# Why is the ideal exploration parameter in the UCT algorithm $\sqrt{2}$?

From Wikipedia, in the Monte-Carlo Tree Search algorithm, you should choose the node that maximizes the value:

$${\frac {w_{i}}{n_{i}}}+c{\sqrt {\frac {\ln N_{i}}{n_{i}}}}},$$

where

• $${w_{i}}$$ stands for the number of wins for the node considered after the $$i$$-th move,

• $${n_{i}}$$ stands for the number of simulations for the node considered after the $$i$$-th move,

• $$N_{i}$$ stands for the total number of simulations after the $$i$$-th move run by the parent node of the one considered

• $$c$$ is the exploration parameter—theoretically equal to$$\sqrt{2}$$; in practice usually chosen empirically.

Here (and I've seen in other places as well) it claims that the theoretical ideal value for $$c$$ is $$\sqrt{2}$$. Where does this value come from?

(Note: I did post this same question on cross-validated before I knew about this (more relevant) site)

• It's not the same question, but the answer to this question should contain the answer to your question. You may want to write a formal answer to your own question, once you understood the explanation in the paper and/or answer. – nbro Dec 10 '20 at 16:28