Optimum set
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It is not that I do not want to talk to you but I can not answer your question for these reasons:
- I do not have all results on all lotteries, although it is feasible to get this information, I have decided to maintain databases on only 3 lotteries: Canadian 6/49, Québec 49 and UK 6/49.
- to me, the term Optimum Set has never been formally defined; here are some questions that come to my mind:
--- how many numbers should be be included in the Optimum Set: 15 numbers has been mentionned often, but also 12 and why not 10, 16, 18 or any other number? As the number increases, so does the number of possibilities to verify.
--- what constitutes an Optimum Set? The set with the most 3 winning numbers (WN) for past draws? Or the set with the most 4 WN? Or the set with the most 5 WN? Or the set with the most 3+4+5 WN? Should 4 WN weight more than 3 WN in the total and if so, what weight should be given? And what about 5 WN?
--- Another important issue to consider is: Are past results indicative in some predictive way of draws yet to come or are the upcoming draws independant and unrelated to past draws?
Once you have answered these simple questions to define the Optimum Set, the principle to obtain what you want is quite simple. Let's say you have decided to find a 10-number Optimum Set:
1 - Identify each of the 10-number sets possible from the 49 numbers in your lottery. Luckyly, with 10 numbers, the possibilities are not that great, only 8,217,822,536.
2 - For each 10-number set, identify each 6-number possibility. At least, this number of combinations is manageable (210).
3 - Using past draw results (slightly more than 2000 for Canadian 6/49), with each 6-number possibility, verify how many 3WN, 4WN, 5WN and 6WN this combination has got and keep this in memory.
4 - Keep going until you have gone through all possibilitie and you have your answer.
This might not be the most efficient one but will get you an Optimum Set based on your criteria.
And thenchanging your criteria will require you to start over. And by the way, this does not take into consideration the bonus number. Adding it will only increase the time required.
Obviously shortcuts are possible to reduce calculation time, but then the only way to be 100% sure is to look at all possibilities.