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# Nakamura performance stats, clearly explained

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It does not take a PhD in Statistics to understand the basic fallacy of which Mr Kramnik is a victim. If a player plays someone 300 Elo lower, obviously they have a high winning chance. Over the course of 46 games, it is however likely that the lower-rated player will win at least one game. Mr Kramnik's assessment would be true in the following scenario: Hikaru never played an online game, and takes on the challenge to play the lower-rated player for 46 games without loosing. One-shot. In that scenario, he would have indeed only a small chance to succeed. However, as he continuously plays online, he is de facto trying this challenge over and over again, and on the long-term what has only a small chance of happening every single time, ends up happening eventually.

Flip a coin ten times, you'd have only a 1/1024 chance of getting all heads. Try this every day, and you have a 30% chance of having one successful attempt in a year. Actually, you would need 709 days in average (the log in base 1023/1024 of 0.5). Now, flip the same coin continuously, and notice that as the "runs" overlap you now get a much lower count: at every coin flip, you can take the previous ten into account, you don't need to "finish your series" as you can re-compute the statistic every time.

It is weird that someone smart enough to win a WCC can fail to understand such a simple statistical fallacy. I think Mr Kramnik should consult with some of the many great scientists in Russia, who will maybe find the examples to convince him that he is understanding something wrong.

Cheating in chess does happen and is enough of a threat to the sport that we don't want people crying wolf all over the place.

What is up with you and hans nieman brother💀💀💀💀💀💀💀💀
alexlehrersh wrote:

So then did you defend Nieman too or not?

You again...

What does anything have to do with niemann? (you even spelt niemann wrong) Do you not comprehend the statistics? Please don't compare irrelevant cases.

Have you even taken a look at the statistics? these cases differ a lot

alexlehrersh wrote:
justinpro0715 hat geschrieben:
alexlehrersh wrote:

So then did you defend Nieman too or not?

You again...

What does anything have to do with niemann? (you even spelt niemann wrong) Do you not comprehend the statistics? Please don't compare irrelevant cases.

Nopethe statistics are the same

And "you again" shows that you stalk me when you anwered to 3 day old comment

I am not in any way interested in you

It just so happens that you are making laughable comments all over chess.com forums