Consecutive numbers in the Pick 6 lottery have surprisingly high probability but still < 50%Previous TopicNext Topic

Found this formal paper on the subject, hope it can benefit anyone developing winning strategies, paper uses Pick 6 game for its study model, and results will most likely be different for some other lottery system.

Paper formulates calculation as function of a distance between winning lottery numbers and could have further applications in studying other types of relations between winning lottery numbers.

The fact that chance is < 50% (sort of surprising)  to a degree does substantiate using non-consecutive numbers but also bare importance to keep a record and bet accordingly if such number relations occured in the past.

Reference:

http://arxiv.org/PS_cache/math/pdf/0507/0507469v1.pdf           Distances between the winning numbers in Lottery by Konstantinos Drakakis

Want to add that on page 6 of this paper a fascinating table is displayed (hesitant to reproduce it here due to possible copyrights)

"Table 1: The probabilities that the winning set of numbers of the standard Lottery has a minimum distance k"

The probability as function of distance between numbers (starting with k=1 for consecutive numbers) increases and reaches 100% when k >= 10

Nice "median" point seem to be for distance k = 4, where probablity jumps to 90% (from 76% for 4) after k > 4 it steadily varies ~ 90% to 100%

Found also that the formulas are general enough to yield probability results for any lottery game.

I can see where this article might be important and infomative.  I will read it later.  Thanks for bringing it to our attention

Thanks Edge. I will read this.

Speaking of consecutives:)

New Jersey Cash 5 winning numbers Today (Friday , April 03, 2009 ) were: 09-19-31-37-38  jackpot rolled to $290,000.

so... we have almost perfect agreement between theoretical paper and practice (every second draw) (almost perfect as of 4/1 draw had 2 pairs of consecutives not 1)

04/03/2009 09 19 31 37 38

04/01/2009 11 12 13 25 33

oops, paper was based on the 49 numbers game (not 40 numbers game) so i still owe to myself and you firm confirmation of the 50% probability for varieties of game systems.

Thanks edge, you also gave me an idea about deducing...Don't worry what deducing is..

Not only could it be consecutives, but it could be 2 numbers difference, like instead of being: 8-9-22-29-36-39.. it could be 8-10-22-29-36-39....I wonder how many combinations that have 2 number difference exist? I know there are a few just like consecutives...

for like in Powerball from november of las year to present i noticed that there was like 2 consecutives but there were more 2 number differences...

another idea is that one could look at the ending digits for this consecutives...

Like if you knew that the numbers 8-9 were coming on the next drawings..You could ask how many combination are there that have 8-9 consecutives...

i am starting to notice that your system/observation can be lethal...but more experiments/research/observations are needed....Not research from the internet but research from LP members, that's what i mean...

solid ideas!

Important though is to get idea about probability differentials, (will need to enroll back in combinatorics class at some college:) why i say differential is that although is quite a feat to get exact numbers right,  any slight probability % variation (as ie < 50% for 49 game for consecutives and therefore play the opposite and skip draws when some high occurance of consecutives happen) will give you an advantage over reasonable amount of time, all of it can be calculated and probably will amount to year-length of game play if not longer, to get to some low tier-prize:) but still, we are facing one unimaginably unfavourite odds games constructed by humanity:) i will take any, even slightest "imbalance" in the game structure.

And look, the almost 50% comes as a surprise! because intuitevly you count consecutives in the set of 49 numbers and it doesn't appear that probability should be so high.. but it is.. therefore i think this opens up ideas (as you pointed out) to search for other "relations" and calculate their's probabilities and build this in into game strategy.

plus the "even/odd" filters, plus high/low filters, plus high ending digits/low ending digts filter, plus spread filters....That's if you like, but i think you would have to do it because Powerball has some staggering odds/amount of combinations...

if you get into combinatorics and get the right consecutive you will still need to lower the amount of combinations...I think....

fyi recent news:) consecutives is something that abs can not be ignored...

Mega Game 4/3/2009 Winning Numbers: 16-22-38-39-48 +42   (with 1 consecutive number pair: 38-39)

As far as combinatorics, i am keenly interested in truncations such as above (01 thru 15 lost) these are commonly called groups, its not so much relation, so skip the thought:) but relations odds/even is a good question insofar as what is the probability of having an odd-odd or even-even pair in set of let say 56 while leaving rest of pairs in an arbitrary state... one can go crazy with relations for sure, and many have done it: key is to identify some "imbalance" (< or > 50%, in that neighborhood) you want be able to isolate more precisely. if you could you would have retired by now in Hawaii let say:)

I also wanted to point out that if you use the Ending digits: it will be 1-2, 2-3, 3-4, 4-5, 5-6, 6-7, 7-8, 8-9, 9-0...Basically 5 consecutives to choose from, then if you pick 1 of them for instance let's say if you pick: 2-3, then it will be 2-3, 12-13, 22-23, 32-33, 42-43, in total 5....Just let's pray that those 5 combined have less combinations...

And not only that but consecutives in the same ending digit don't repeat from the previous drawings so that's 4 consecutives that you have to choose from....

example: if 2-3 plays the next time a consecutives plays it will not be 2-3 but something else...This occurs most of the time...

Well, I read the article.  Rather I tried to read the article.  I am afraid the math is way over my head.  Either that or I am too short.

Consecutive numbers do ocurr about 50% of the time.  That is enough of a pattern to be important.  What would also be important are patterns that ocurr only 10% of the time.  Or 90% of the time.  Those 50-50 patterns are so durn troublesome.  I would much rather have a pattern that sits at one end or the other of the spectrum.  Got any of those you would care to share?

Ran this through my computer. Of the 13,983,816 total possibilities 6,924,764 combinations contained consecutive numbers - that is - IF my programming is correct.

I've never looked for consecutive numbers but I'm looking at Little Lotto 5/39 from all angles so here goes: Out of the last 68 games(Feb. 1st to present March 9th) 32 games had at least one pair of consecutive numbers. Out of these..... 15 pairs came from the number group 30-39 and 12 pairs came from the number group 10-19. And out of these 32 pairs.....12 contained at least one number from the previous draw. (I still need to look at the numbers individually to figure out how I would choose a set of numbers to play. ) I'll be watching consecutive numbers from now on!