Markov Chains in Lottery Games

Reply #26

SergeM — Thu, 27 Nov 2014 23:48:00 GMT

x 1 2 3 4 5 6 7 8 9 10 11 12

1 12 5 4 8 8 3 10 6 5 13 10 8

2 7 7 12 11 15 7 12 14 8 7 7 3

3 10 12 6 5 6 7 8 9 12 7 6 5

4 6 11 5 6 10 8 5 8 4 13 8 8

5 8 8 7 6 5 8 9 11 11 8 9 9

6 6 5 7 7 9 7 8 9 12 4 7 13

7 9 9 7 7 8 9 14 11 7 5 5 12

8 10 6 6 14 8 8 6 10 9 1 11 14

9 11 10 6 6 12 8 13 9 8 6 8 5

10 12 12 5 5 4 10 9 7 7 11 10 4

11 6 11 9 8 7 6 8 12 6 8 8 10

12 10 12 6 8 6 8 7 8 6 9 6 5

... 45 * 45

Reply #25

SergeM — Thu, 27 Nov 2014 23:42:40 GMT

Column A: trailer frequency

Column B: frequency (trailer frequency)

0 2

1 5

2 22

3 51

4 108

5 164

6 224

7 261

8 309

9 225

10 207

11 153

12 115

13 93

14 38

15 23

16 14

17 8

18 1

19 1

20 1

Some boring statistics

Reply #24

SergeM — Thu, 27 Nov 2014 23:38:15 GMT

I had a look, how the distribution is for trailers. It appeared that for some time a number wouldn't follow another number. That gap is eventually filled some day, avg 0.04 value below, for two numbers count. The graph won't paste, it has a Poisson shape.

0,04

0,11

0,49

1,13

2,40

3,64

4,98

5,80

6,87

5,00

4,60

3,40

2,56

2,07

0,84

0,51

0,31

0,18

0,02

0,02

0,02

Reply #23

RJOh — Tue, 11 Nov 2014 18:47:01 GMT

True but software not only track past drawings but assists a player in developing a strategy for future drawings. I always assumed software doesn't have a working strategy or it wouldn't be for sale, a players have to develop his own using lottery software only as a tool.

Reply #22

RL-RANDOMLOGIC — Sun, 09 Nov 2014 23:06:21 GMT

RJ

I came away from the article with the opinion that expert lotto offered no mathematical advantage.

Every lottery system I have ever tested relies on some type of conditional element. If the elements

are factored back in then the we will wind up back where we started. Some software's require the

user to make choices while others make choices for us but in the end nothing will ever move us any

closer to a JP win unless we are able to calculate the seed value for RNG based draws.... [ More ]

Reply #21

SergeM — Sun, 09 Nov 2014 22:46:24 GMT

After that you need to check what your automated picks have cost and what they paid over a long period. How good does your system do compared to the expectancy of the game plaid

Reply #20

stoopendaal — Sun, 09 Nov 2014 20:56:40 GMT

Hi,

I added a quick pick generator to the program using the generated Markov Chains/followers from the imported lottery draw results.

Instructions:

step 1. Import lottery draw results

step 2. Hit the button 'C.Generate Markov Chains'

step 3. Select the number of picks to generate (5 up to 50)

step 4. optional: sort numbers, show average occurrence, show match with numbers

step 5. And finally hit the 'Generate Picks' button

I have also added a feature that shows the match... [ More ]

Reply #19

RJOh — Sat, 08 Nov 2014 17:52:56 GMT

It's interesting that your link had a link to Expert Lotto software. In the past there have been several members that used that software exclusively and while their prediction statistics were among the top 10% they never scored a major hit. Perhaps it's time to take another look at it with a fresh approach.

Reply #18

Tialuvslotto — Sat, 08 Nov 2014 13:01:53 GMT

Very interesting link, Stoopendaal! I would agree with the author that the accuracy of this method is only around 20%.

Reply #17

stoopendaal — Sat, 08 Nov 2014 10:38:04 GMT

The program is merely a Markov Chain text generator for (lottery) numbers. All the tool does is to link each number to a list of numbers for the imported draw results. Like Tialuvslotto said Still, any information is useful, and this is one tool to help dial in good numbers to play

No transition matrix is needed to be described because the previous state (winning numbers) has no influence on the next state when lottery draws are trained.

Here an interesting post about studying the be... [ More ]

Reply #16

SergeM — Fri, 07 Nov 2014 21:39:13 GMT

The question is what are the probabilities. Than what will be the outcome after a series of experiments.

The post is mainly about followers and their frequencies as I could read. Mainly it is not about Markov, as I saw no probability and no decisions model. I saw no Euler and no matrix. The post must be about a program, not about Markov chains.

Reply #15

GASMETERGUY — Fri, 07 Nov 2014 17:46:07 GMT

I would think that using Markov chains for the powerball or mega number would be effective than using the theory on combinations of numbers.

I could be wrong; I usually am. Have you tried this on the bonus ball drawings? If so, what were your results.

Reply #14

SergeM — Fri, 07 Nov 2014 16:43:41 GMT

I took the time to split 0 to 999 in four groups.

My trailer function fails with VBA for bigger data, so I had to do this differently.

Unfortunately Excel VBA isn't the best solution for methods.

Using a sub on four groups:

!32 507

!31 426

!23 385

!43 358

!13 322

!33 322

!22 234

!21 227

!12 225

!11 217

!34 132

!44 129

!24 119

!14 106

I cannot take the time to do more of this. Checking by games out for the grou... [ More ]

Reply #13

SergeM — Mon, 03 Nov 2014 11:30:53 GMT

Let's be real for a minute. State that lottery is having pick 3 outcomes like following:

000 000 000 000 000 000

What do you think will be the reaction of the lottery, the players, the press, the mathematicians and others?

Would the lottery close the game for investigation? Are you supposing that there is collusion? ...

Reply #12

SergeM — Mon, 03 Nov 2014 11:26:31 GMT

To me, you are already successful if you loose half of your budget consistently

Reply #11

SergeM — Mon, 03 Nov 2014 11:16:05 GMT

I generally don't mix the subjects. You didn't mention the balancing, you stated that it stays unbalanced! Now you mix probabilities with counts. - I did such tests using Excel. What came out, like I posted it, in other threads, is that it is close to probability for the pick 3 that I searched in. P(STRAIGHT)=.001 AND PAYOUT(STRAIGHT)=500. If you double your chance with a condition that you stated, you might get: (CONDITIONAL)P(STRAIGHT)=.002.

Seeing the problem with lottery playing is a budg... [ More ]

Reply #10

stoopendaal — Sun, 02 Nov 2014 17:32:33 GMT

Yes, you're right I made an incorrect statement about the likelihood of followers. I Googled on 'sample and population'...it's now more clear to me

For pick 3 a balance is faster restored than for a lottery game like Power Ball == In another post you stated it's all about timing. How many pick3 results did you test to calculate the followers probabilities and were you able to track the increase/decrease (differences) of the probabilities of the digits?

For example you have 10.000 pick 3... [ More ]

Reply #9

SergeM — Sat, 01 Nov 2014 22:22:09 GMT

As you can see here, digit 7 is more likely followed by digit 8 than for example digit 4 ( and 2,3,7, etc.) for the 1131 tested pick 3 draw results.

You are referring to the past situation, where 8 followed 7 more often. Your statement that it is more likely that 8 follows 7 is incorrect. You mix up sample and population.

For pick 3 a balance is faster restored than for a lottery game like Power Ball. I posted followers for pick 3 several times and proved it. The difference for catching up... [ More ]

Reply #8

Tialuvslotto — Sat, 01 Nov 2014 16:12:04 GMT

I used numbers by position.

For example, for the digit 3 in the first position, my spreadsheet tells me that there is:

0.1 probability of a repeat in position 0.7 probability of a higher number in this position 0.44 probability of a number between 1-4, 0.27 between 5-9 2 4 are good next draw numbers, happening about 0.15 each

For the digit 3 in the second position, I get different results:

0.00 probability of repeat in position probability near 1.0 of a higher number in this posit... [ More ]

Reply #7

stoopendaal — Sat, 01 Nov 2014 13:55:00 GMT

Hi Tialuvslotto,

Thanks for the information about Markov predictions for jackpot games. I like your idea to create chains for a range of numbers and I tested it for a pick 6 lottery game (New Jersey).

First I created the range data for this game. In this example I created groups each having 3 numbers.

49 numbers has 16 groups of 3 number and 1 group with one number (49). So there is a total of 17 groups to analyse.

Group 1: {1,2,3}

Group 2: {4,5,6}

Group 3: {7,8,9}

.etc... [ More ]

Reply #6

Tialuvslotto — Fri, 31 Oct 2014 14:00:34 GMT

Hi Stoopendaal,

Interesting post.

I have tried Markov Chains in a jackpot lottery game. They turned out to be quite good at predicting a range (e.g. 37 followed by 42-49), but not so good on pinpointing a following number. Also, on many draws the Markov predictions would be very good for 2 or 3 of the numbers, fairly close for another 2 and wildly inaccurate for one number. Unfortunately, one could never tell which predictions would be good.

Still, any information is useful, and th... [ More ]

Reply #5

destinycreation — Wed, 29 Oct 2014 22:28:02 GMT

Is it really necessary to make Pick 3 this COMPLEX, in order to Win ??? People Win Pick 3, with much Simpler systems. If you are going to put this much effort into making the game MORE COMPLEX than it needs to be, you should put this effort into the Pick 4 game instead, b/c the payout is higher, and therefore more worth this amount of effort.

Reply #4

ALX — Mon, 27 Oct 2014 13:01:51 GMT

Thank you very much for your help.......I'll try it.

Reply #3

stoopendaal — Sun, 26 Oct 2014 20:23:41 GMT

Hi ALX,

How do I input my state lottery game please? :

I copied the lottery results (raw data) from the website of the lottery to notepad and saved it as a text file.

First I imported the text file with the lottery results into Excel and removed the dates and other data from the draw results. Secondly I copied the results to a tool (topdown) to revert the results to get the oldest drawings at top and the most recent at the bottom of the list. Finally I saved the results to a text file

Reply #2

ALX — Sun, 26 Oct 2014 15:58:32 GMT

Wow. I really like this idea and the generator. Thank you. How do I input my state lottery game please

Reply #1

stoopendaal — Sun, 26 Oct 2014 10:52:23 GMT

As early stated, Markov chains don't depend on past history (for random process a lottery unless it's flawed )other than the current state of the system. For example, Markov modelling of a lottery would predict (with a certain probability) the next number based on the current number, but not looking any further back than that.

However I believe the Markov model can be used for analyzing a lottery game in which there is some dependence of a number and the the next number following this number... [ More ]

Markov Chains in Lottery Games

stoopendaal — Sat, 25 Oct 2014 21:08:55 GMT

Hi,

Here a brief explanation about markov chains (source: http://techeffigy.wordpress.com/2014/06/30/markov-chains-explained)

Markov Chains is a probabilistic process, that relies on the current state to predict the next state. For Markov chains to be effective the current state has to be dependent on the previous state in some way; For instance, from experience we know that if it looks cloudy outside, the next state we expect is rain. We can also say that when the rain starts to subside