This document discusses efficient selection and backup operators in Monte-Carlo Tree Search. It describes the selection principle where moves that look best are searched deeper, while bad moves are searched less. It also explains that Crazy Stone selects each move probabilistically based on the move's statistics. Finally, it mentions that Crazy Stone uses a "Mix" backup operator that takes a linear combination of the mean, max, and robust max values of child nodes to update internal nodes after simulation.

1. Efficient Selectivity and Backup
Operators in Monte-Carlo Tree Search
Presented by Melvin Zhang
R´emi Coulom, Computer and Games 2006

2. http://rusgo.org/crazystone/

3. http://www.wired.com/2014/05/the-world-of-computer-go/

8. Selection
Principle: Move that look best should be searched deeper, and
bad moves should be searched less

9. Selection
Principle: Move that look best should be searched deeper, and
bad moves should be searched less
Crazy Stone: Each move i is selected with probability
proportional to
exp −2.4
µ∗ − µi
2(σ2
∗ + σ2
i )
+ i

10. Backup/Update
Update the statistics at internal nodes base on result of
simulation. Affects subsequent selection.

11. Backup/Update
Update the statistics at internal nodes base on result of
simulation. Affects subsequent selection.
Crazy Stone: Uses “Mix” operator, linear combination of mean
and robust max
mean
average of child nodes
max
max of child nodes
robust max
child node with the most simulation

12. http://peepo.com/go.html

13. https://code.google.com/p/magarena/