Sums & even/odd relationships

[maryd]

Hi:
I am new to the lottery; I actually started it as an experiment in statistics. Now, I guess it has grown into a bit of a passion...
I have read a lot in a short time, but there is something I have noticed in the Canada 6/49 and the Ontario 6/49 that I am not sure is worthy of note, but I find interesting.
For some reason, nearly all 50/50 even odd number combinations total an odd sum whereas most 4/2 or 2/4 even/odd ratio totals an even number.
I am currently not in the position to spend money on even an abbreviated wheel, I have tried to use this to "verify" my choice in numbers.
So far, I have only managed 2 $5.00 winnings, but only started playing about 3 weeks ago.
Is this of any worth, or am I just reeallllly stretching..?
By the way, thank you Lotto-Tutor and everyone else out there who posts free info (especially the definitions) that helped me from feeling like a total dolt from all the jargon etc.

 

[johnph77]

If you have an odd number of odd integers the sum of those numbers will always be odd.

If you have an even number of odd integers the sum of those numbers will always be even.

Welcome and gl

j

 

[CMF]

Hi:
I am new to the lottery; I actually started it as an experiment in statistics. Now, I guess it has grown into a bit of a passion...
I have read a lot in a short time, but there is something I have noticed in the Canada 6/49 and the Ontario 6/49 that I am not sure is worthy of note, but I find interesting.
For some reason, nearly all 50/50 even odd number combinations total an odd sum whereas most 4/2 or 2/4 even/odd ratio totals an even number.
I am currently not in the position to spend money on even an abbreviated wheel, I have tried to use this to "verify" my choice in numbers.
So far, I have only managed 2 $5.00 winnings, but only started playing about 3 weeks ago.
Is this of any worth, or am I just reeallllly stretching..?
By the way, thank you Lotto-Tutor and everyone else out there who posts free info (especially the definitions) that helped me from feeling like a total dolt from all the jargon etc.

MaryD

2 4 6 7 9 11 when added = 39
2 4 6 8 9 11 when added = 40
2 4 5 7 9 11 when added = 38

I see what you are saying - but the numbers are only identifiers. They have no magnitude.

Regards
Colin Fairbrother

 

[GillesD]

Numbers for a 6/49 lottery

CMF

You may call the results of a draw in a 6/49 lottery whatever you want (identifiers or whatever) but they are numbers and as such, they must follow the laws of mathematics. As johnph77 pointed out, 1,3 and 5 odd numbers in 6 will give alwys give an odd sum and an even sum if you get 2, 4 or 6 odd numbers.

And if you believe 3 numbers will be under 10, then you can expect that the sum will be always over 39 (at least 99.99999% of the times). And for 3 numbers 40 and over, the sum will certainly be (with the same percentage) 140 and over. There is no way out of this.

And from my experience, if the number of draws is large enough, the actuel results (even/odd ratio, sum of numbers, numbers within each decade, etc.) will be very near what the laws of probability can predict, but not perfectly obviously.

 

[CMF]

GillesD

When you are able to distinguish between integers being used to identify identical objects and integers being used to show magnitude all will become clear!

On the way it may also dawn on you that a Lotto draw is according to the " laws of mathematics ..." an independent event which means any like history is just as irrelevant as another.

Supporting tests and lengthy explanations are on my reference and information website.

Regards
Colin Fairbrother

 

[GillesD]

Clarification

CMF

If you take the time to read some of my postings (if not all, as this may be long), you will find that my position is exactly what you say: "a Lotto draw is ... an independent event which means any like history is just as irrelevant as another". You will notice that, in my quote, I remove the words "according to the laws of mathematics ..." from your post. I would rather say that a draw follows the laws of probability, like having a 33.29% chance for a 3/3 even/odd ratio or having a 49.52% chance for at least 2 consecutive numbers in the 6 numbers.

But after the winning numbers are out (and you win based not on their magnitude but whether they match those on your ticket), the laws of mathematics apply (as johnph77 pointed out) if you decide to calculate any statistic (sum, differences between numbers, standard deviation, etc.).

 

[CMF]

Numbers are not necessary in a Lotto game!

GillesD

A Lotto game such as the 6/49 game has these requirements.

1. 49 objects with identical properties each with a distinguishing mark.
2. the 49 objects to be such that they can be mixed randomly.
3. the method of random mixing treats each object equally.
4. tickets sold with at your choice any combination of those 49 objects.
5. tickets sold are applicable to one or more future draws as paid for and specified.
6. random selection of 6 of those objects from the 49 objects for a winning ticket.
7. prizes awarded based on how many of the objects in the winning selection are in the ticket selection

In those requirements you do not see that it is mandatory that the objects be confined to the integers between 1 and 49. You could use whatever integers you liked - they could be all odd or all even or 3 digits etc. In fact you don't have to use integers at all - you could for example use 49 of the 52 playing cards.

What you are doing is treating a convention as being obligatory. To trot out simple arithmetic results as somehow being supportive is nonsensical. This issue has been looked at by me in these and other articles -
Sums return less than Random Selections
SUMS Lotto Myth

Regards
Colin Fairbrother

ps " ... Mathematics Laws ... " was your term. Yes, I do have a passing knowledge of probability as applied to Lotto - in fact I have a website practically devoted to it!

 

[northlight]

GillesD

A Lotto game such as the 6/49 game has these requirements.

1. 49 objects with identical properties each with a distinguishing mark.
2. the 49 objects to be such that they can be mixed randomly.
3. the method of random mixing treats each object equally.
4. tickets sold with at your choice any combination of those 49 objects.
5. tickets sold are applicable to one or more future draws as paid for and specified.
6. random selection of 6 of those objects from the 49 objects for a winning ticket.
7. prizes awarded based on how many of the objects in the winning selection are in the ticket selection

In those requirements you do not see that it is mandatory that the objects be confined to the integers between 1 and 49. You could use whatever integers you liked - they could be all odd or all even or 3 digits etc. In fact you don't have to use integers at all - you could for example use 49 of the 52 playing cards.

What you are doing is treating a convention as being obligatory. To trot out simple arithmetic results as somehow being supportive is nonsensical. This issue has been looked at by me in these and other articles -
Sums return less than Random Selections
SUMS Lotto Myth

Regards
Colin Fairbrother

ps " ... Mathematics Laws ... " was your term. Yes, I do have a passing knowledge of probability as applied to Lotto - in fact I have a website practically devoted to it!

Hi CMF,

Thanks for sharing the knowleadge, I read through found it interesting and actually what you say is correct I believe, but one question is, the 1-49 number can be replaced by any chracters, like A-Z, or any stones, that is true, but why would be trying to predict it here? This make me confusing as it really contridict.

A guy in my hometown plays pick 5, or pick 3 I forgot exactly, he predicted and bought same one ticket 800 copies, i.e, 800 tickets and each ticket have exactly same strings on it, he is that confident and in fact he won and won 1M for 800 tickets, each tickets won 1200$. Sees he did very well and soon eailier he Won 5Million by the money pool he operated, this fact does confuse me again.

looking forward to your opinion.
Thanks

 

[CMF]

Northern Lights from NorthLight

NorthLight

I haven't visited this forum for quite a while until I received an email advising that GillesD had replied to a post I made nearly 12 months earlier. My new year resolution was to maintain the info on my website and withdraw from monitoring what goes on in our little Lotto Forum community - full as it is with sensitive souls. I can honestly say I have not so much as taken a 1 second look at the forum that caters for dream book people etc and I can tell you I am very glad of that - it is not the centre of the Universe as it's members would have you believe.

Recently, I became interested in Forex or Foreign Exchange. Prediction is relevant as you can look at the history and for a given scenario see what happened before. This is by no means accurate as sentiment, irrationality, skittish behaviour, downright manipulation by the big players and economic fundamentals play major parts. (An excellent result recently for the Australian CPI triggered a sell off from record highs because a rise in interest rates was not imminent and the carry trade thought it might do better elsewhere - it pays not to be too rational with Forex - think of the most stupid thing to happen and you could be right on the money. Anyway, prediction is not really possible with Lotto as the past results have no influence on future results.

Here is a link to an article I wrote on the winner's of the UK Lottery - I happened to have dinner while sitting next to the brother of one of the winners. I look at the cosmetic things you can do with the numbers you play in that article.
Professor's, Printers & 1st Prize Win UK Lottery

Regards
Colin Fairbrother

 

[Bertil]

Sums Lotto Myth

Hi Colin,
Your posting with "All World's Lotto 649 sums analyzed" is very interesting
and I wonder it you generated a distribution graph and what did it look like?

Also, did you calculate the std.dev. from the mean 150. A formula says it
is likely to be very close to 32.8. Can you verify this number? I'm unable to print or download your data and thus cannot do the calculation.

Stig Holmquist

 

[CMF]

World's SUMS data for the World's greatest Lotto Standard Deviation Enthusiast.

Stig

If you look in the same place you should see the data in rtf format and a nice little graph for all to swoon over.

As much as some would like to see an advantage in using numbers that add up to 150 there isn't any - more of them but the incidence is proportional to the quantity.

Regards
Colin

 

[Bertil]

Sums myth

Hi again Colin,
I looked at both sites mentioned above but found no graph. Would you please be more specific about where I can locate it.

I'm not trying to win a jackpot. I find lotto numbers mathematically interesting. Also, I asked you for the std.dev. from the mean sum 150. Did you calculate it and if so, what value did you get? I wonder how fast it approaches the theoretical value 32.8 and I plan to try shorter runs if I will be able to get the data on a spreasheet and use Excel.

Hope you can help.

Best regards,

Stig

 

[CMF]

Seek and ye shall find with Stig!

Howdy Stig

Try this link and it should take you to what you are looking for.

All the World's 649 Sums analysed with ding-a-ling chart

I still buy the occasional ticket in Lotto especially when they do promotions like the $20 million jackpot mid next month. I simply randomize the order of the numbers and then use my 17 line matrix. Your chances don't increase - it's more in the line of a fashion statement in choosing one's numbers. For a few dollars the jackpot lotteries still represent the best possible windfall.

Regarding Standard Deviation I think this would be more pertinent if I did each 649 Lotto history separately then looked at the variance from the average of the histories. Problem is not a lot of history available - 17,850 draws I am using to push the point that the sums with the greater quantity are not necessarily the better performers.

Regards
Colin Fairbrother

 

[Bertil]

All Worlds 649 sums

Colin,

Your graph is very impressive and I'm surprised at the large variations at the peak.I had expected more uniformity. I'm wondering how you constructed the normal curve simulation. It seems to me it needs to have the same std.dev. as the actual data or did you base it on some form of approximation?

Thank you for your cooperation.

Stig

 

[CMF]

Stig

The calculated Sums arrived at by adding the integers together (putting aside whether this is a valid thing to do) when plotted produce a smooth Bell Curve. A scaled down version of this for 17,850 draws also gives a smooth curve.

The purpose of the exercise is to see whether one Sum group is favoured over another when comparing the 17,850 draw results with the theoretical. As you see even for our small sample the point is made that it does not. If there were say, 100,000 draw results the data line would be much smoother but this would mean using my RNG and while I am happy with that others use it as an excuse to dispute the validity of the exercise.

Regards
Colin Fairbrother