Colin Fairbrother

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whether other than through sheer luck the odds can be bettered.

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Pick 3 Lotto Chances of Success
after Multiple Consecutive Doubles or Unmatched

by Colin Fairbrother

Toss an unbiased coin a large number of times and note what follows after say, 9 heads up. You will find that as expected given there are only two possibilities that what follows is 50% heads. This is what probability theory teaches us and what applies to a simple coin also applies to Lotto.

The Pick 3 or Cash 3 Lotto game has 1,000 3 digit number possibilities each of which can be played straight which can be divided into 3 basic sub sets. There are 10 Triples where all the digits are the same such as 000 or 999 and which can only be played straight - 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 as 011 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 as 012 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 it is more likely a Double will occur - the reality is that what follows is in accordance with the odds. After 1 Unmatched or 19 Unmatched consecutively you will get 72% of the time another Unmatched, 27% a Double and 1% of the time a Triple. Positively speaking you will find if you are considering a number of State Games that as the consecutive Unmatched or Doubles increase your choice of State is narrowed so you can use this as an alternative to a random State Game selection.

Now, I realize that the people who study the numbers in Lotto are in the main an extremely hard bunch to convince on anything rational - bizare is easily accepted! If you have read just a little of what I have written you will realize that I am not fazed by that and treat it as a challenge to convince the unconvinceable. One can learn new things oneself from this, as pushing yourself to the limit to explain things in the simplest way can open new frontiers.

To convince you I call upon the same mechanism I used with Jackpot lotteries - Signatures. In this case I shall use Signatures of a length 20. So if we have a draw with an Unmatched as the winning number and the previous draw was a Double and the previous 18 draws were Unmatched this is denoted as UDUUUUUUUUUUUUUUUUUU. In a short hand way we can use UD18U. So we can cycle through all the 54 State Games and draws (the code is not difficult for a Relational Database 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 determine what followed 19 (or a lesser number) Unmatched. As shown in the graph below where we have considered from 1 to 19 consecutive Unmatched the resulting win whether it be an Unmatched, Double or Triple is consistent with the odds, that is 1% for Triples, 27% for Doubles and 72% for Unmatched. In other words whether it be 1 or 19 consecutive Unmatched the following win will be in accordance with the odds.

Moreover, from the 136,753 Signatures irrespective of the 90,309 group configurations the resultant percentage of wins follows the odds - namely, 72% Unmatched, 27% Doubles and 1% Triples.

Colin Fairbrother

ps I am quite proud of this article as for the first time it provides proof that the increased absence of a number in Lotto does not ensure that it will fall in any other way other than what the odds determine. Some would argue this has to be so logically - to that I say convincing the "pundits" in Lotto requires more detail.

There are plenty in this field who are incapable of logical thought but for those who can I'm sure this has been a severe blow to the processes they have used. The next step is convincing them that digit position analysis achieves nothing other than weirdly constructing a number whose chances of success are determined by its entirety. 

This article first published on the web 19/7/2006 and has been viewed 64942 times.
The author may be contacted at To generate sets of Lotto numbers to play for most Lotto games around the world go to LottoToWin ® where for a US$5.00 annual subscription you can store the numbers as well, to check later for wins. The numbers produced have no duplicate subset combinations of two integers (if applicable) or three integers, use all the integers for the particular Lotto game and maximize the coverage of the potential winning main number. The articles on this site have been selected from the many at the forum LottoPoster
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