View
213
Download
0
Tags:
Embed Size (px)
Citation preview
Games Search
Neil Heffernan
Some of these slides are screen shots from the the slides my professor at
CMU (Andrew Moore) used. (Sorry for the low resolution)
Questions About Mini-max
• Last week when looking at search algorithms we saw that they al returned a path to the goal. Why doesn’t mini-max?
• Is minimax recursive? Is it efficient?
• What if loops in the search space are possible?
Can you use your cut-off tricks if you don’t know the range of possible values for the payoff
function?
General Rule: We can be sure a node will not be visited if either player has a better alternative at
any ancestor to that node.
Alpha-Beta Pruning Effectiveness
• Does keeping track of alpha and beta cost much?
• Hard to analyze. Depends on how lucky you are.
• In practice, Alpha-beta pruning can allow you to search twice as deep as compared to mini-max for the same amount of time.
State of the Art
• Chess- Easy
• Othello- Easy
• Go- very hard
• Checkers- world champions
• Why? What is the average branching factor
Backgammon
• What is the complexity if we add chance nodes?– B- average branching factor
– N-number of distinct chance outcomes
– M-the average number of moves needed.
– Backgammon n=21, m~20 (sometimes 4000)
• Turns out search is prohibitive and better to get a good evaluation function (using a neural network)
General Principle
• When uncertainty enters the picture, we have many more possibilities.
• Can you do alpha-beta trick with backgammon?
Discussion
• When playing tournament chess, players get 2 hours for the first ~moves. How does that effect our search?
•