I am not saying that BI didn't cheat. I'm saying that your statistics argument is silly, your P-values are sillier, and you have not a clue what you are doing.
"Abuse of mathematics" is not a very big term and it clearly applies to the silly calculations you have done here. You did a Bayes calculation that includes a subjective probability. That means you just threw in some number that seemed okay to you and out the back you got a subjective probability for a non-random event and advertised that as meaning something. The only thing it means is that if you believe that it is incredibly unlikely that BI matches Houdini you think it is very likely he is cheating. Big deal. My Mom understands that and doesn't need to throw bogus Bayes theorem calculations at it.
The rest of your post is just stacking up more assumptions that mean nothing. If I was BI and you came to me and said that I ought to be as consistent as Carlsen or Hou Yifan or Pfren, I would shrug and say "Why?".
"Statistics is based upon consistency."
Huh? Your statistics are based on a whole bunch of clearly made up, unsupported assumptions and really fuzzy thinking about what random means. There is a notion of consistency in statistics (it means that a statistic converges in some sense to the parameter it is estimating as the sample size increases) but that has nothing to do with your discussion here.
@chiaroscuso62: Irrespective if you in your first sentence refer to your own sentence or to my post, I have to disagree with you. If you, however refer to your own post, then I agree with your first sentence. :-)
ad 1. If you have any knowledge of chess, how chess engines work and how the human brain works, then will you accept this possibility as a fairy tale. Just impossible, not worth any further discussion from my side. The chance that you look outside the window and you see a real unicorn with a fairy on it is bigger than the possibility that a human makes use of the same heuristics of a chess engine.
ad 2. Abuse of mathematics is a big term, for sure when you do not read accurately and you do not draw the proper conclusion yourself:
BI has not a higher match probability, he has a certain match with Houdini3. A higher match probability is not an exact term. Higher match probability than what? If you meant to say that his match probability conforms to a higher rating, then will I agree with you. His match rating conforms to a significant higher rating then he had at the time of the event.
That is still nothing to worry about as it happens to all chess players. Hou Yifan has scored ratings far above her current rating for instance and Ivanchuk far above and under. I know for Ivanchuk that he scored once 300 points lower than his own rating. That is where my 300 points came from. But the difference in ratings of B.I. is even more. Much more if you take his other tournament directly after Zadar into account. The man that could beat a GM above 2600 lost from someone in the 1800's and suddenly could not play in a style that matched the style of Houdini 3 at all.
We all suddenly change of playing style and skill, do we? Uhuh. In one tournament he had a higher match with Houdini 3 than Magnus Carlsen (he thinks similar to Houdini 3), in the next tournament he has lost all of those skills and has a very low match with Houdini 3 (where have his abilities gone? Suddenly disappearing?)
The cheating only becomes the best explanation when you have to explain his worst results too. If you only focus on his good performance, then will you have draw the same conclusion as I did: the rating of that performance is significantly different from the rating he had at the start of the tournament.
ad 3. Consistency is all. If someone does not perform consistently, then can I not conclude that that person has that certain capacity. Statistics is based upon consistency. B.I. is not consistent at all, that makes this statistics so compelling.
I expect you to disagree with my post. I will read your post with respect for you, but I will not respond anymore. Have a nice day.