Hope Merchant - Lotto Statistics and Ball Draw Algorithms In C

This program provides statistics such as how many times the numbers in the previous draws came out, how many times the numbers that came out together in the draws came out together and how many days apart.

It allows you to draw a lotto by using the information of the past draws.

We can't say that after 3 heads in a row in a coin toss, the probability of getting heads is higher on the 4th toss. The probability of heads or tails is always equal on each toss. However, if a large number of tosses are made, the heads and tails numbers converge.

If a statistically infinite number of draws are made, the number of draws of all numbers may be equal.

If the numbers that came out a lot in the previous draws were due to a systematic error caused by the machines and the balls, then it may make sense to draw according to the statistics of the past draws.

For example, in the "Çılgın Sayısal Loto" game which is played by drawing 6 balls out of a total of 90 balls, in two draws made with 5 days apart, if 4 balls reappear due to a systematic error, it may be useful to draw according to the statistics of the past draws.

23.11.2020 :  8 22 42 52 55 71        18.11.2020 :  8 22 50 55 71 87       5 days   ( 8,22,55,71)

UINT8 gaussIndex(UINT8 ballCount)
{
	UINT16 node=0, leftnode=0, level;

	for (level=1; level<ballCount; level++)
	{
		if (rand() % 100 < 49 + rand() % 2) {
			node = node + level;
		} else {
			node = node + level + 1;
		}

		leftnode = leftnode + level;
	}

	return node - (leftnode-1);
}

 Figure: Pascal's triangle with 54 nodes

The gaussIndex function simulates that a ball dropped at node 0 of Pascal's triangle hits the nodes and moves left or right each time (just like tossing a coin) reaching the base of the triangle and selecting the number at the node it hits at the base.

For example, we have a lotto game with a total of 10 balls in a globe. Let's draw from these 10 balls. Let's examine how the gaussIndex(10) function works:

A ball dropped at the top node (0) of Pascal's triangle falls to the left (1) or right (2).

Suppose the ball follows the path 0-1-4-7-12-18.

Ball hitting knot 18, It will land on one of the nodes:

node = node + level = 18 + 6 = 24

or

node = node + level + 1 = 18 + 6 + 1 = 25

Suppose the ball then follows the path 25-32-40-49 and reaches the base of Pascal's triangle.

gaussIndex(10) = node - (leftnode-1) = 49 - (45-1) = 5

gaussIndex(10) will return ball number ⑤

The probability that a ball dropped on node 0 will always go to the left or always to the right is very low. Usually the ball lands somewhere in the middle at the base of the triangle. If more than one ball fell from above, the balls would pile up in the middle just like in a normal distribution. Based on data from previous draws, the balls are sorted according to certain sorting orders (with the ballSortOrder array) to the base of the triangle. The function was named gaussIndex because an index of this array is returned.

In the draws we will make, if we want the balls to be drawn mostly from the balls that came out the most in the past draws, At the base of the triangle, we should place the balls that appear the most in the middle, and the balls that appear the least on the sides.

Let the number of balls appear in past draws be as follows:

• ① => 56 times
• ② => 14 times
• ③ => 97 times
• ④ => 48 times
• ⑤ => 27 times
• ⑥ => 21 times
• ⑦ => 41 times
• ⑧ => 33 times
• ⑨ => 16 times
• ⑩ => 47 times

If we order the balls according to the normal distribution, that is, the balls that come out the most are in the middle:

• ballSortOrder[0] = ② => 14 times
• ballSortOrder[1] = ⑥ => 21 times
• ballSortOrder[2] = ⑧ => 33 times
• ballSortOrder[3] = ⑩ => 47 times
• ballSortOrder[4] = ① => 56 times
• ballSortOrder[5] = ③ => 97 times
• ballSortOrder[6] = ④ => 48 times
• ballSortOrder[7] = ⑦ => 41 times
• ballSortOrder[8] = ⑤ => 27 times
• ballSortOrder[9] = ⑨ => 16 times

The gaussIndex function following the path 0-1-4-7-12-18-25-32-40-49:

index = gaussIndex(10)-1 = 5-1 = 4

ballSortOrder[index] = ballSortOrder[4] = ①

• source : C source files

  • sayisal.c : Turkey Sayisal Lotto
  • super.c : Turkey Super Lotto
  • sanstopu.c : Turkey Sans Topu Lotto
  • eumillions.c : EuroMillions Lotto
  • eujackpot.c : EuroJackpot Lotto
  • powerball.c : American PowerBall Lotto
  • megamillions.c : American MegaMillions Lotto

• dist

  • ...-win32.exe ...-win64.exe : Windows 32 bit and 64 bit executable files. These files were compiled with the gcc compiler on the windows 10 operating system.

  • ...-mac : macOS executable files. These files were compiled with the gcc compiler on the macOS Catalina 10.15.7 operating system.

  • ...-linux : Linux executable files. These files were compiled with the gcc compiler on the centOS 7 Linux operating system.

  • ....txt : TXT files are statistics files containing the results of previous draws. These files must be located in the same directory as the executable files.

• DOS : For DOS operating system.

  • ....EXE : MS-DOS executable files. These files were compiled with the 16-bit Borland Turbo C++ compiler on the MS-DOS 5.0 operating system.

• gcc 11.2.0 compiler and successfuly tested on

  • Windows 10
  • macOS Catalina 10.15.7
  • centOS 7 Linux

• Borland Turbo C++ 3.0 compiler and successfuly tested on

  • MS-DOS 5.0

• gcc sourcefile.c -o outputfile -lm