# Difference between UCB1 and UCT

In Bandit Based Monte-Carlo Planning by Levente Kocsis and Csaba Szepesvári (2006) they propose the UCT algorithm which is derived from the UCB1 algorithm.

UCB1 algorithm:
$$X_j + \sqrt{\frac{2\ln n}{n_j}}$$

where $$X_j$$ is the average reward for machine $$j$$, $$n_j$$ is number of times $$j$$ has been played and $$n$$ is the entire number of games played.

In comparison, UCT is $$\frac{W_i}{n_i} + c \sqrt{\frac{\ln N_i}{n_i}}$$ where $$\frac{W_i}{n_i}$$ is win:lose ratio (the same as $$X_j$$),
$$c$$ is temperature parameter, which is often set to $$\sqrt{2}$$ (so they just put it in front...)
and $$\frac{N_i}{n_i}$$ is number of total games played for parent Node / number of games played for the corresponding node, which is the same as $$\frac{n}{n_j}$$.

So what's new here?