Question for the math experts

[winhunter]

I need to find a simple equation that provides the expected match count based on random chance for any given amount of predicted numbers. Let's say for example that I predict 25 numbers for the Florida Lotto 6/53. How many numbers should I expect to match (based on random chance) out of those 25 numbers? What if I predicted 49 instead?

How would I calculate that on a draw per draw basis.

Also, What if I predicted an average of 20 numbers over 100 draws. What would be the average expected match count for those 100 draws? How would I calculate that?

I need these calculations in order to better determine whether or not WINHunter optimizations are on the right track, or if they are way off base.



Andrew

 

[charles2]

I need to find a simple equation that provides the expected match count based on random chance for any given amount of predicted numbers. Let's say for example that I predict 25 numbers for the Florida Lotto 6/53. How many numbers should I expect to match (based on random chance) out of those 25 numbers? What if I predicted 49 instead?

How would I calculate that on a draw per draw basis.

Also, What if I predicted an average of 20 numbers over 100 draws. What would be the average expected match count for those 100 draws? How would I calculate that?

I need these calculations in order to better determine whether or not WINHunter optimizations are on the right track, or if they are way off base.


Andrew

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this is the way i do it Andrew, so for your 6/53 i divide 53 by 6 = 8.833, so then i just divide any number of balls that i play by 8.833 to give me an @ number of hits with those number of balls predicted.

so for you 25 numbers / 8.833 = 2.83 = @ 3 hits on average etc etc

20 balls / 8.833 = 2.264 = @ 2 hits etc etc

 

[winhunter]

Thanks!

Seems simple enough! This will help determine if elimination levels and optimizations fit certain criteria. I don't want to eliminate numbers and it be way BELOW an acceptible standard.



Andrew

 

[NmbrsDude]

something to consider...

Andrew,

When I first started designing lottery prediction systems, I used to measure the potential of any resulting theory by the average amount of numbers I got right out of say, 20 for a 6/49 game. (2.45 according to the formula above which I also use).
Funny thing I found out along the way is that the average, although it's a good overall first indication of how your system is doing, it can be deceiving. Take for example the 10 results below out of 20 numbers:

3 2 2 3 4 2 2 3 3 2

The average is 2.8/20 which is much better than 2.45! The problem comes when you try to wheel these numbers. You would be hard pressed to even win back 25% of your money with those results.
On the other hand, consider the results below:

0 1 5 1 2 4 1 0 5 1

The average is 2.0/20 but you hit 4 or more 3/10 times. I'm sure you'll agree that you will probably make more money back with those results than the ones above.
Simply stated, the average doesn't matter as much as how high the peaks are because that's where you'll make your winnings.
Just my observations...

ND

 

[hot4]

Re: something to consider...

Andrew,

When I first started designing lottery prediction systems, I used to measure the potential of any resulting theory by the average amount of numbers I got right out of say, 20 for a 6/49 game. (2.45 according to the formula above which I also use).
Funny thing I found out along the way is that the average, although it's a good overall first indication of how your system is doing, it can be deceiving. Take for example the 10 results below out of 20 numbers:

3 2 2 3 4 2 2 3 3 2

The average is 2.8/20 which is much better than 2.45! The problem comes when you try to wheel these numbers. You would be hard pressed to even win back 25% of your money with those results.
On the other hand, consider the results below:

0 1 5 1 2 4 1 0 5 1

The average is 2.0/20 but you hit 4 or more 3/10 times. I'm sure you'll agree that you will probably make more money back with those results than the ones above.
Simply stated, the average doesn't matter as much as how high the peaks are because that's where you'll make your winnings.
Just my observations...

ND

And very good ones. The *average* is not enough.

We need to pay attention to the *hypergeometric distribution* ( the frequency of hits=6 and frequency of hits=5 ... and frequency of hits=0).

Your example shows an observed frequency of hits=0 bigger than expected, however the observed frequency of hits=5 is bigger than expected too!

Indeed, what you want is that observed frequency of hits >=3 beats the odds the most of the time and in a very good percentage.

The meaning of this, depends on the amount of numbers we are speaking about.

Frank

 

[Dennis Bassboss]

That is pretty interesting....Here's my toughts and opinion on that....
The average and the expected values are good stats to look at but they are not the ultimate data to considers...Frank last line ''The meaning of this, depends on the amount of numbers we are speaking about.'' says a lot here... I would add that ...It depends on when and what population we are dealing with too...In other words if I analize some sets and use these for the expected values the 6 hitters..the 5 hitters all to the 0 hitters are different when compared to the overall population...Lets say you take all the chunk of 100 draws and analyze them seperately...You will notice some changes...The logic behind this is that some individual numbers are hitting more than others in any given time period and some sets of numbers too..To see if any predicting device is doing great its results have to be compared to the best sets at a given time...knowing that the best sets won't be the same in these time periods ...if it beats them or comes close to these best sets results than we can say that we are doing great...and automatically we are over the overall expected values...I remember not so long ago in a 6/49 thread I compared the hits from both sets made up of the prime numbers to the dancing set...and even if the dancing set is composed of only 12 numbers versus 15 for the prime numbers set (and some numbers are in both sets)..the dancing set in that time period was doing much better than the prime numbers set...So for that time frame the dancing set was doing great...
When I play a set for a draw...I don't really care if it is doing better than the overall expected values of the entire history...But I do care about how it is doing at the moment that I play it...
There are many expected values to look for...Only taking the kind of static overall expected values in order to compared results is rushing for an erronous answer at a specific time because if I do take the best set from every chunk of 100 draws I will beat this static overall expected value badly...And this is also why it is not so wise to play the lets say most 5 hitters in the entire history draw after draw in certain time frame....
Using a static approach like a best performing set has its + but using a dynamic approach like Win Hunter can do has its + too...
And Win Hunter can produce so many sets from different settings that you can't compared its performance base only on what a few stacks produces...The trick is to play what the right stack produces at the right time...And to be fair when comparing Win Hunter to the overall expected values ...We should use different stacks every draw taking only the best ones...Why? Because the 49 balls are used in every draw...
Some stacks from history within history loaded into Win Hunter can outperformed any best stack taking the entire history into consideration at any given time...
Example a glimpse of the 20-43 history predictions results using one of my Banco optimized stack
15:10,3 of 6
14:11,2 of 6
13:14,3 of 6
12:14,4 of 6
11:12,5 of 6
10:14,2 of 6
09:10,3 of 6
08:10,4 of 6
07:10,3 of 6
06:10,2 of 6
05:10,2 of 6
04:11,3 of 6
03:12,4 of 7
02:10,4 of 7
01:12,2 of 7
Geee...That takes care of any expected values....So please Andrew don't compare Win Hunter to oranges...Your device is already beating the odds badly!!O:K: the bad tongue will tell that I already have 2 known numbers that will come up in these stacks...Of course...And this is where these Hints...Hints...are so important...The once in a while can be very rewarding....Knowing that many stacks rescued from the dunp directory will produce 1 or 2 good number(and many times from only 2 or 3 numbers) using its specific history will capture more....And this is where the announcers processor is so helpfull....
I am currently building some stacks using only the histories of the hot numbers from the last 10 draws...We'll see where its lead...