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Can I random walk myself to 2300?

#2

I love this kind of experiments. Thank you!

I love this kind of experiments. Thank you!
#3

I used to have a rating 2200 at bullet chess and I started playing my own nonsense b3, Bb2, Qc1, Nc3, Nd1, f3, g3, Nh3, Nhf2, 0-0 in every game. Now my rating is 2500, and if I play normally without that nonsense, I can reach max 2200-2300, my play strength didn't really go higher, so have I walked myself randomly to such a high rating?

I used to have a rating 2200 at bullet chess and I started playing my own nonsense b3, Bb2, Qc1, Nc3, Nd1, f3, g3, Nh3, Nhf2, 0-0 in every game. Now my rating is 2500, and if I play normally without that nonsense, I can reach max 2200-2300, my play strength didn't really go higher, so have I walked myself randomly to such a high rating?
#4

my guy here pulling greek letters as excuse not to study chess, respect

my guy here pulling greek letters as excuse not to study chess, respect
#5

While the monotonicity of tanh preserves the symmetry about R_real, and the drift guarantees a unique stationary distribution, I do not think that it is Gaussian. While there are a number of mathematical ways to try and show this, the easiest counter example is to probably just overlay the plot of your "analytic" solution with a Gaussian density with the same mean/variance (or just compute the L2 distance between them as functions over your support).

While the monotonicity of tanh preserves the symmetry about R_real, and the drift guarantees a unique stationary distribution, I do not think that it is Gaussian. While there are a number of mathematical ways to try and show this, the easiest counter example is to probably just overlay the plot of your "analytic" solution with a Gaussian density with the same mean/variance (or just compute the L2 distance between them as functions over your support).
#6
<Comment deleted by user>
#7

I believe if the drift is linear then the resulting distribution will be gaussian. The tanh function is probably close enough to linear over the range of interest (+-100) that you would struggle to see any difference.

(to see the linear case: if there is no restoring drift, then the limit distribution is a gaussian with increasing variance, this being an expression of the central limit theorem. A linear restoring drift is just a rescaling that doesn't change the shape.)

I believe if the drift is linear then the resulting distribution will be gaussian. The tanh function is probably close enough to linear over the range of interest (+-100) that you would struggle to see any difference. (to see the linear case: if there is no restoring drift, then the limit distribution is a gaussian with increasing variance, this being an expression of the central limit theorem. A linear restoring drift is just a rescaling that doesn't change the shape.)
#8

@jdannan said in #7:

I believe if the drift is linear then the resulting distribution will be gaussian. The tanh function is probably close enough to linear over the range of interest (+-100) that you would struggle to see any difference.

(to see the linear case: if there is no restoring drift, then the limit distribution is a gaussian with increasing variance, this being an expression of the central limit theorem. A linear restoring drift is just a rescaling that doesn't change the shape.)

Agreed. The difference would mostly be in the tail behaviour. I only mentioned it because it was hinted they were trying to prove it was exactly Gaussian, which I dont think will be true.

@jdannan said in #7: > I believe if the drift is linear then the resulting distribution will be gaussian. The tanh function is probably close enough to linear over the range of interest (+-100) that you would struggle to see any difference. > > (to see the linear case: if there is no restoring drift, then the limit distribution is a gaussian with increasing variance, this being an expression of the central limit theorem. A linear restoring drift is just a rescaling that doesn't change the shape.) Agreed. The difference would mostly be in the tail behaviour. I only mentioned it because it was hinted they were trying to prove it was exactly Gaussian, which I dont think will be true.
#9

Fun insights aside, I enjoyed the tone and the jokes of this post :)

Fun insights aside, I enjoyed the tone and the jokes of this post :)
#10

The random walk resulting from the rating fluctuations has a mean reversal property and with some assumptions... I think this could be modelled as an Ornstein-Uhlenbeck process (https://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process).

Questions like how long before I hit a certain rating .... how much time/ many more games before I return to a some rating after a losing streak... can then, in principle, be solved analytically as function of:

  • The players current rating (R)
  • The players true skill level (R_real)
  • The target rating of interest

I think...

The random walk resulting from the rating fluctuations has a mean reversal property and with some assumptions... I think this could be modelled as an Ornstein-Uhlenbeck process (https://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process). Questions like how long before I hit a certain rating .... how much time/ many more games before I return to a some rating after a losing streak... can then, in principle, be solved analytically as function of: - The players current rating (R) - The players true skill level (R_real) - The target rating of interest I think...