&ldquo;Money won is twice as sweet as money earned.&rdquo; A well-known proverb used in the gambling stands for the fact that the money earned in gambling or by the luck feels more exciting and exaggerating than the hard-earned money of business or service. In our last family trip to Hong Kong during the Chinese New Year, we have planned a stay in Macao for two nights. It was my first interaction with gambling when we visited the biggest casino in China &ndash; The Venetian Macao. I came across the power of gambling which may either take one to the height of lifestyle, or to the world of depression due to huge of debts. However, the game of roulette has significantly drawn my attention. It was my belief that there is a scientific approach, if followed, may lead to winning the game.

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After my holiday, I went deeper into procedure of the game &ndash; Roulette. After studying about the game from various articles, research projects that were previously carried on prediction of correct calls, my interest took a shape of a project. It was in 2017, when I was introduced with concepts and applications of probability in mathematics. It has a significantly contribution behind the mathematical exploration of the analysis on determination of corrected calls in Roulette. My project went well but the Future Prospect of the project was analysis on Red Envelope of WeChat.

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This was the moment when I came across the concept of Red Envelope. However, due to some circumstances further work was not carried on at that time. But recently my interest developed again on this field.

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I have done a thorough research on the feature of Red Envelope on WeChat. I have gone through a number of research articles and journals where I learnt the algorithm which is followed by WeChat to offer the sum of money in each drawings of Red Envelope. Moreover, I have analyzed several data sets on disbursing cash in each drawing from several newspapers and news articles. However, the answer to the question which was partially answered in the last project on Roulette, was not answered this time, in case of Red Envelope &ndash; which term will disburse the maximum amount of money?

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Heaped with worries, I decided to research and find the answer to my query. This IA is about the same.

The main motive of this exploration is to determine the variation in probability of determining the maximum share drawn at each drawing. This is to determine a correlation between the number of drawing from the Red Envelope and the amount drawn in each drawing so that any relationship can be derived which may lead to determination of term offering the maximum share.

What is the variation in probability of determining the maximum share of a Red Packet in WeChat at a particular drawing based on five different raw data sets (each of width 30)?

Red Envelope is a feature offered in Chinese multipurpose, social media, messaging and mobile payment app made by Tencent &ndash; WeChat. This feature acts as a metaphor to the famous tradition in China &ndash; gifting red envelope during any occasion, specially, Chinese New Year. Each envelope usually contains some amount of money which is gifted to the friends and family members as their love, affection, relationship and often as a vode of thanks. WeChat added a feature naming Red Envelope which offers the same, virtually.

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Here, a person can send a red envelope with a fixed amount of money in Chinese Yuan (CNY) in a WeChat group. The app gives the user, the liberty to set his desired amount of money and the number of drawings that could be made. Once the settings are done and the envelope is sent, the other members of the group will be able to draw from the envelope. It should be noted that the money disbursed in each drawing is not pre-determined and works on an algorithm. Neither the user who sent the envelope, nor the other members of the group can pre-determine the amount of money disbursed in each drawing.

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Once the number of drawings set by the user is reached, no more members can draw money from that red envelope and the envelope will be terminated. The money received by the members will be directly deposited in their bank accounts linked with WeChat. It should be noted that the total amount of money sent in the envelope will be disbursed only if the number of drawings is reached. The envelope remains valid only for a day. Thus, if the total number of drawings is not reached by the end of the day, the remaining amount of money is refunded to the user.

As discussed in the previous sub-heading, the distribution of share is determined by an algorithm. The amount of money disbursed in each drawing ranges widely. There is a coefficient of maximum share which determines the range of money which can be disbursed in each drawing. Usually, this value is equal to 2.1. Thus, in case of each drawing, the amount of money to be disbursed ranges&nbsp;between 0.01 CNY and average residual amount of money times the coefficient of maximum disbursement. The average residual amount of money is defined as follows:

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Average Residual =&nbsp;\(\frac{Residual\ Amount\ of\ Money}{Residual\ Time\ of\ Drawings}\)

The maximum amount of money that could be added in a red envelope is 200 CNY and the maximum number of drawings could be set to 100.

The probability of occurrence of an event is:

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Probability (P) =&nbsp;\(\frac{Number\ of\ Favourable\ Outcome}{Total\ Number\ of\ Sample\ Spaces}\)

Regression correlation coefficient is a tool to measure the strength of the correlation between the independent variable and the dependent variable. The set of values (x1,y1), (x2,y2), (xn,yn) are used to find the value of r as stated by the formula below:

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r =&nbsp;\(\frac{n\big(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-\big(\sum x\big)^2][n\sum y^2-\big(\sum y\big)^2]}}\)

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In the above-mentioned formula, x is the value of independent variable of each observation, y is the value of dependent variable of each observation, xy is the value of the product of the independent and the dependent variable of each observation, n is the number of observation and &sum; denotes the sum of all the observation of the mentioned variable.

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By squaring the value of r, the value of the regression coefficient (r2) will be achieved. The value of r2 lies between 0 and 1 where 1 signifies maximum correlation whereas 0 signifies null correlation.

Chi squared test is a kind of analysis which predicts the existence of any correlation between an independent variable and a dependent variable. The Chi squared value of any given set of data is firstly calculated. Now, based on the type of data, for example, paired data or independent data, the Chi squared value is checked in the Chi squared table which further predicts the existence of any correlation.

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The formula of Chi squared value is given below:

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X2 value = &Sigma;&nbsp;\(\frac{(O_i-E_i)^2}{E_i}\)

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Here, Oi is the observed value, Ei is the expected value, &sum; denotes the sum of all the observation of the mentioned variable.

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Now, the Chi squared value is checked in Chi squared table which predicts the existence of any correlation. The Chi squared table is shown below:

Python is a high-level programming language which is used to serve several purposes in the domain of information technology. In context with this exploration, python programming language can be used to develop a prototype of the feature of red envelope only with respect to the amount of money that should be disbursed.

It is assumed that there does not exist any correlation between the number of drawing and probability of getting the maximum share.

It is assumed that there exists a correlation between the number of drawing and probability of getting the maximum share.

A data sheet has been prepared based on several news articles, reports and surveys in money disbursed in each drawing in Red Envelope WeChat. It has been possible to record the data of number of drawing and amount as these amounts directly reflect in bank statement.

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Justification of the Source and Interval of Raw Data

Data sheet has been prepared based on the amount of money added in the red envelope by the contributor. In all the data sets, the number of drawings is set to 30. This is treated as a controlled variable to keep a uniformity to study the correlation. The amount of money added in each trial is increased linearly at an interval of 30. This is done to ignore more complex calculations as the number of drawings is kept fixed to 30.

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Investigation On The Variation Of Probability Of Getting The Maximum Share Of A Red Packet In WeChat At A Particular Drawing Based On Five Different Raw Data Sets (Each Of Width 30)