Finally find one article i will copy past it from other forum
Here is about finding bias but the same all is when to apply in detecting best distance.
Someone ask about detecting two most biased numbers and gave 6*37 =222 spins data . Where are in these two numbers 22 hits.
Chi square is an essential part in all statistical analysis, including tracking results in VB. Having said that, the correct way to bias spot, is to find the bias first, visually, and then from this assumption measure the Std/Chi Square. If the the Std is peak picked from random numbers its not quite valid. Laurance has recently done a very good explanation on advantageplayer.com heres a copy and paste, you will then as a bonus get the formula for
** calculating the standard deviation.**
Laurance writes:
The formula for STDEV is: SQRT(NPQ)
In this case, N = 6 * 37 = 222
I assume you are playing a single zero wheel, so the probability of winning § = 2/37, and the probability of losing (Q) is 35/37. P = .054, Q = .946
SQRT(222.054.946) = SQRT(11.34) = 3.37**
So, 3.37 hits represents one Standard Deviation (STDEV) from expectation given 222 trials and two numbers bet.
So, we now need to know what expectation is. Expectation = N * P (Number of spins * Probability of winning).
E = 222 * .054 = 11.988. Let’s call it 12. Your expectation is 12 wins in 222 trials.
You have 21 hits, so you are 21 - 12, or 9 hits above expectation.
9 / 3.37 = 2.67 STDEV from expectation.
But wait … there’s more.
The 2.67 STDEV only has meaning IF you predicted the two numbers in advance of the 222 trials.
If you just took 222 trials, and then “Peak Picked” the top two numbers, the traditional STDEV does not apply. It only applies in the case where the outcome is predicted IN ADVANCE of the sample taken.
So, how rare is it to find two numbers which, combined, have a 2.67 STDEV over 222 trials? To answer this question, we need to run a simulation. I have a simulation program, and these are the results:
I ran 10,000 games of 222 trails each on a single zero wheel. I counted all of the games where there were at least two numbers, which combined, had a STDEV >= 2.67 (e.g. there were 21 hits or more).
8,025 of those games passed. In other words, if you don’t predict the numbers IN ADVANCE, there is an 80% chance you will encounter two random numbers that, combined, will have 21 hits over 222 spins.
But, what if the two numbers are contiguous? The 80% figure applies if you pick ANY two numbers on the wheel. If you are looking at a contiguous 2 number section, this becomes a rarer event, but not that rare. The chances of a 2 number contiguous section rising to the 2.67 STDEV level is 28% (again, determined via simulation).
So, if you predicted the number IN ADVANCE of the 222 spins, the chance of those two numbers having 21 hits is about 1 in 50 (98% = 2.67 STDEV). If you peak pick the top two numbers after the fact, the chances of randomly winding up with two numbers hitting 21 times is 8 in 10. The chances of randomly finding two adjacent number >= 2.67 STDEV is about 1 in 4.
Hope this answers your question.