Math or Data help please

Reply #30

SergeM — Thu, 02 May 2013 22:21:40 GMT

and the next doesn't look healthy

eventually just one f(x) or ff(x).

Reply #29

JADELottery — Thu, 02 May 2013 01:40:34 GMT

To find higher Work Equations, use the following

Reply #28

JADELottery — Thu, 02 May 2013 01:13:22 GMT

Here are the reoccurrence probability and first 4 work equations.

We would like to post the others beyond 4, but they are Huge.

Reoccurrence Probability

First Order Work Equation

Second Order Work Equation

Third Order Work Equation

Fourth Order Work Equation

Reply #27

JADELottery — Wed, 01 May 2013 23:25:42 GMT

Next we can look at the sub components.

The sub components for a Double are the three different ways a double can happen.

These are: XXN, XNX and NXX, where X is the doubled number, N is some other number and X N.

If we divide these up and look at the individual draw differences for this event, the average rate of reoccurrence is 1000 / 90 = 100 / 9 11.1 .

We can apply this average rate to the same Potential Reoccurrence Distribution to see how this looks and compare it t... [ More ]

Reply #26

JADELottery — Wed, 01 May 2013 22:51:38 GMT

We have made a graph showing a few more levels above the First and Second Order Work Equations to see how the increasing levels become very erratic at the beginning then smooth out.

This is what we can do when the sample rate is increased between draws.

Out at 20 levels, the Work Equation is extremely erratic near 1 draw difference from the last event.

Continues...

Reply #25

JADELottery — Wed, 01 May 2013 22:23:06 GMT

Let's carry the Work Equations out to 20 levels.

When we do that, the curve looks a little less like a curve, or at least at this sample rate.

Below is the graph and shows the erratic nature of including more levels.

If we set a threshold of 0.75 as a limit and anything above that threshold is playable, then we can see the play times happen at {1, 2, 3, 4, 5, 6, 10, 11} draws later after the last event.

If we use the previous post as an example, then with a threshold of 0... [ More ]

Reply #24

JADELottery — Wed, 01 May 2013 22:03:47 GMT

We combined the individual probabilities by summing them and then do a Normalization of the curve to get it fit between a value of 0 to 1.

Below we can see how the combined probability curve looks.

It starts high at the beginning, does a little bounce at about 3 draws later, goes high again at about 6 draws later then begins to fall off to 0.

We can also see that at about 10 draws later from the previous event the probability drops below 0.5.

This may also explain the bey... [ More ]

Reply #23

JADELottery — Wed, 01 May 2013 21:45:08 GMT

The First and Second Order Work Equations were derived from the Potential Occurrence Probability and Reoccurrence Probability.

Each Work Equation has its complement and is used to derive the next order level.

The equations were setup to balance the possibility of an event happening at a given instant and how long it will be from the last time it happened.

Each is also based on the Draw Difference.

We can plug in some values like we did in the Potential Reoccurrence Probab... [ More ]

Reply #22

JADELottery — Wed, 01 May 2013 20:44:51 GMT

Before we move on, let's work on the Draw Difference.

The Draw Difference is just how many draws between events.

If we saw that an event happened at these draws: {3, 9, 18, 21, 37}, then the Draw Difference is: {9 - 3, 18 - 9, 21 - 18, 37 - 21} or {6, 9, 3, 16}.

To get to the next draw, if we say we are looking for someting to happen again, then we would add our estimated Draw Difference to the last time we knew when it happend to get the next approximate draw we need to play.

Let's... [ More ]

Reply #21

JADELottery — Wed, 01 May 2013 20:11:57 GMT

We have thought about this question, too.

When is the optimal time to play knowing when something has just happened?

Well, it does look like the optimal time is just after when the event has occurred.

However, there is another aspect of the event happening again, it's the Potential Occurrence Probability.

This just simply means how long does it take, just after the event occurred, for it to happen again.

The Occurrence Probability is complement the Reoccurrence Probability.

T... [ More ]

Reply #20

JADELottery — Wed, 01 May 2013 19:53:34 GMT

Now, getting to the other observations of the 8, 9, and 10 Draw Differences.

We need to expand this a little bit.

There are two different routes to follow.

The first is the expansion into the First and Second Order Work Equations, and possibly higher order work equations we have not posted here.

The second is the examination of the sub components that make up a Double, sub components meaning the different kinds of Double possible and how it relates to the overall Doubles

Reply #19

JADELottery — Wed, 01 May 2013 19:40:55 GMT

The Draw Difference distribution is related to the Potential Reoccurrence Probability.

The basic equation is y = e-(Δd / ).

This shows the draw relative probability of the event reoccurring again.

For the Doubles, we can see the probability of a Double happening again is pretty high just after is has happened and begins to dimish as more draws go by.

About 48% of all doubles will reoccur within the next 3 draws.

Continues...

Reply #18

JADELottery — Wed, 01 May 2013 19:15:42 GMT

Below is a graph of the calculated approximation and the actual observation.

The actual tends to follow the calcualtion, dimishing in frequency with increasing Draw Difference between events.

Continues...

Reply #17

JADELottery — Wed, 01 May 2013 19:08:17 GMT

If we look at the expected and the actual distributions of the Draw Differences for my state's lottery MN Daily 3, we can see how the Discharging Reoccurrence Distribution equation looks compared to the actual observations.

We will use the past year's drawings from 2012-05-01 to 2013-04-30 in this example.

The basic equation is y = (d / 2) e-(Δd / ) , where y is the approximate expected frequency, d is the total number of draws, Δd is the draw difference, and is the average rate of reoccur... [ More ]

Reply #16

JADELottery — Wed, 01 May 2013 18:28:41 GMT

Before we get started.

There are a few posts we made that may help understand the timing of your plays as it relates to the Reoccurrence of Doubles.

They are:

Discharging Reoccurrence Distribution

Potential Reoccurrence Probability

Potential Occurrence Probability

First and Second Order Work Equations

Also, for reference, when we write about Draw Difference it is similar to the common terms: Skip, Hit.

The Draw Difference is how many draws between events.

If an ev... [ More ]

Reply #15

adobea78 — Wed, 01 May 2013 14:46:56 GMT

Wind, I understand and get all pertaining to stats, probabilities etc, but be mindful that all these concepts started with assumptions and logic, hence mathematical formulas!. I am not discarding these concepts, I am trying to understand randomness, probability(very fluid concept). The Brain is not just a data reservoir, our perception is limitness, thanks for the sarcasm about your sister, nice ad hominen!.

Reply #14

adobea78 — Wed, 01 May 2013 14:25:49 GMT

These are generated strings based on sequential difference between ' elements of drawn set. Your point of reference is 'digits diff.', so if your draw set is 123, your sequential difference is 1-2 and 2-3=1 and 1(regular math with absolute interger). Now, form a combined string for 1 and 1(follow the sequence of subtraction in combo formation). Now from the chart , 1 strings 13708 and 1(could be different digit) strings 13708 , and my combo string is 1370813708= 1133770088(everything is in seque... [ More ]

Reply #13

WIN D — Wed, 01 May 2013 14:00:57 GMT

Hi adobea78 ! Speaking of doubles... LOL Right?

How about a philosophical focus on that doubles question up there.

I had a sister that worked very hard getting her degree in philosophy.

Boy, was she was surprised at the end of her fourth year when her college had career day .....and none of the big Philosophy Companies even showed up! LOL

Reply #12

adobea78 — Wed, 01 May 2013 13:41:59 GMT

Sorry, but you got to read between the lines, philosophical approach encompasses all, including ' bets and payouts

Reply #11

WIN D — Wed, 01 May 2013 13:38:52 GMT

Hello SergeM ..... thanks for those figures up there. Thank you as well Carbob. Finding the best 3 day window for a trap may not be a static situation. In fact the length of the window may also need to be examined again.

Speaking of doubles. I have been looking over the doubles and trying to remember a very old stat from years ago.

It was ..... How many times does a double hit back to back in 365 draws......on average of course? All I seem to remember right now is concerning the odd... [ More ]

Reply #10

SergeM — Wed, 01 May 2013 09:58:38 GMT

I read words like statistics, academic, analysis, probability, theory, mathematical ... . I read dialect like doubles. I did not read the word bet and payout. You just failed in statistics and probability.

Reply #9

adobea78 — Wed, 01 May 2013 00:44:56 GMT

''Probability and statistics are two related but separate academic disciplines. Statistical analysis often uses probability distributions, and the two topics are often studied together. However, probability theory contains much that is of mostly of mathematical interest and not directly relevant to statistics. Moreover, many topics in statistics are independent of probability theory''.- Wikipedia.

When dealing with random events, philosophical approach is your best bet. You want to bet only d... [ More ]

Reply #8

CARBOB — Tue, 30 Apr 2013 18:04:46 GMT

Serge, you are correct! Nice work,

Reply #7

SergeM — Tue, 30 Apr 2013 17:18:33 GMT

CB CB CB CB SKIP F CF RF CRF

D 1 150 29% 0 150 150 29% 29%

D 2 243 48% 1 93 243 19% 48%

D 3 319 63% 2 76 319 15% 63%

D 4 386 76% 3 67 386 13% 76%

D 5 417 82% 4 31 417 6% 82%

D 6 443 87% 5 26 443 5% 87%

D 7 458 90% 6 15 458 3% 90%

D 8 469 92% 7 11 469 2% 92%

D 9 479 94% 8 10 479 2% 94%

D 10 490 96% 9 11 490 2% 96%

Should be this.

Reply #6

CARBOB — Tue, 30 Apr 2013 17:05:04 GMT

skip 1 is retition

Reply #5

SergeM — Tue, 30 Apr 2013 16:45:26 GMT

Is skip 1 in your reasonning a skip 0 or repetition

Reply #4

SergeM — Tue, 30 Apr 2013 16:39:08 GMT

Since you started with mathematics, why don't you solve the problem with mathematics

Reply #3

CARBOB — Tue, 30 Apr 2013 16:27:42 GMT

Chaz,

For Fla Eve, the windows are these, the first column are the skips, second column the hits. We are currently at 9 skips. The max skip is 23. There are a total of 510 hits.

D 1 150 29%

D 2 243 48%

D 3 319 63%

D 4 386 76%

D 5 417 82%

D 6 443 87%

D 7 458 90%

D 8 469 92%

D 9 479 94%

D 10 490 96

Reply #2

Ronnie316 — Tue, 30 Apr 2013 16:07:39 GMT

Good questions. I hope someone can help narrow down which window looks best.

Reply #1

WIN D — Tue, 30 Apr 2013 14:34:47 GMT

On first consideration we are pulled toward the fact that Doubles on average.... hit approx 99 times a year for a 365 draw game......or about 27% of the time and normally around every 3.7 draws.

So, right off the bat..... is a 4th 5th and 6th draw play window more effective? .....or perhaps a 5-6-7 draw window.

Math or Data help please

WIN D — Tue, 30 Apr 2013 13:46:28 GMT

We are looking for some help for a Doubles Trap in Pick 3. What is the best strategy math wise....and perhaps backed up with some data.

question: What is the most effective Window of Oportunity to catch a double play.....any double?

Here is a pretty effective day to day strategy suggestion over in the Systems forum.... https://www.lotterypost.com/thread/259964

We need to check our ......3 day window suggestion. The current KILL Zone suggestion is the 8th. 9th an... [ More ]