#game tree

AN ANALYSIS OF WAR GAME THEORY AND GAME TREES

If you were a child of the 1980’s you probably remember watching the movie WarGames with Matthew Broderick and perhaps even developed fascination with computers and the possibilities for gaming.  In the case of the film NORAD’s computer Joshua becomes involved in a serious war game after a teenage computer hacker attempts to play a set of computer games on the machine.  While the film ends…

Did you know you can improve your Pokémon battle skills with math? One of the key ingredients for winning a battle is the ability to predict your opponent. Due to the complex nature of prediction, mathematicians developed a theory on making strategic decisions: game theory.

Read on Bulbapedia how game theory helps you choose the best move during a battle. In combination with graph theory (a useful tool for solving the ice sliding puzzles as well) this leads to the concept of game trees, which made it possible for Deep Blue to beat Garry Kasparov at chess.

Becoming a grandmaster in Pokémon, it all comes down to math.

so remember those cheap cheap cheap Dragon Age games i bought?

i am an idiot.

you can't run them on my operating system. the next one up will cost $29.

20+30=50 (regular price of games)

50-13.45=36.55 (savings)

36.55-29=7.55 (savings after purchasing OS update)

i have saved 7.55 on these games.

clearly this has all be a clever ploy by Apple to get us to update to Snow Leopard. 

on top of that, i still have to figure out if i even have enough room for these games. on top of that, the Sims barely runs well at all on this shit. this is not a gamer's computer and never was.

A133046 - Starting from the standard 12 against 12 starting position in checkers, the sequence gives the number of unique move sequences after n moves

1, 7, 49, 302, 1469, 7361, 36768, 179740, 845931, 3963680, ...

A game tree is a tree that can be traversed downward to follow a game's progression. The root node represents the starting game condition, and it has a child for every one of the first player's possible legal moves. Tic-tac-toe has a pretty simple game tree (the subject of a recent XKCD comic) -- its game tree has 26,830 leaf nodes.

Checkers (known as "draughts" outside of the USA) is a game played on a board similar to chess, but with much simpler rules. But even those simple rules yield a complex game: the game tree has approximately 1031 leaf nodes. After each player has made two moves, there are already 1,469 different possibilities (a(4) in the above sequence).

Even with that many leaf nodes, however, Checkers was completely solved just a few years ago. The Chinook project knows every possible game, and can thus make the perfect move. Note that despite the fact that computer Chess players can reliably beat even the best humans, Chess is far from solved. In fact, there's some debate about whether solving Chess is even possible.