tag:blogger.com,1999:blog-4081946784040239088.post838948392820611454..comments2014-04-08T04:44:47.169-05:00Comments on Viviomancy: Wow... (update on Zilch research)Leadhyena Inrandomtanhttp://www.blogger.com/profile/00597365838412115319noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-4081946784040239088.post-19144071195053990682008-11-30T16:39:00.000-05:002008-11-30T16:39:00.000-05:00So I was playing Zilch and came across your blog y...So I was playing Zilch and came across your blog yesterday. I thought you were going to do math in your next post, not more programming? :)<BR/><BR/>I'm wondering where you came up with the 64 trillion game states.<BR/><BR/>Like ThetaPi and Bartolomew, I also approached this problem by formulating the Expected Score. My analysis only depends on number of dice, not game state. (Rationale: if you are rolling 6 dice, the score you expect to get is the same regardless of your previous score). My equations are complete, but I stopped short of computing actual values due to a small problem... see my article.<BR/><BR/>I don't have a blog, and since I wanted LaTeX to make my equations anyway, I wrote up a whole document at <A HREF="http://zalbee.intricus.net/zilch.pdf" REL="nofollow">http://zalbee.intricus.net/zilch.pdf</A>Alberthttp://www.blogger.com/profile/18001231100277526077noreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-31413079201504065512008-11-23T06:44:00.000-05:002008-11-23T06:44:00.000-05:00Hi, i hope you are still working on the project. I...Hi, i hope you are still working on the project. I'm still very excited about the outcomes.<BR/><BR/>As for the "free roll" problem I think you could just start with scoring free rolls with 0 points and see what expected score (lets call it s) you get out of 6 dice without taking free rolls (e.g. forfeiting instead of making a free roll). Also note the expected probability p for scoring a free roll. Then you have a formula like this for the expected free roll score (or effective expected score with 6 dice) x:<BR/><BR/>x = SUM(n=0..inf)(p^n) * s<BR/><BR/>I'm sure I'm missing something here, as it seems so simple right now.<BR/><BR/>I use "expected" instead of "average" as i assume an "intelligent" choice of dice to score. A problem i see there is that deciding what is "intelligent" depends on what your expected score with a free roll is. So maybe for choosing scoring options you'd have to assume some number for x first and revisit that later.Bartolomewnoreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-14732653347019229602008-11-19T09:55:00.000-05:002008-11-19T09:55:00.000-05:00I'm surprised the game space is finite ^^ I'm in t...I'm surprised the game space is finite ^^ <BR/><BR/>I'm in the preparation stages to write an EV function (expected value) which should take as parameters the game state and a decision (which dice to score and whether to bank or to roll) and returns the expected score.<BR/><BR/>The first problem that comes to mind is that in case all dice get scored, you enter a new iteration with all six dice. In theory you could enter infinite recursions, but thankfully the probability of multiple free rolls converges towards zero fast. Now I have to come up with a series that models this...ThetaPhinoreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-78694202840024391512008-11-10T00:13:00.000-05:002008-11-10T00:13:00.000-05:00At least the search space is smaller than Checkers...At least the search space is smaller than Checkers, and that has been solved. LOLLeadhyena Inrandomtanhttp://www.blogger.com/profile/00597365838412115319noreply@blogger.com