The algorithm uses a binomial distribution, in which the number of tickets correlates from the total sum of the lottery.
To participate in lottery you need 0.1 mBTС or 0.0001 BTС, that is, 10 tickets.
The cost of 1 ticket is 0.01 mBTC or 0.00001 BTC.
The probability of a ticket win equals the golden ratio:
The lottery amount is distributed between win tickets.
Regardless of the amount of participation, the chance of winning ticket will always strive for the value approximate to 0.618.
Now for a improve understanding, we will take the theoretical example and demonstrate the work of the algorithm on it.
We will analyze the theoretical example for a more detailed understanding of the practical part of the function.
This model is of a theoretical character, therefore does not take into account the transaction costs and the service fees.
Suppose there are the following players.
Players: A, B, C, D, E
The number of players' tickets are equivalent.
A = 100
B = 100
C = 100
D = 100
E = 100
Total Lottery 500 tickets.
Each player has 100 tickets.
Next, the function calculates the result of each ticket and calculates the number of winning tickets.
The probability of winning each individual ticket is 0.618.
Below is a test result with an indication of the number of winning tickets of each participant.
A = 75
B = 54
C = 66
D = 49
E = 57
Next, the algorithm calculates the amount of the winning of each winning ticket.
Summ = 75 + 54 + 66 + 40 + 57 = 292
Profit per one = 500 / 292 = 1.712
Profit for users.
A = 75 * 1.712 = 128.42 = + 28.42%
B = 54 * 1.712 = 92.46 = - 7.54%
C = 66 * 1.712 = 113.01 = + 13.01%
D = 49 * 1.712 = 83.9 = - 16.1%
E = 57 * 1.712 = 97.6 = - 2.4%
You will not be able to lose all funds in one lottery, as well as get a jackpot.
The average deviation of the magnitude of the winnings or loss is 1 – 0.618 = 0.382 or 38.2%.
This means that with a probability of 95% you will not win and do not lose more than 38.2% of the initial amount.
With games on small amounts due to a decrease in tickets, the number of attempts is reduced, which significantly weakens the effect of averaging.
For example, with minimal participation at 0.0001 BTC, the participant receives only 10 tickets and the number of winning ticket, as well as the result will be less stable, on the other hand, it allows with a probability of 6.18% to go abroad of maximum yield in 38.2%.
This is due to the fact that with 10 attempts to play with a probability of 61.8%, the real probability can differ significantly from the theoretical due to the small number of attempts.
In case of an increase in attempts, that is, 100 or 1000 attempts (tickets), the real probability will strive for 61.8%.
This part is dedicated to those who just want to know about golden ratio more.
This part is not mandatory since it is not necessary for reading, it does not expand knowledge about the algorithm and does not affect our rules or principles of work.
There are many versions on the origin of knowledge about the golden ratio in humanity.
In fact, it is one of the prior knowledge, knowledge from the outside.
Anyone who owns the fundamentals of mathematical computing can come to a golden ratio.
0 + 1 = 1
So we got the order of numbers, known in the world as numbers of Fibonacci.
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34
21 + 34 = 55
34 + 55 = 89
55 + 89 = 144
89 + 144 = 233
144 + 233 = 377
233 + 377 = 610
377 + 610 = 987
But where is golden ratio?
The ratio of numbers from a given series called golden ratio.
We will produce calculations for research purposes.
3 / 5 = 0.6
If you continue the series, you will get the next value:
5 / 8 = 0.625
8 / 13 = 0.615384
13 / 21 = 0.619
21 / 34 = 0.617647
34 / 55 = 0.6181818
55 / 89 = 0.617977
89 / 144 = 0.618
144 / 233 = 0.6180257
233 / 377 = 0.6180371
377 / 610 = 0.6180327
610 / 987 = 0.6180344
It was this relation that we have been based, when choosing a probability of a winning ticket.
You can continue the study of Fibonacci numbers and a golden ratio further independently.
Any person who owns mathematical knowledge could come to the numbers of Fibonacci and the Golden ratio.
The first person who gave a detailed description of golden ratio is Pythagoras.
There is an assumption that Pythagoras got his knowledge of the golden ratio from Egyptians and Babylonian.
The proportions of the pyramid of Heops, temples, bas-reliefs, household items and jewelry from the tombs of Tutankhamon show that Egyptian masters used the golden ratio when creating them.
The French architect Le Corbusier found that in the relief from the Temple of the Network I in Abidos and in the relief depicting the Pharaoh Ramses, the proportions of the figures correspond to the values of golden ratio.
The Khesira, depicted on a relief of a wooden board from the tomb of his name, holds measuring instruments in his hands, in which fixed proportions of golden ratio.
Plato also knew about golden ratio.
His dialogue "Timaeus" is dedicated to the mathematical and aesthetic views of the school of Pythagoras and the issues of the golden ratio.
In the facade of the ancient Greek temple of the Parthenon there are golden proportions.