Findlay, Ohio United States Member #4855 May 28, 2004 400 Posts Offline

Posted: November 11, 2006, 5:51 pm - IP Logged

Do you know a formula for finding the probability of the same boxed number being drawn in several states over about a one month period of time? Bryan made the following post and I can't seem to come up with a true probability for it:

"For 30 days, this combo has not gone more than 3 days without being drawn. That is incredible...As matter of fact, it has almost hit solid for the last 3 months...wow!"

I think there was a combined total of 979 games played between the first hit during the EVE draw on Oct 11th and the last hit for the EVE draw on Nov 8th. There were 1000^979 total possibile outcomes that could have transpired over the course of those drawings. Of that total amount, there should be (1000^979)-(994^979)=X permuations that contain 014 boxed AT LEAST ONCE. How do I find out exactly how many of those X possibilities contain exactly 21 occurrences of 014 boxed?

Note: I removed the two Iowa hits from the 23 listed above because they use the Illinois Pick 3 to derive their number and dont really count.

For much smaller numbers, I usually list the partitions (combo in basic form) to get the arrangements and permutations in order to find the true probability. I did this once for a Pick 22 Scenario (...like pick 3 and pick 4 except 22 at a time lol) ...and there were 804 basic combos totaling 10^22 total permutations = 10,000,000,000,000,000,000,000.

There's gotta be a more practiclal way to do this for this situation, any help/lesson would greatly be appreciated!

West Concord, MN United States Member #21 December 7, 2001 3819 Posts Online

Posted: November 11, 2006, 11:30 pm - IP Logged

Thoth,

Just replying to say I'm working on the problem you stated, "Do you know a formula for finding the probability of the same boxed number being drawn in several states over about a one month period of time?"

To understand this a little better, I think you are looking for the probability of successfully matching any single boxed permutation in several different pick 3 drawings per day for about 30 drawings.

Does this sound about right?

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Order is a Subset of Chaos Knowledge is Beyond Belief Wisdom is Not Censored Douglas Paul Smallish Jehocifer

West Concord, MN United States Member #21 December 7, 2001 3819 Posts Online

Posted: November 12, 2006, 4:49 am - IP Logged

Thoth,

After thinking about this a while and looking over some of the other posts, I think I have a solution. In order to solve this problem, I had to approach it from a different view. First, the fact that the numbers are being drawn by different states at different times on different days does not matter. Only the draw count of how many selections matter. A sample is a sample, regardless of it's source. If we look at the inverse of what you are doing by state, we can also ask the question, "What is the probability that 22 bets place on a single draw in a state are the same single boxed permutation?" There many hundreds to thousands of bets place per day by many people, just like there are many hundreds of draws per month to many thousands of draws per year by many states. With that said, here's what I came up with. First we need to find the average number of hits based on some sample count. Next, we need to find the standard deviation from that average to calculate a probability of the number of hits that may deviate from the average.

Boxed-6 Hits Probability Base on Sample Size

y = (1 / Ö0.012 p s) e^{-((x - 0.006 s)²/(0.012 s)}

x - number of hits based on a given sample size s - number of samples

y - probability that x number of hits will have happen by s number of samples

note: to get percent probability multiply y by 100%

Presented 'AS IS' and for Entertainment Purposes Only. Any gain or loss is your responsibility. Use at your own risk.

Order is a Subset of Chaos Knowledge is Beyond Belief Wisdom is Not Censored Douglas Paul Smallish Jehocifer

West Concord, MN United States Member #21 December 7, 2001 3819 Posts Online

Posted: November 12, 2006, 5:10 am - IP Logged

Quote: Originally posted by JADELottery on November 12, 2006

Thoth,

After thinking about this a while and looking over some of the other posts, I think I have a solution. In order to solve this problem, I had to approach it from a different view. First, the fact that the numbers are being drawn by different states at different times on different days does not matter. Only the draw count of how many selections matter. A sample is a sample, regardless of it's source. If we look at the inverse of what you are doing by state, we can also ask the question, "What is the probability that 22 bets place on a single draw in a state are the same single boxed permutation?" There many hundreds to thousands of bets place per day by many people, just like there are many hundreds of draws per month to many thousands of draws per year by many states. With that said, here's what I came up with. First we need to find the average number of hits based on some sample count. Next, we need to find the standard deviation from that average to calculate a probability of the number of hits that may deviate from the average.

Boxed-6 Hits Probability Base on Sample Size

y = (1 / Ö0.012 p s) e^{-((x - 0.006 s)²/(0.012 s)}

x - number of hits based on a given sample size s - number of samples

y - probability that x number of hits will have happen by s number of samples

note: to get percent probability multiply y by 100%

The equation I posted was derived this way.

Normal Distribution - y = (1 / sÖ2 p) e^{-((x - m)² / s²)}

m = (6 / 1000)s = 0.006 s

s = Öm = Ö0.006 s

Plugging in the values gives this equation.

y = (1 / Ö0.012 p s) e^{-((x - 0.006 s)²/(0.012 s)}

Presented 'AS IS' and for Entertainment Purposes Only. Any gain or loss is your responsibility. Use at your own risk.

Order is a Subset of Chaos Knowledge is Beyond Belief Wisdom is Not Censored Douglas Paul Smallish Jehocifer