6. Forecasting Lottery Numbers

6.1 Several Basic concepts

6.1.1 One Round
6.1.2 Natural Course
6.2 Data Set 6.2.1 CASH 3 Data
6.2.2 Data Set
6.3 Preparations

6.4 Five Steps for Using the Predictor

6.5 Examples

6.5.1 Example 1: Cash 3 (x)
6.5.2 Example 2 Cash 3 (y)
6.5.3 Example 3 Cash 3 (z)
6.6 The Software Parameters
 


Forecasting Lottery Numbers

Attrasoft Predictor is a universal predictor, which can be applied to any prediction problem. The Predictor reads a sequence of numbers and predicts the distribution for the next row of numbers in line.

Let us apply this tool to lottery forecast. The lottery is designed such that each possible number has equal odds, regardless of the past history of winning numbers. Mathematically every number has an equal probability to appear. In the long run, the statistics obtained by the Predictor should indicate that each possibility appeared with an equal probability. In the short run, the probability distribution might be a bit different from the perfectly random case because of statistical fluctuation. Of course, the difference is expected to be small.

Throughout this chapter, we will assume we are playing a game called "CASH 3". This is a real game in Georgia, USA. All it takes is the right 3 numbers and you could win $500. You pay $1.00 for selecting a 3-digit number between 000 and 999. All data used in this chapter will be real lottery data (actual winning CASH 3 lottery numbers in Georgia, USA).

A round is defined as the number of attempts it takes for you to win once. In the long run, according to the odds, you will lose half of the money you have played each round in the CASH 3 game. Just to come out even, you have to beat the odds by a factor of two. If you can consistently beat the odds by a factor of four, you will double the money you have played in each ‘round’.

When implementation of a random system is perfect, mathematically speaking, it is impossible to win. Predicting the lottery is much harder than predicting the stock market, the weather, or an earthquake, even though lottery dynamic systems are much simpler than stock market. Everyone knows this theory: each possibility has an equal probability, regardless of the history. The theory also indicates the next number is not predictable. We believe all lottery-picking software operates under this rule.

If you have a scientific mind, this rule is enough to turn you back, i.e. the lottery is not your game. In reality, millions of people do play the lottery; most of the people do understand the lottery theory--each possibility has an equal probability. For those who are not yet familiar with this rule, reality will make them learn this rule in a hurry. Most people choose their numbers at random (according to a daily event or plug in dates that have significance to them, such as anniversary dates or family birthdays); meaning, most people do not have a tool to pick numbers systematically. There is a market demand for such a tool, from those who understand the theory of lottery numbers. This tool turns playing the lottery into a systematic game, with a clearly defined strategy and outcome (win or lose).

Attrasoft Predictor offers such a tool for the game. Loosely speaking, this tool will:

This is a highly personal game, if 1000 people play the same game on exactly the same data, there will be 1000 different outcomes. There are two reasons for this: The method you play might be continuously changing because you are constantly comparing your results with the correct answer.

There is one criterion and two states for the game:
 

The criteria for the CASH 3 game is to make 10 wins within 2500 attempts. What if you pass, that means with the help of the software, you had the ability to predict the winning numbers with a probability of 0.004 for the CASH 3 game.

The two states are the simulation-state and the real-state. You start the game by learning the tool and getting a feel of how to use this tool.
 

After learning the tool, you begin to enter the simulation-state. In this state, you simulate playing the lottery on paper. You stay in this state until you meet the criteria (10 winning numbers within last 2500 attempts), then you switch to the real state, where the real money is involved. In the real state, you monitor your performance to make sure you meet the criteria (10 winning numbers within 2500 attempts). Once you fall below the required standard, you switch back to the simulation state. This rotation between the simulation state and the real state can continue forever.

When making a prediction using the Attrasoft Predictor, it is important to set the correct expectation. You must know what to expect from the Predictor. You have to play the game systematically and switch states as required. The purpose of the prediction is to increase the chance of winning, compared with the natural course. This game requires a trail of records to check your performance. If you do not have time to track your record, this is not your game. If you can not switch the state, from real state to simulation state and back again according to the criteria given above, this is not your game.

Remember, the normal probability of winning is 0.001; the Predictor is a systematic tool, which allows you to play a highly personal game (if 1000 people play the lottery on exactly the same data, there will be 1000 different outcomes). As a result, some people will deviate the normal probability of 0.001 sufficiently to reach 0.004. However, once you have reached 0.004 probability, you are not expected to stay there forever. At some point later, you are expected to leave the real state (your luck has run out) and to switch back to the simulation state so that in the long run, you are not too far away from the normal probability of 0.001. In the short run ( for the CASH 3, this means in the order of 1000 attempts), it is justifiable that your chance can differ from the normal probability of 0.001. However, in the long run (for the CASH 3, typically 10,000 to 10,0000 attempts), your chance is expected to be around 0.001. For the Predictor, the typical play is 2500 attempts, which is considered a short run; therefore, the probability of 0.004 for some person is achievable.

To use the Predictor, You must learn two simple things:


Several Basic concepts

One Round

We define "one round" as your continuously selecting a 3-digit number randomly until you win. The length of one round is the number of attempts you have completed until you win. If you play once and win, the length of one round is 1 attempt. If you have played 2,000 times ($2,000) and win, then the length of one round is 2,000 attempts.

Natural Course

The odds for winning "CASH 3" is 1:1,000. In other words, on average it takes you 1,000 attempts to win. To estimate the number of attempts in one round, just use the inverse of the odds:

Odds = 1/1,000

Average Length of One Round = 1/ Odds

= 1/ (1/1,000) = 1,000

Therefore, on average, the length of one round is 1,000 attempts. Result: on average after one round, you will spend $1,000 and will have won once to get $500 back, i.e. you will lose half of the money you have played in one round.

If you start with $2,000, after one round, on average you will have $1,000 (2000/2 = 1000) left; after two rounds, you will have $500 (1000/2 = 500) left. After three rounds, you might have nothing left.

The time required to play one round depends on you. You can play all 1,000 numbers in one day and finish one round in one day, or you can play one number every other day and finish the round in 2,000 days.


Data Set

CASH 3 Data

The data used here is obtained from Georgia-State-Lottery-Office, which is real data. It consists of the history of the winning numbers. We will call the three digits (x y z). It looks like this:

Date        x y z
----------------------------------------

01-Jan-97 6 2 7

02-Jan-97 6 0 5

03-Jan-97 1 8 8

04-Jan-97 5 1 2

05-Jan-97 4 0 3

06-Jan-97 6 0 8

07-Jan-97 9 9 9

08-Jan-97 2 2 2

09-Jan-97 0 1 9
 
 

. . .
 
 

11-May-97 5 1 3

12-May-97 1 5 9

13-May-97 7 2 3

14-May-97 6 4 0

15-May-97 6 7 6

16-May-97 3 4 2

17-May-97 6 4 5

18-May-97 9 7 4

19-May-97 4 2 0

20-May-97 7 5 9

21-May-97 4 3 0
 
 

Note: the data left out above for saving space. Just click the command "Example/Cash 3 (x y z)", and you will see all the data.


Data Set

A data set is a set of variables used for a prediction. There are seven possible data sets in CASH 3:

  1. Predict x;
  2. Predict y;
  3. Predict z;
  4. Predict xy;
  5. Predict xz;
  6. Predict yz;
  7. Predict xyz.
There are several ways to predict (x, y, z) in CASH 3 game:
 
A combination of 1 through 3; or

A combination of 3 and 4; or

A combination of 2 and 5; or

A combination of 1 and 6; or

7 alone.

It makes sense to predict one digit at a time, because the winning numbers are generated one at a time. However, you can also predict two digits at a time or three digits at a time, by using the Predictor.


Preparations

Before you play real games with real dollars, you should make at least 10 rounds of simulations with past data, or future data (pretending you have bought the tickets for certain numbers without the economic cost of your learning experience). Do not jump into the game directly without any experience. You should simulate the game for 10 rounds before actually switching to the real state.

This is not your game:
 

(1) If you do not have time for a long-term plan:
To meet the criteria, you must simulate the game until you win 10 times. If you "spend" $2,500 on paper and "win" 10 times on paper, you have achieved the simulated criteria. If you do not have time for this, consider other games.

(2) If you can not achieve the desired rate:

Suppose you have gone through the simulation of a game for 100 rounds, and you can not achieve the desired success rate, then you should not play the game.
 
 

Five Steps for Using the Predictor

The Predictor looks at the history of winning numbers and predicts the next row of numbers. The Predictor is a tool for ranking all possibilities in the CASH 3 game. The results of this tool are still subject to human interpretation. You should develop your own system when using the Attrasoft Predictor.

The procedure is:
 


Now we list the details of each step:

Step 1 Collect data and choose a data set

Lottery data is the history of wining numbers. The data can be collected easily. Contact the state lottery office; they are more than happy to offer you all the data you need. You can also search from the Internet. The Predictor provides you with seven different examples to predict numbers in CASH 3, as we have discussed in the last section.

If you are serious about playing the lottery, learn how to use Microsoft Excel or any other spreadsheet. Excel gives you the power to prepare data used by the Predictor easily. Your original data should be in one Excel file. Predictor only takes text files, this is not a problem, just click "File/Save as" in Excel to save the data to another file in the text format.
 

Example Cut and Paste in Excel

Assume your data is in the following format
 
  x y z

____
 
 

5 0 6

7 1 8

9 2 0

1 3 2

3 4 4

5 5 6
 
 

and assume you want to predict (x, z) together; how to set up the input file?
 
 

Open a new spreadsheet and copy the above data in the new sheet; then cut the y-column and "File/Save as" to a new text file. Now you will have the following:
 
 

x z

___
 
 

5 6

7 8

9 0

1 2

3 4

5 6
 
 

The above steps prepared the "data section" of the Predictor's input file. The Predictor input file has three sections:
  Please read chapter 3 to see the details.
 

Step 2 Link (first of three clicks, please see chapter 3).
 

Step 3 Click command: "Integer/+ Linear Enumerative"

Step 4 Click command: "Integer/-- Linear Enumerative"
 
 

The Predictor will give the range of possible numbers. The command "Integer/+ Enumerative" gives you the upper bounds of the predicted winning number and the command "Integer/-- Enumerative" gives you the lower bounds of the predicted winning number. The winning number is expected to be somewhere between the upper bound and the lower bound.
 
 

Step 5 Analysis
 
 

From the above two clicks, you will get a upper-string and a lower-string. The basic information from a prediction includes:
 
 

Play at your own risk You play at your own risk. Attrasoft Predictor is nothing more than a tool for ranking all 3-digit numbers. It is your responsibility to use the tool. You must understand that the most likely possibility is that you will lose half of the money you played in one round. Understand the expectation. You must understand the objective of the game. The objective is not to predict winning numbers, but to achieve a higher chance of winning consistently; for example, to achieve odds four times higher than the natural course. You have to keep a record to inform yourself so you can switch between the real and simulation states. Otherwise, do not use the Predictor.
 

Examples

This section is intended to show you how to use the Predictor as a tool. Specifically, the Predictor helps you rank the possibilities.

It is completely up to you to decide how to use this tool:

The Predictor will help you to rank all possibilities in a sequence, but will not give you the complete ranking.

The data used in this section has been listed earlier, i.e. Georgia (USA) CASH 3 winning numbers (1/1/97 - 5/21/97). There are seven examples packed in the Predictor, each one can be generated by one click. On the menu bar, the Example menu can generate the following examples:
 

The examples use the real data of Georgia CASH 3 game from 1/1/1997 to 5/16/1997 and tries to predict the next number. The next winning number on 5/17/97 is: (6 4 5). Our criterion is to predict the winning number for 5/17/97, which is 645, with a probability of 1:250.


Example 1: Cash 3 (x)

Click "Example/Cash 3 (x)" to generate the example. This example attempts to predict the first digit in Cash 3. The data file is "D_ch3X.txt". If this is your data, you have to link the data. Here is how to link:
 

After this step, the input file is linked and opened. The file looks like:
  *

GA Cash 3

First Digit

(x)

*
 
 

1
 
 

6

6

1

. . .

6

6

3
 
 

Please read the rest of this data file from the Predictor.

Click command: "Integer/+ Linear Enumerative" (the second click), you will get:
 

Possibility Confidence*Probability

1             5122

2             2

3             576

4             2

5             130

6             64

7             139

9             18

---------------------------------------------------

Weighted Average

1

Highest Probability

1 5122

Error of each number

0.495

Please read chapter 3 to learn about the output file. The Predictor will produce a distribution. The command "Integer/+ Linear Enumerative" gives you the upper bounds of the predicted winning number, and the command "Integer/-- Linear Enumerative" gives you the lower bounds of the predicted winning number. The winning number is expected to be somewhere between the upper bound and the lower bound.

The confidence for this prediction is 5122. The upper bound is most likely to be 1, but can also be 3, or 7. To rank the upper bound, the Predictor gives the following list:
 

1; 3; 7; 5; 6; 8; (2, 4); (0, 9).


Here 2 and 4 have an equal ranking, with rating = 2; and 0 and 9 have an equal ranking, with rating = 0. For simplicity, we pick us 3 numbers:

Upper string = 1, 3, 7.
 
 
Click command: "Integer/-- Enumerative"(the third click) and you will have: Possibility Confidence*Probability

0             8

1             1280

3             8

4             256

5             272

---------------------------------------------------

Weighted Average

2

Highest Probability

1 1280

Error of each number

0.495
 

The confidence of this prediction is 1280. The lower bound is most likely to be 1, but can also be 5, or 4. To rank the lower bound, the Predictor gives the following list:
 
1; 5; 4; (0, 3); (2, 6, 7, 8, 9).


Here 0 and 3 have an equal weight 8; and (2, 6, 7, 8, 9) have an equal weight 0. For simplicity, we pick us 3 numbers:
 

Lower string = 1, 5, 4.
 
Analysis

The Predictor indicates:

Upper string = 1, 3, 7.

Lower string = 1, 5, 4.
 

If the lower bound = 1 and the upper bound = 1, then we get 1.

Next, if the lower bound = 1 and the upper bound = 3, then we get 1, 2, 3.

Next, if the lower bound = 1 and the upper bound = 7, then we get 1, 2, 3, 4, 5, 6, 7.

The ranking is 1 (because we get 1 first), then 2, 3 (because we get 2, 3 next); then 5, 6, 7, 4. The ranking string is:

1; (2, 3); (5, 6, 4, 7); …
 
The above prediction uses the default values, i.e. 5-trend, 10-precision level. There are many other ways to use the results:

Example 2 Cash 3 (y)

This example is can be generated by clicking "Example/Cash 3 (y)".

Click command: "Integer/+ Linear Enumerative" (the second click), you will get:

Possibility Confidence*Probability

0 256

3 16

8 512

9 8

---------------------------------------------------

Weighted Average

5

Highest Probability

8 512

Error of each number

0.495
 

The confidence of this prediction is 512. The upper bound is most likely to be 8, but can also be 0. The upper string = 8, 0.
 

Click command: "Integer/-- Enumerative"(the third click) and you will have:
 
 

Possibility Confidence*Probability

2 16

3 4

4 1

7 16

9 9

---------------------------------------------------

Weighted Average

5

Highest Probability

2 16

Error of each number

0.495
 

The confidence of this prediction is 16, which is very low. The lower string is 7, 2.
 

The Predictor indicates:
 

Upper string = {8, 0},

Lower string = {7, 2}.
 

If the lower bound = 7 and the upper bound = 8, then we get 7, 8.

Next, if the lower bound = 2 and the upper bound = 8, then we get 2, 3, 4, 5, 6, 7, 8.

The ranking string for the second digit is 7, 8, 2, 3, 4, 5, 6.


Example 3 Cash 3 (z)

This example is also packed in the Predictor, which can be generated by clicking "Example/Cash 3 (z)".

Click command: "Integer/+ Linear Enumerative" (the second click), you will get:
 

Possibility Confidence*Probability
 
 

Can not make a Prediction.

To get a prediction, you can:

(1) Add more data;

If you do not have more data; then click 'Data/Link' and:

(2) Reduce Trend; or/and

(3) Reduce Precision level;

You may also consider:

(4) Reduce the number of variables in your data set.

See the User's Guide

---------------------------------------------------
 
 

In this case, no prediction of the upper bound is available from the data. Now we change the Precision level from 10 to 9 (clicking "Data/Link" and enter 9 as a Precision-levels); here are the results:
 
  Possibility Confidence*Probability

8             64

---------------------------------------------------

Weighted Average

8

Highest Probability

8 64

Error of each number

0.555556
 
 

Therefore, the upper string is {8}.

Click command: "Integer/-- Enumerative" (the third click) and

Possibility Confidence*Probability

1             9

3             8

4             546

5             528

6             514

7             49

8             2

9             145

---------------------------------------------------

Weighted Average

5

Highest Probability

4 546

Error of each number

0.555556
 

The confidence of this prediction is 546. The lower string is {4, 5, 6}.

The Predictor indicates:

Upper string = {8},

Lower string = {4, 5, 6}.
 

If the lower bound = 4 and the upper bound = 8, then we get 4, 5, 6, 7, 8. To rank these 5 numbers, note that 8 is the first in the upper string and 4 is the first in the lower string, pick them up first, then pick up 5, 6, and finally 7.

The ranking string for the third digit (4, 8), 5, 6, 7.
 

To collect the predictions, we have (given the order):
 

x: 1; then 2, 3; then 5, 6, 7, 4.

y: (7, 8); then 2, 3, 4, 5, 6.

z: (4, 8); then 5, 6, then 7.


The first picks are
 

(1 7 4) (1 8 4) (1 7 8) (1 8 8).
 
The correct answer on 5-17-97 was (6 4 5). If you buy all the above 7*7*5 = 245 numbers, you will win. The 245 numbers are generated as follows:
 
select any x-digit from {1, 2, 3, 5, 6, 7, 4},

select any y-digit from {7, 8, 2, 3, 4, 5, 6}, and

select any z-digit from {4, 5, 6, 7, 8}.


All combinations of the above xyz values give 245 numbers. Let the objective of the game be emphasized again: the criteria is to increase the winning chance by a factor of 4, compared with natural course, i.e. instead of winning once per 1000, we try to win once per 250.


The Software Parameters

Standard version has 10,000 neurons, and a certain number of internal neurons. If you need a larger software, please contact http://attrasoft.com.

In your prediction, if you set

then the Predictor uses N*M*K neurons. Therefore, the limit is:

N*M*K <= 10,000 neurons ……. Standard version;

This number can go as high as 1,000,000 in a customized version.