Nice problem in game theory?
Suppose we have three rows of coins. The first row has 6 rooms, the second 5 and the third 4. There are two players play a game where each player can choose (take) as many coins as he likes in a corner but only from a line. Which player can have a strategy to win the match and that is the strategy? Problem Nice, is not it? If you have any ideas please post them. Thank you very much in advance! Oh … I forgot! The winner is the player who picks up the last piece!
This is called Nim. The basic idea is, if the number of pieces in each row is represented as a binary string, the player who takes an even number of 1s in each position is a guaranteed winner. For example: 6 = 110 5 = 101 4 = 100 There are three in the first column, and one in the second and third. As a player, if "Evens" these columns are guaranteed a win. He (among others) by taking three of the stack 5. 6 = 110 2 = 010 4 = 100 Player continues this strategy, and is guaranteed a victory. Steve
Intro Game Theory (2007) Lect 17 of 23
|
|
Mastering Chess Vol. 12: New Improvements in Opening Theory for the Competitive Player $19.99 Roman’s Lab Volume 12: New Improvements in Opening Theory for the Competitive Player New Chess Theory on DVD! Roman, one of the worlds leading authorities on opening theory, shares his new analysis and improvements in the opening, allowing you to maximize your opening play. This DVD is for the ambitious player who never wants to be without an excellent response when meeting some of Whites most sol… |
|
|
Harrington on Hold ‘em Expert Strategy for No Limit Tournaments, Vol. 1: Strategic Play $18.71 Poker has taken America by storm. But it s not just any form of poker that has people across the country so excited it s No-Limit Hold Em the main event game. And now thanks to televised tournaments tens of thousands of new players are eager to claim their share of poker glory. Harrington on Hold Em takes you to the part of the game the cameras ignore the tactics required to get through the hundr… |
|
|
Harrington on Hold ‘em Expert Strategy for No Limit Tournaments, Vol. 2: Endgame $18.33 Poker has taken America by storm. But it’s not just any form of poker that has people across the country so excited it’s no-limit hold ‘em the main event game. And now, thanks to televised tournaments, tens of thousands of new players are eager to claim their share of poker glory. In the first volume of this series, Harrington on Hold ‘em: Volume I: Strategic Play, Dan Harrington explained how to … |
|
|
The Art of Strategy: A Game Theorist’s Guide to Success in Business and Life $11.39 “I am hard pressed to think of another book that can match the combination of practical insights and reading enjoyment.”—Steven Levitt Game theory means rigorous strategic thinking. It’s the art of anticipating your opponent’s next moves, knowing full well that your rival is trying to do the same thing to you. Though parts of game theory involve simple common sense, much is counterintui… |
|
|
Tom Clancy’s Splinter Cell Chaos Theory $19.20 Splinter Cell Chaos Theory GC… |
