Message text I have decided to start and maintain an official bad luck thread. I will define a statistical method to analyse games, and check whether the random number generator of the website is good or not.
--==## THE RULES ##==--
You have to read these
1) A statistical sample is declared before it is generated. For example, games XXX and YYY and ZZZ are requested for analysis before they start. This is extremely important to deal with samples that are unbiased.
2) All the rolls of ONE of the players within the list of games constitutes a sample. So if 35 games are listed to be analysed, and a total of 6 players take part in the games, we will have 6 samples.
3) For each sample, the average die roll will be computed by the player requesting the statistical analysis to be done.
4) For each player, the z value will be computed using the following formula. Let N the number of times a certain player has rolled dice, and let A be the player's average. The z-value can then be computed via Google Calculator by substituting N and A in the following link:
z = http://www.google.co.uk/search?hl=en&safe=off&q=(A-3.5)%2F(1.71%2Fsqrt(N
5) According to the Central Limit Theorem,
http://www.intmath.com/Counting-probability/z-table.php
* 75.0% of the samples will have z between -1.15 and +1.15
* 90.0% of the samples will have z between -1.64 and +1.64
* 95.0% of the samples will have z between -1.96 and +1.96
* 99.0% of the samples will have z between -2.58 and +2.58
* 99.5% of the samples will have z between -2.81 and +2.81
* 99.9% of the samples will have z between -3.30 and +3.30
--==## THE FINE PRINT ##==--
You can skip this
6) Caveat. For small samples (N = 1, 2, 3) the z-values are only approximately reliable. The approximation becomes good for N = 4, 5 for all practical purposes, and is essentially perfect already at 10.
7) In keeping with the need for the analysis to be unbiased, no other quantity will be computed in this thread besides the z-values of samples as defined in (1-4) above.
8) If we manage to collect a good number of samples (tens of them) and find a surprising number of outliers, the matter will be investigated further by myself (flying_neko).
9) Great Grand Samples (GGS). For each player taking part in this experiment, we will compute his or her GGS. This is obtained by putting together all of that player's z values, and computing the great grand z value (GGz) according to the following formula. Let GGA be the average of all the z's of the player, and GGN be the number of all such samples. Then
GGz = http://www.google.co.uk/search?hl=en&safe=off&q=(GGA)*sqrt(GGN
10) GGz is statistically distributed exactly as z in (5) (marvels of the Central Limit Theorem).
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