Posted by Ion Saliu on June 27, 2000.
Esteemed Mr. Joytsar Kokostirk,
I would like to abide by your request today and use the MP (Member of Parliament) language you have tried so hard and diligently to acquire and master. I may have been on the opposite side. If it was offending to you, I truly apologize. I thought that expressing the truth requires the most direct linguistic form. I would not hesitate to truly express the truth, even if it used Dracula's idiom. It may lead to negative connotations, but the truth should always be above its form(s) of expression. You know, Vlad Tepes Draculea made his own contribution to history, as tiny as it may be. Maybe we are talking now by this means because he put his body in the way of the Ottoman flood. What would have happened if such historic flood had reached the land of the Renaissance (it wasn't too far away, after all)? I want to express an idea that's in most people's minds, although not very clear in all situations. Your language is determined by your opponent (PowerBASIC, Visual Basic, C++, Java, etc.)
Sir, I am saying here that Content is more important than Form.
You repeatedly asked me the following question:
“Can you simply answer the following one question:
1. Will the 416 lines in your wheel produce more 3-, 4-, 5-, and/or 6-number winning combinations in 6/49 games than would be produced by 416 different lines according to random expectation?”
I certainly answered it, my personal way, several times as well. I thought, however, that my answer was clear and “covered” all the aspects of your question. Apparently, my answer failed to reach your understanding as set forth by the specifics in your question, as such specifics may and do vary from cognitive entity to cognitive entity. I would like to be more universally specific now using the language of numbers. Nothing is more encompassing than the language of numbers.
It all started with my 49-number wheel assuring the '3 out of 6' minimum guarantee. I agree with your friend Wheely (Kotkoduck) that the more correct form would be 'ISO~3if6' (ISO probably means "Is System Okay"). You counter-attacked with what you claimed to be “416 bona-fide randomly generated combinations”.
Sir, generating 416 random lotto combinations DOES NOT assure the '3if6' minimum guarantee (ISO or not ISO). I showed you previously a number of 6-number combinations that are not covered by your 416 random
combinations (a.k.a. “Wheel 501”). I can put all those uncovered combinations in a file and post it, if you wish. Would you please check the following combinations and see if they meet the '3if6' minimum guarantee set forth by your set of 416 random combinations?
1 2 9 23 37 42
1 4 17 23 27 46
1 8 15 16 45 48
2 4 14 25 32 47
There are many more such uncovered combinations. I would dare a
metaphor. You take a bath every day and step in to a public place. How would you feel some days to step in to a public place “uncovered”, after taking a bath?
My WHEEL49.36 was created by a system-generating engine. The engine insured that each and every 3-number group in the 49-number field was covered at least once. Generating random combinations DOES NOT assure that each and every 3-number group will be generated.
As stated, WHEEL49.36 contains all the 3-number groups in a 49-number field. That is, it contains at least once each 3-number group. How many 3-number groups are there in a 49-number field? Easy answer: We apply the combination formula of “49 taken 3 at a time”.
C(49,3) = 18,424 combinations.
Meanwhile, your 416 random combinations contain this amount of 3-number groups (one 6-number group consists of C(6,3) = 20 lotto combinations): 416 x 20 = 8,320 combinations.
Considering the main purpose of the two sets of numbers -- “3 out of 6 minimum guarantee” -- WHEEL49.36 is 18,424 / 8,320 = 2.2 times more efficient than a 416-combination random set. The random set does not cover the main condition. That's why WHEEL49.36 always offers at least 2 or 3 “3-number winners”, while your random-set will fail in some drawings.
We can extend it to “minimum 4 out of 6” guarantees. Suppose a system- generating program (such as one of LotWon modules) creates a 5000- combination lotto wheel. You generate bona-fide 5000 random combinations. It is not guaranteed that your random-set will cover each 4-number
combination in the 49-number wheel. Most likely, it won't. A system- generating module, on the other hand, makes sure that the minimum guarantee is met.
So, regardless if one generates bona-fide random combinations, or uses modified previous drawings from various lotto games, the selected sets are not guaranteed to meet a minimum assurance. Only a system-
generating program can assure a minimum guarantee.
And , again and again, the best way is to use WHEEL-6.EXE. The lotto conditions vary widely, from drawing to drawing. Therefore, the “wheel” (the set of lotto combinations) played must change from drawing to drawing. Let me give you a brief example here. It is common occurrence that a drawing does not repeat 3-number groups from the previous 10 drawings. If you don't trust LotWon in this regard, you can check it manually. Now, one 6-number drawing can be expanded to C(6,3) = 20 combinations. The remaining 49 – 6 = 43 numbers can be expanded to C(43,6) = 12,341 combinations. Therefore, one 6-number combination can eliminate: 20 x 12,341 = 246,820 lotto 6/49 combinations. If we don't want to play any 3- number groups from one drawing, we discard of 246,820 combinations. Theoretically, for 10 previous drawings, we can eliminate 246,820 x 10 = 2,468,200 combinations. That's about 18% of the total 49-number lotto combinations. Why should we consider them if we know that none of them will come out next drawing?! Plus we can consider many other filters.
“Dynamic” is far superior to “static”…
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