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Topic: DUPLICATION = CHANCES WASTED OF PRIZES IN LOTTO.  
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: DUPLICATION = CHANCES WASTED OF PRIZES IN LOTTO. Posted: February 02 2008 at 11:18pm 
Duplication of 3's, 4's, 5's and 6's in a Lotto playset
equals chances wasted
by Colin Fairbrother
Just as you wouldn't knowingly play a number set in say a Pick 6 Lotto game where you have repeated a 6 integer combination so the same should apply to the 5's, 4's and 3's subsets in those 6's. Each subset gives you a chance at the equivalent prize and the only time consideration of repetition should come into play is where you are constructing your playset and you have used up the 450 sixes in a 6/49 Lotto game or 332 sixes in a 6/45.
A very noteworthy fact is that when you do random selections of 6 integer combinations from the 49 integers for say 200 lines or less in a 6/49 Lotto game you do not get repeat 5's. For 15 lines or less you don't get repeat 4's and for 10 lines or less there is just a whisk of 3's repeated ie less than ½ of 1%. For the 1's and 2's there are no prizes and duplication there doesn't really matter; the so called "balanced" concept of having an equal distribution of the integers, when it does occur it's interesting but it has no bearing other than to limit the number of combinations for a given pool  in other words it's nonsense as an objective. Contrast this with the two tables below for a 6/49 Lotto game showing the amazing extent of repetition of the paying 3's, 4's and 5's in so called (Full) System plays ie all the combinations of 6 integers from a given pool of the integers. The first table shows the incredible percentage repetition for the 3's while the second shows the extent of repetition in all subsets. To the best of my knowledge these figures have never been published before (although I know of one site where they will probably appear with a duly backdated fictitious date and a spurious claim of authorship).
Threes Repetition in Full Wheel or System Playsets for Pick 6 Lotto Games
Pool Combs Possible Distinct 3's Repeat 3's Repetition
7 7 140 105 75%
8 28 560 504 90%
9 84 1680 1596 95%
10 210 4200 4080 97%
Looking at the popular System 8 we see that for the 28 Combs played 56 of the 5's are repeated 3 times. This means we have wasted 112 chances with some other 5's and Lordy, Lordy with nearly 2 million to choose from in a 6/49 Lotto game there is no shortage. Similarly, with the 4's there are 350 chances wasted and for the 3's 504 chances. Why your chances are reduced is covered (excuse the pun) in Probability Theory under Double Counting and with all the probability pundits about why it has never been raised as an issue defies my comprehension. A good read can be had generally and in particular on the subject at the Hong Kong University site at Critical Thinking, Logic and Creativity by Dr Joe Lau and Dr Jonothan Chan. (Have a look at Game Show which is an interesting probability scenario. Before you look at the answer think about the fact that the game show host never shows you the car only a goat! The satisfaction is greater when you work it out yourself.)
The interesting bit is that from the pseudo gurus System Plays are criticised because there are too many combinations for the pool size and not for how the set is constructed ie with so many repeats. The reason for this is that usually these "critics" are promoting all Covers or Wheels with Guarantees which can be just as contorted and distorted a set of numbers as the System Plays and have with the exception of the few that fall under my Unique 3's™ umbrella excessive repetitions as well!
An indication of how bad the wastage of chances by repetition in Covers or Wheels with Guarantees can be in a Pick 6 Lotto game is shown by looking at the guarantee of a Five win if 5 of the winning integers are in the nominated Pool: 
Cover Combs Repeat 3's Repeat 4's Repeat 5's
5 if 5 in 8 12 76.67% 62.22% 22.22%
5 if 5 in 9 30 86% 72% 30% 5 if 5 in 10 50 88% 72% 16%
What it all stems from of course is the misguided belief that a particular pool of integers has a greater chance of giving a prize in the next draw based on their appearance in previous draws (history) for a particular Lotto game which is just plain baloney.
The guiding knowlege is that the more you repeat 3's, 4's and 5's the bigger is the divergence from the average of your return or if you like a greater standard deviation. Yes, you do get more multiple hits but that doesn't always make up for the decreased incidence of overall hits. Ask yourself  "If I am shooting blind which is the more preferable  a rifle or a shotgun?" The upshot is that you could do very well or very badly with a high degree of repetition in your number set over say 500 draws and in the long term be below expectation. If you keep your repetition low then you are more likely to be closer to what probability says you should expect.
Regards
Colin Fairbrother 

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