An academic paper examining Kramnik's moonhowling concerning Nakamura

[Paul McKeown]

See: https://phys.org/news/2025-07-im-statis ... world.html

[Christopher Kreuzer]

Thanks, Paul. That is Rosenthal's blog for phys.org (dated 9 July 2025)

Actual paper (Havard Data Science Review from April 2025) is here:

https://hdsr.mitpress.mit.edu/pub/ex6vbavk/release/2

Rosenthal, J. S. (2025). An Investigation Into Probabilities of Streaks in Online Chess. Harvard Data Science Review, 7(2).

https://doi.org/10.1162/99608f92.6939122d

Pretty heavy going (as you would expect from a formally published academic statistics paper) but also not too technical and written at a level that is accessible to those with some knowledge of the mathematics and modelling.

What surprised me is that the actual published paper allows comments (presumably moderated) so that you can see the dispute between Kramnik and Rosenthal continuing in the comments down the bottom of the article...

That is either a robust review system or a slippery slope into chaos!

[Roger de Coverly]

Pretty heavy going (as you would expect from a formally published academic statistics paper) but also not too technical and written at a level that is accessible to those with some knowledge of the mathematics and modelling.

The author is presumably the equivalent of a GM in the field of statistics. What then is Kramnik's standard?

I would summarise the conclusion as being that if you play lots of players weaker than yourself, that long winning streaks are plausible enough when you play lots of games.

[Christopher Kreuzer]

And OMG the language Kramnik uses in those comments...

[Christopher Kreuzer]

Pretty heavy going (as you would expect from a formally published academic statistics paper) but also not too technical and written at a level that is accessible to those with some knowledge of the mathematics and modelling.

The author is presumably the equivalent of a GM in the field of statistics. What then is Kramnik's standard?

I would summarise the conclusion as being that if you play lots of players weaker than yourself, that long winning streaks are plausible enough when you play lots of games.

I would have thought that in practice, when a strong GM like Nakamura plays much weaker players, that the statistics effectively break down. You would expect 100% of the games to be won by Nakamura. I am presuming that the statistics say there is a small chance of the weaker player drawing or winning, but we all know that would never happen.

So the question become one of how much weaker (or rather, how strong) the opponent needs to be before this "in practice 100%" starts to become non-zero. Handling very small chances is maybe something that statistics handles well, or maybe not.

https://www.johndcook.com/blog/2015/03/ ... abilities/

When model probabilities are extremely small, factors outside the model become more important than ones inside.

Admittedly, most of the examples in that blog and in the comment involve thermodynamics or chemistry, with large numbers of atoms or other particles. Comparatively speaking, the numbers involved in statistics for chess ratings and games are much less (and humans are not atoms, well, you know what I mean). But it still feels like an impossibility that strong GMs ever lose to much weaker players. You could set as a lower bound the lowest rated player that Nakamura has ever lost to, but then you might start to question how accurate that rating is.

[Ian Thompson]

I am presuming that the statistics say there is a small chance of the weaker player drawing or winning, but we all know that would never happen.

They do say that. The paper says Nakamura's average expected score was 99.985%. In online blitz, I'd question whether it would never happen, e.g. mouse slips, disconnections and external distractions are all liable to occasionally cause a loss.

[Nick Burrows]

Kramnik is approaching cheating in online blitz chess with a blitz chess mentality - arguing the case for intuition ahead of statistical rigor.
Intuition is notoriously bad when applied to very small or very large numbers.
Multiplying uncertain estimates does not lead to a meaningful or trustworthy number.

[Matt Mackenzie]

Why is Kramnik like this? He is doing genuine harm to those serious about combating cheating at chess.