto the free Covermaster program by John Rawson is no doubt familiar; if not it can be downloaded here.
You can easily build a C(49,6,3,6)=163 line cover by merging a C(22,6,3,3)=77 with a C(27,6,3,4)=86. This cover will guarantee a Three win every draw as at least one three in each of the 13,983,816 sixes is covered by the 163 line set.
The C(22,6,3,3)=77 is easy to build in CoverMaster  just don't check auto optimize  and has all the 1540 combinations of three that can be formed from a pool of 22 integers. This is a one off bonus and is why for the larger 3if6 covers these 77 lines are always used. In other words it is maximum packed for the number of lines with the possible distinct threes. As each six can only hold 20 threes (77x20=1540) it is impossible to do it in a lesser number of lines. You should note though that only 15 lines are needed for a C(22,6,3,6). Also note that for the 2600 combinations of 6 from a pool of 26 a C(26,6,3,3)=130 can be obtained (130x20=2600).
The C(27,6,3,4)=86 is impossible to the best of my knowledge and attempts to produce in CoverMaster without some manual intervention for the last 275 or so. There are lots of ways you can go about it eg Generate some 77 lines or so with your hits parameter set to 3 and then do a bit of manual scrutiny using whatever you have to assist  Access, Excel, MSQuery etc or you can do it in CoverMaster using techniques that don't seem to be well known in the Lotto crowd.
Using Covermaster optimization has only got me to 99.5% so far for a C(27,6,3,4)=86 so you are forced to use other means. You can try building it manually from scratch  just load your parameters  Pool, Pick, Match (Prize or Guarantee) then test and you will have a list of fours appear in a popup. Change the max. entries to a higher number than 25 and test again to get a bigger list of fours. From the menu bar ToolsSearchBest Play will give a list of sixes with coverage. Initially, the 435 means that in the list of uncovered fours using the 20 threes as criteria from that six a coverage of 435 is attainable. The difficulty lies in choosing which six  given that quite a few can have equal coverage. Which six you choose has repercussions on the later makeup of the overall set. After building the 163 line cover in Covermaster choose from the menu
ToolsReportsQuick to get the following report.
Before considering this report in detail let's recap on the basic odds for a 6/49 Lotto game.
With one ticket your chances of getting the winning number are 1 in :
If you buy two tickets then bearing in mind there is only one winning ticket, dividing the 13,983,816 possible numbers in no particular order into two sets of numbers each containing 6,991,908 numbers you are guaranteed the winning number will be in one of the sets but it's still just a ratio. If you continued doing this ie divide the 13,983,816 combinations into 163 sets of around 85,790 then you know the winning six is in one of these sets but if you forked out some $42,900 to play one of these sets your chances of getting the winning number are only 1 in 163. Multiplying this by the extreme Monte Carlo factor of 26 (black came up 26 times in succession in 1913) you could spend some $182 million to get a million or so!
Your chances of getting a :
The chances of getting a three of 1 in 56.6 in relation to the 163 line cover is very relevant. Put another way we are expecting 3 of the three prize wins on average every 170 plays. Now, the 163 line cover may guarantee just 1 of these three prizes but good old Mr Random is relied upon for the other 2. As I have pointed out before there is no appeal in paying some $82 to be guaranteed $2 with no increase in your chances of a higher prize  see Test C(49,6,3,6). If you played a 56 set of numbers with a good spread of the threes then you will average a three win every draw and even if you played just a 28 set of numbers you would average a three win every other draw. Firstly, looking at the Covermaster report we see that Covermaster does validate the cover and this is a handy feature as one can use it to verify any Cover. If you delete lines and use MenuToolsSearchBest Play to reconstruct the cover the limitations of the algorithm used soon become apparent. Yes, with one or two or even 10 selections deleted it can reconstruct to 163 lines but try deleting the last 10 lines and you end up with a 166 line cover.
Secondly, from the 18,424 possible threes only 3,007 are included in the cover ie 16.32%. So, for every draw 83.68% of the threes are excluded ie if we divide our threes into roughly 6 bands then using the cover we are confining ourself to 1 band with a particular mathematical relationship for each random draw where all integers or threes are given an equal chance.
If you look at MenuToolsReportsDetailed this will show you the repetition of threes in the cover. Each six can hold 20 threes. Of the 3,007 threes used to make the cover:
A valid question to ask is if you are really after a few threes wouldn't it be better to do a random selection of 163 lines from my Unique Threes 450 line Cover which has 9000 distinct threes? In other words you would have 163 lines with 3,260 distinct threes.
The first line used in constructing any cover for a 6/49 Lotto covers 260, 624 sixes. ie at least 1 three in the six. For example using 01 02 03 04 05 06 we are covering all the 15,180 '01 02 03' threes and for the other 19 threes 3x14,190, 6x 13,244 and 10x12,341. Compare this with MenuToolsReportsChartsDependency where we see that 5 of the sixes included are covering only between 3,000 to 4,000 sixes. Does the thought cross your mind that choosing a six made up from the 84% of the threes unused has some merit?
Covers may be used as an alternative to random selections when choosing one's lotto numbers but they do not perform over a reasonable period of time any better. There is a challenge in creating some of the larger covers and where there is a will there is a way for Covers come from the discrete side of mathematics  which means all the different ways it can be done are known and if tested then the optimum result can be obtained.
Below is the detailed report from CoverMaster: 
Win 6 Win 5 Win 4 Win 3 Comb 6's Comb 6's % Cum %
    1 3595746 25.71362 25.71362    2 3261643 23.32441 49.03804    3 1114905 7.97282 57.01086    4 2858548 20.44183 77.45269    5 476971 3.41088 80.86357    6 223556 1.59868 82.46225    7 93980 0.67206 83.13431    8 64089 0.45831 83.59262    9 37278 0.26658 83.85920    10 220944 1.58000 85.43920    11 11270 0.08059 85.51979    12 3665 0.02621 85.54600    13 1290 0.00922 85.55522    14 348 0.00249 85.55771    15 139 0.00099 85.55871    16 29 0.00021 85.55891    17 6 0.00004 85.55896    18 8 0.00006 85.55901    20 2476 0.01771 85.57672   1 017 1781368 12.73878 98.31550   2 115 165076 1.18048 99.49598   3 113 25917 0.18534 99.68132   4 010 2138 0.01529 99.69661   5 27 207 0.00148 99.69809   6 07 53 0.00038 99.69847   7 35 8 0.00006 99.69852   9 2 1 0.00001 99.69853  1 04 015 41942 0.29993 99.99846  2 12 38 44 0.00031 99.99878  3 0 47 8 0.00006 99.99883 1 0 03 013 163 0.00117 100.00000 13,983,816 Summary
Regards
Colin Fairbrother


Lotto Draws have no relationship to one another; the integers serve just as identifiers. Any prediction calculation on one history of draws for a same type game is just as irrelevant as another.


IP Logged  
Forum Jump 
You cannot post new topics in this forum You cannot reply to topics in this forum You cannot delete your posts in this forum You cannot edit your posts in this forum You cannot create polls in this forum You cannot vote in polls in this forum 