1,2,3,4,5,6: Probable but not likely

Posted by Jim Schutte on October 18, 2000.

I am not a maths expert but I argued with my brother on a gut feeling that in a lotto 6 draw it is extremly unlikley that lotto combination 1,2,3,4,5,6 will be drawn. He maintains that it is a random series of numbers which are as likely to be drawn as any other set. I think that you agree with me when you say that such numbers are extremely rare and will be left out of selections along with strings of odd or even numbers etc.
Can you explain in laymans terms why this is so?

Can you do a page on your site on the basics of probability. You mention guassian curves and the law of big numbers. What are these? without being to technical of course.

Great site.

Regards,

Jim

Resources in Theory of Probability, Mathematics, Statistics, Software

• Theory of Probability: Best introduction, formulae, algorithms, software.

• Lotto Combination '1,2,3,4,5,6': Probability and Reality;
  ~ Consider the standard deviation as well!
• Probability, Odds of New York Lottery Draw 911 on September 11.
• Software to generate combinations and find the probability of a lottery drawing to match its date.
• Probability That Player Index N Draws Ticket Number N.
• Enigma: Encryption decryption, cipher, code breakers.
• Probability of perfect shapes in nature: rivers, mountains, trees.
• Geometric or regular patterns on lotto play slips, cards, grids.
• Coin tossing hits by date: heads = 1st day, tails = 2nd day.
• Randomizing: An Art of Scientific Philosophy, Science of Philosophical Art, Philosophy of Artistic Science.
• 1,2,3,4,5,6: Probable but not likely.
• Software and formulae to calculate lotto odds using the hypergeometric distribution probability.

  Of interest:
  

• Fundamental Formula of Gambling (FFG).
• Mathematics of Fundamental Formula of Gambling.

• Download Probability, Mathematics, Statistics, Combinatorics Software.

• Lotto combination probable but not likely Ion Saliu. 10/21/2000.
• Lottery combination odds, statistics BigJer. 10/19/2000.

Comments:
: : Lotto Combination 1,2,3,4,5,6: Equal Probability Low Appearance. I am not a maths expert but I argued with my brother on a gut feeling that in a lotto 6 draw it is extremly unlikley that 1,2,3,4,5,6 will be drawn. He maintains that it is a random series of lotto numbers which are as likely to be drawn as any other set. I think that you agree with me when you say that such numbers are extremely rare and will be left out of selections along with strings of odd or even numbers. : It would take a lot more than a Web page to tackle theory of probability and lottery . Online probability tutoring would require a full-time job, and then some. At this time, I can only offer so much on my website. But what I offer is undeniable mathematically. Your observation on the "1-2-3-4-5-6" type of lotto combinations is also on many people's minds. Indeed, every lotto combination has the same individual probability: p = 1/N. There are 13983816 lotto 6/49 combinations, therefore any lotto combination, including 1-2-3-4-5-6, has a 1 in 13983816 chance to hit. That's one step of the theory, the first one. We can look at simpler lottery games, where the total of possible combinations is much lower, therefore easier to analyze. For example, the pick-3 game has only 1000 outcomes, from 000 to 999. The individual probability is 1/1000. One should expect one particular combination to appear every 1000 drawings. Further, since p is constant, all pick-3 combinations should appear equally (in multiples of 1000 drawings). Thus, 2000 lotto drawings, every combination should have come out 2 times, etc. There are lottery combinations that come out 10 times in 5000 drawings, while other lotto combinations do not appear at all. Briefly, there is more to lottery than just the individual probability. Look at many lotto drawings, thousands if possible. You can easily calculate the average of a lotto game. A lotto 49 game has an average of 1+49=50/2=25. You can use Gauss's formula and notice something. The sum-totals of most drawings fall within the Gauss (bell) curve. It's hard to find a 1-2-3-4-5-6 combination anywhere, or a 44-45-46-47-48-49 combination. There is a much more complex explanation for the absence of such combinations. It can use Markov's decision-making theory (Markov chains). The easiest path in a Markov chain is totally random. A combination like 1-2-3-4-5-6 would require additional steps, which dramatically decrease the lotto probability. Title of the article is "The Lotto Drawing 1,2,3,4,5,6: Same Probability, Lower Degree of Certainty". The lottery combination 1,2,3,4,5,6 has an equal probability of appearance as any other but will be drawn far less frequently because of a lower degree of certainty.