@4718
"the probability of the events is not independent of each other."
++ You do not know if they are dependent or by how much.
Now assume they are independent and Poisson applies.
Then the result is that there is only 0 or 1 error.
So even if they were dependent it does not matter as there is no more than 1.
So the assumption was valid and Poisson applies.
"By how much the probabilities are off with poisson distribution is pure speculation."
++ Poisson is a plausible distribution. There being a large interdependence is pure speculation. Even if there is some interdependence, it plays no role, as there are only 0 to 1 errors.
"The point is that we cant rely on it to rule out error distributions that poisson does not support." ++ But then you have to say what error distribution you find more appropriate and calculate what results it yields.
"play with scenarios where you have ie. a series of 100+ games where the errors would divide unevenly in clusters, just like they can in a chess game."
++ I am not talking about blitz games between 1700 rated players.
I talk about the ICCF World Championship Finals, with ICCF (grand)masters with engines and 50 days per 10 moves. So I start with conditions that lead to sparse errors.
@4716
"Problem is as follows: I explain why poisson distribution isn't accurate here to predict errors"
++ It need not even be accurate, approximate is enough.
"it could be a huge margin" ++ That is for you to prove. It is a plausible distribution.
It is used for many similar problems. It can be slightly off, but not by a huge margin.
"using poisson distribution to show how many errors per game there are"
++ That is what is done in many sciences.
Example:
A voltage V accelerates an electron with charge e and mass m, what velocity v does it reach?
Answer:
Assume that v << c speed of light.
Thus Newtonian mechanics applies
thus mv² / 2 = eV
thus v = sqrt (2V e / m)
Now check
if v << c then that calculation is valid, else relativistic calculation is needed.
"Amount of wins and draws is not enough to determine error probability because the errors don't follow poisson distribution." ++ Poisson is a plausible distribution, it cannot be far off.
"We are in the dark." ++ We are in the light, but you make it dark.
"Because when we can't rule it out we have to consider it as an option even if its unlikely."
++ I did consider a white win or a black win as options, found them incompatible with the observed data, and also incompatible with other inductive and deductive evidence.
Now come back to: 9 games with 2 errors ++ 6 white wins with 2 errors (?), (?) that undo each other and 3 black wins with a white blunder (??)
Here are the 6 white wins:
https://www.iccf.com/game?id=948179
https://www.iccf.com/game?id=948250
https://www.iccf.com/game?id=948217
https://www.iccf.com/game?id=948198
https://www.iccf.com/game?id=948222
https://www.iccf.com/game?id=948273
And here are the 3 black wins:
https://www.iccf.com/game?id=948180
https://www.iccf.com/game?id=948268
https://www.iccf.com/game?id=948246
I say I can pinpoint the 1 error (?) in all 9 decisive games, usually the last move.
Can you pinpoint the white blunder (??) in the 3 black wins?
"It need not even be accurate, approximate is enough"
The point is that we know for a fact that errors in chess don't follow poisson distribution because the probability of the events is not independent of each other. By how much the probabilities are off with poisson distribution is pure speculation. The point is that we cant rely on it to rule out error distributions that poisson does not support.
If you really want to see how much poisson can be off, just play with scenarios where you have ie. a series of 100+ games where the errors would divide unevenly in clusters, just like they can in a chess game. You'll notice that a probability of a high error game is calculated way lower than it could in reality be.
"Can you pinpoint the white blunder (??) in the 3 black wins?"
I'm not trying to solve chess here unless I'm payed money