|Posted: July 16, 2009, 1:42 pm - IP Logged|
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Toss an unbiased coin a large number of times and notewhat follows after say, 9 heads up. You will find that as expectedgiven there are only two possibilities that what follows is 50% heads.This is what probability theory teaches us and what applies to a simplecoin also applies to Lotto.
The Pick 3 or Cash 3 Lotto game has 1,000 3 digitnumber possibilities each of which can be played straight which can bedivided into 3 basic sub sets. There are 10 Triples where all thedigits are the same such as 000 or 999 and which can only be playedstraight - your chances of getting one of these is 10/1000 x 100 = 1%.There are 270 Doubles where only two of the digits are the same such as011 or 900 - your chances of getting one of these is 270/1000 x 100 =27%. There are 720 Unmatched where all the digits are different such as012 or 789 - your chances of getting one of these is 720/1000 x 100 =72%.
So, if we have 10 Unmatched or 4 Doubles drawn consecutively is it more likely that the converse will occur on the next draw?Intuitively we tend to think that after a long run of Unmatched that itis more likely a Double will occur - the reality is that what followsis in accordance with the odds. After 1 Unmatched or 19 Unmatchedconsecutively you will get 72% of the time another Unmatched, 27% aDouble and 1% of the time a Triple. Positively speaking you will findif you are considering a number of State Games that as the consecutiveUnmatched or Doubles increase your choice of State is narrowed so youcan use this as an alternative to a random State Game selection.
Now, I realize that the people who study the numbers inLotto are in the main an extremely hard bunch to convince on anythingrational - bizare is easily accepted! If you have read just a little ofwhat I have written you will realize that I am not fazed by that andtreat it as a challenge to convince the unconvinceable. One can learnnew things oneself from this, as pushing yourself to the limit toexplain things in the simplest way can open new frontiers.
To convince you I call upon the same mechanism I usedwith Jackpot lotteries - Signatures. In this case I shall useSignatures of a length 20. So if we have a draw with an Unmatched asthe winning number and the previous draw was a Double and the previous18 draws were Unmatched this is denoted as UDUUUUUUUUUUUUUUUUUU. In ashort hand way we can use UD18U. So we can cycle through all the 54State Games and draws (the code is not difficult for a RelationalDatabase person as in yours truly and only takes a few seconds to run)and come up with some 136,753 Signatures to play around with.
Using the Pick 3 Signatures we are able to determinewhat followed 19 (or a lesser number) Unmatched. As shown in the graphbelow where we have considered from 1 to 19 consecutive Unmatched theresulting win whether it be an Unmatched, Double or Triple isconsistent with the odds, that is 1% for Triples, 27% for Doubles and72% for Unmatched. In other words whether it be 1 or 19 consecutiveUnmatched the following win will be in accordance with the odds.
Moreover, from the136,753 Signatures irrespective of the 90,309 group configurations theresultant percentage of wins follows the odds - namely, 72% Unmatched,27% Doubles and 1% Triples.