Comments on: A Simple but Challenging Game: Part II http://nerdwisdom.com/2007/08/15/a-simple-but-challenging-game-part-ii/ Algorithms, Physics, AI, Games, Biology, Software, etc., with Reviews and Explanations Mon, 16 May 2011 14:33:36 +0000 hourly 1 http://wordpress.com/ By: Rock-Paper-Scissors Without the Luck « Nerd Wisdom http://nerdwisdom.com/2007/08/15/a-simple-but-challenging-game-part-ii/#comment-211 Sun, 07 Oct 2007 02:54:47 +0000 http://nerdwisdom.com/2007/08/15/a-simple-but-challenging-game-part-ii/#comment-211 [...] As I’ve mentioned before (click here for his “Duke and Pawn” game, or click here for a more game-theoretical type of game), my son Adam enjoys designing games. Here’s a game he designed, with very simple rules but [...]

]]> By: A Simple but Challenging Game, Part I « Nerd Wisdom http://nerdwisdom.com/2007/08/15/a-simple-but-challenging-game-part-ii/#comment-144 Sun, 23 Sep 2007 20:08:49 +0000 http://nerdwisdom.com/2007/08/15/a-simple-but-challenging-game-part-ii/#comment-144 [...] tell you more in a later post, but for now why don’t you think about [...]

]]> By: Duke and Pawn Endgames « Nerd Wisdom http://nerdwisdom.com/2007/08/15/a-simple-but-challenging-game-part-ii/#comment-64 Mon, 03 Sep 2007 20:59:12 +0000 http://nerdwisdom.com/2007/08/15/a-simple-but-challenging-game-part-ii/#comment-64 [...] I mentioned in an earlier post, my son Adam likes to design games, and he designed this very clever variant of the King and Pawn [...]

]]> By: On Rationality « Nerd Wisdom http://nerdwisdom.com/2007/08/15/a-simple-but-challenging-game-part-ii/#comment-45 Tue, 28 Aug 2007 05:37:33 +0000 http://nerdwisdom.com/2007/08/15/a-simple-but-challenging-game-part-ii/#comment-45 [...] I want to expand a bit on what I said previously in “A Simple But Challenging Game: Part II, this time focusing on Rosenthal’s Centipede Game. To remind you of the rules, in that game [...]

]]> By: Emin Martinian http://nerdwisdom.com/2007/08/15/a-simple-but-challenging-game-part-ii/#comment-43 Mon, 27 Aug 2007 01:39:56 +0000 http://nerdwisdom.com/2007/08/15/a-simple-but-challenging-game-part-ii/#comment-43 Interesting game. I think that leaving probabilistic strategies out may be the cause of the counterintuitive result you are getting. I haven’t done the game theory analysis, but I suspect that the problem with the first player passing is that the second player will interpret it as a sign of weakness and immediately challenge. Thus the first player might as well challenge immediately so as to remove any optionality from the second player.

If you allowed probabilistic strategies, then the first player would have the option of occasionally passing when he has a strong hand so that he can also pass when he has a weak hand without giving away that he has a weak hand. Basically, probabilistic strategies allow bluffing.

Another interesting variation might be to add risk aversion. That is instead of the goal being to maximize expected wealth, the goal could be to maximize expected wealth minus standard deviation of wealth.

In any case, it’s an interesting post.

]]> By: Anonymous http://nerdwisdom.com/2007/08/15/a-simple-but-challenging-game-part-ii/#comment-18 Thu, 16 Aug 2007 03:36:21 +0000 http://nerdwisdom.com/2007/08/15/a-simple-but-challenging-game-part-ii/#comment-18 I found your website a few days ago and it’s great!

Another simple problem (not game theory) I found intriguing is
this one on Tom Cover’s website.

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