There may be a few mistakes so if something does not add up it may be a type-o.
I wanted to run a few figures by you for groups that may help you decide the best way to set them.
Recently we formed a pool for Mega millions and I asked each member to submit their top 6 groups
from the 10 possible that they felt were most likely to show in the next draw. The topic of this post
is to show how using random to select values may be exploited to increase the odds of matching a
greater percent of the groups correctly then using the historical draw history.
If I choose 4 groups at random then the odds all 5 winning numbers will come from these 4 groups are
1 in 210 for a TG=4 setup. If I can predict the TG filter correctly and for this example I will base the calculations
on a TG=4 play then the odds change. There are 15 combinations of 4 in 6 so each set of 6 groups has
15 different ways the sets could be wheeled so that the entire set comes from 4 of these groups. For any
6 groups I select the expected chance that one of the sub-sets of 4 will match the drawing is 210/15=14.
Lets say that I generate at random 15 sets of 6 groups then I can say with a very high level of certainty
that one of the sets of 6 will contain the 4 correct groups. You may be asking how this can help because
you not only have to select the 1 out of the 15 group sets of 6 but you also have to select the correct 4 of
the 6 from the second subset.
As I mentioned above that any six groups have a 1 in 14 chance of matching all 4 groups in a TG=4 draw but
we can make a few other calculations to help decide subset #1 and subset #2 to use. Example, lets say that
we generate 15ea 6 group sets and calculate all the odds for each one for not only the 4 of 4 but also the 3of4
2of4 and 1of4. There are 120 different combinations of 3 in 10 and 4 combinations of 3 in 4 so that gives us
the odds of matching 3 of the correct groups for any one of the #2 subsets 1 in 30, 120/4=30. Now from this
we know that from a random set of any 6 groups we have a 25% chance of matching at least 3 of the 4 groups.
If we generate one subset of 6 of 10 then this won't help much but what if we generated 15 or so subsets of
6 of 10. We know that every one of these 15 subsets has a 7% chance of matching 4 of the 4 correct groups.
and each of these subsets have a 25% chance of providing 3 of the 4 correct groups. Some may be syaing "so
what" but read on. With 15 sets of 6 groups we can be relealtivly sure that one of the 15 subsets will have
all 4 correct groups. 7% * 15 = 1.05 so the odds are 1 in 15.
Remember that probability would say that 25% of the 15 groups match 3 of the 4 correct groups and this is
where we go outside the box a little. If 25% are expected to match 3of4 and 7% are expected to match 4of4
then 25+7=32 and 100-32=68% are expected to have less than 3. Lets go over this a little and see where we
stand, we have not calculated for 2of4 or 1 of 4 but and I may not get to them in this post I will try to address
them in general.
What we now know, in 15 randomly generated sets of 6 groups each we can expect one of them to match 4of4.
We know that of the 15 group subsets that 25% will have 3 of 4 and 68% will match 2 or less on average. 25%
of 15 = 3.75, rounded = 4. This means that for the 15 subsets we expected 1+4=5 of them to have at least 3
of the 4 and the remaining 10 to each contain less than 3. This is where it takes a little more than pen and paper.
Next we calculate the probabilities for how many 2of4, 1of4 and 0of4. We start with the first subset and then
compare it to remaining 14 and see how many of each level of matches they each contain. We do this one at a time
selecting one subset at a time and comparing it to the other 14. Each single, pair, tray and quad must be extracted
so that every possibility if covered. The end result is a set of 4 groups that must pass every expected probability
or it is rejected, It will also be a combo of 4 groups that only exist in one of the 15 subsets +/_ some weight given
to allow for deviation. I have been rebuilding the algorithm and adjusting it for the big games but hope to have it
finished very soon. I am also adding the option to input a key group. Running the program several times can give
some very good results because it randomly generates the 15 subsets each run, random-logic at it's finest.
Working on my Ph.D. "University of hard Knocks"