tag:blogger.com,1999:blog-4081946784040239088.post3062379858957814226..comments2014-04-08T04:44:47.169-05:00Comments on Viviomancy: Study of the game Zilch part 1Leadhyena Inrandomtanhttp://www.blogger.com/profile/00597365838412115319noreply@blogger.comBlogger19125tag:blogger.com,1999:blog-4081946784040239088.post-71818618404920601512012-07-17T20:40:06.102-05:002012-07-17T20:40:06.102-05:00the code does not include how u calculate the scor...the code does not include how u calculate the score. u only showed us "calculateScore". so i can't be sure whether u somehow did manage to calculate the average score, and whether it is correct. <br />About the zilch prob, they all can be calculated with high school math, so it remains possible that you're not using your code. The easy ones are 4/6 one die, (4/6)^2 for two, 0 for six, (4/6)^3 - 4/(6^3) for three, then using "tree diagrams" to calculate for four and five. On a side note, i want to point out that since it is true that the zilch prob is so low, players who are unfamiliar with the math behind it will assume the computer is cheating.<br />And you're right about statistical treatment. The mean value is not good, the median score is more useful! so we need the probability function to show us more than the mean. Yes we can use the distribution of the probabilities to really predict what is the best move, but that would be too complicated. Why is everyone using your mean value?! It makes no sense to use mean! i'm very concerned.<br />About how to calculate the score if you rolled the last die and got a free roll, we can use eigenvalue functions, like in google PageRank search algorithm and in genetics, to explain why the ratios of various gene groups tends towards a steady value.<br />@Johnny: About the Realist strategy, i've read on the game coder's blog, it does say the strategy takes into account the current total score. But anyway, i still believe that any strategy shouldn't take into account the past scores. Past rolls do not affect subsequent ones. Don't be afraid when your score is lower than the computer, treat them like sunk costs. But that's jus me.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-32479694363689855332011-03-28T04:00:39.131-05:002011-03-28T04:00:39.131-05:00Zilch has dedicated fans! It's also known as F...Zilch has dedicated fans! It's also known as Farkle: There are many strategies published related to this game.Stefhttp://www.archipelago-of-strategy-games.com/games/Zilch_dice_game.htmlnoreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-37905240567905649672009-09-13T12:06:27.618-05:002009-09-13T12:06:27.618-05:00Hi Leadhyena Inrandomtan,
In the rules you correct...Hi Leadhyena Inrandomtan,<br />In the rules you correctly said:<br />"Once one player gets to 10,000 points, the other player has one more turn in order to attempt to beat the crosser's score."<br />I've started a discussion with Gaby (the maker) on this rule. It is not fair in my humble opinion.<br />For a game like this (it's the same with billiards, libre game) all players should have the same amount of turns. That is the premise. So, no extra turns for a starting player over a follower already reaching 10,000.<br />So my argument is not on your good work, but on the (un)fairness in the game itself. See my point? What are your thoughts?<br />Daviddcoelho1968@hotmail.comnoreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-16576420710294124612008-12-17T17:59:00.000-05:002008-12-17T17:59:00.000-05:00Confirmed that Acrisius' average is correct.You ge...Confirmed that Acrisius' average is correct.<BR/><BR/>You get:<BR/><BR/>422.26 - If you don't consider quad+pair to be 3 pairs. atanner this is probably what you got.<BR/>426.60 - If you always consider quad+pair to be 3 pairs (sub-optimal)<BR/>427.43699 - If you take the better scoring of quad+pair vs 3 pairs.Alberthttp://www.blogger.com/profile/18001231100277526077noreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-82079841258616941732008-12-07T21:16:00.000-05:002008-12-07T21:16:00.000-05:00Not that useful so far :(Can someone of you lovely...Not that useful so far :(<BR/><BR/>Can someone of you lovely nerds please answer some of my questions? <BR/><BR/>1) More wonderful table: number of dice, chance to zilch, chance to score something but not a free roll, average points gained when scoring something but not a free roll, chance to get a free roll, average points when you score a free roll.<BR/><BR/>2) What are the best chices for a strategy "take the money and run", i mean, suppose you bank whenever you can and don't have a free roll, what is better to roll when you cannot bank?<BR/><BR/>3) Bank or roll? You can bank X or roll Y dice, what is best? The more wonderful table may help. (maybe it is usefull to suppose that you apply take the money and run above some amount of points, and that adter some consecutive free rolls you are forced to bank without taking a new free roll).<BR/><BR/>4)Minimize the number of turns you expect to reach 10,000.<BR/><BR/>The case, you score 2000 without taking a free roll, or 1500 with free roll can screw up the more wonderful table. just consider it only free roll, or make 2 tables.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-44397684264493224132008-12-04T03:33:00.000-05:002008-12-04T03:33:00.000-05:00My average for first roll (6 dice) is 427.43699. ...My average for first roll (6 dice) is 427.43699. My logic:<BR/>a) determine if a "special" grouping happened (3 pairs or straight)<BR/>b) calculate any 3+ groupings and add any single or double 1s & 5s<BR/>c) if both a & b come up zero (6-dice zilch), count 500.<BR/>d) take the maximum from a,b,c. Could be anywhere from 50 - 8000.<BR/><BR/>NOTE: don't forget that 4-of-a-kind plus a pair counts as 3 pairs! So, 2-2-2-2-5-5 counts 1500 rather than (400+100).Acrisiushttp://www.blogger.com/profile/03161787259311887825noreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-62646321081375033372008-11-21T11:10:00.000-05:002008-11-21T11:10:00.000-05:00I teach high school statistics and once I found Zi...I teach high school statistics and once I found Zilch, I decided to use it for a semester probability project.<BR/><BR/>I wrote a C# program to calculate the probabilities. After I wrote it, Gaby sent me here. I got the same results as you did for 1-5 dice. But my average for 6 dice is 426.2796. When subtracted from you average and multiplied by 46656, my total is 15000 too low.<BR/><BR/>Could you publish your calculateScore method? Thanks, I want to find the bug in my code and my thinking.<BR/><BR/>Thanks.atanner53http://www.blogger.com/profile/02640964491169678773noreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-64832590502128103002008-11-19T22:02:00.000-05:002008-11-19T22:02:00.000-05:00These are the kinds of posts I'd love to see more ...These are the kinds of posts I'd love to see more of across the board in flash dev... the 'why's and the process behind it.. loved the post man! keep it up!Fadehttp://www.blogger.com/profile/11781613094648188019noreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-32173349775731819572008-11-19T16:07:00.000-05:002008-11-19T16:07:00.000-05:00What perplexes me the most are the apparent incons...What perplexes me the most are the apparent inconsistencies in the realist's strategy. Sometimes it stops with 300 points and 2 dice to roll. Sometimes it decides to roll 1 die when 1000 or more could have been banked. It doesn't seem to be related to relative scores, either, i.e. it takes the apparently foolish gamble even when it doesn't need to. Curious!Johnnynoreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-82914761467437112542008-11-19T10:26:00.000-05:002008-11-19T10:26:00.000-05:00A quick second run might just involve adding in th...A quick second run might just involve adding in the expected value of a reroll (was it about 426?) at 1-p(zilch) right? In other words, just considering the added potential value of getting back to a position with six dice. Obviously there is a long way to go from there, including considering p(zilch), relative scores, etc. I didn't think it'd be so hard to get expected values for rolls: just compute the expected value of a zilch (which will vary depending on previous zilches as well as the points you could potentially bank) and compare it to the expected value of another roll, and you should know probablistically speaking what's the optimal course of action, no?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-72429491151048271662008-11-18T11:44:00.000-05:002008-11-18T11:44:00.000-05:00In the case of having 2,2,2,5,n1,n2where the n's a...In the case of having 2,2,2,5,n1,n2<BR/>where the n's are not 1,2,or 5.. you would bank the set of 2s and the five, you would only have 250 points. three 2's gives 200 points and the five gives you only 50.<BR/><BR/>BioHazzarDofUOAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-49471573719538580772008-11-17T14:43:00.000-05:002008-11-17T14:43:00.000-05:00In that last example, 2-2-2-5-3-4, wouldn't it mak...In that last example, 2-2-2-5-3-4, wouldn't it make the most sense to score both the three 2's and the 5, then bank straight away? Then you have both the highest average score and 0 chance of zilching.dthttp://www.blogger.com/profile/06813823419736789191noreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-74164208573962725932008-11-12T14:40:00.000-05:002008-11-12T14:40:00.000-05:00@anonymous: It only feels one-sided. If you mimic ...@anonymous: It only feels one-sided. If you mimic the realist's strategy, you'll win against it about 50% of the time and 80% against everyone else. Sure you'll have bad luck streaks and it'll feel biased, but that's what probability is all about.<BR/><BR/>@patrick, birdseed: I haven't completed the full analysis... and that's why the concerns you mentioned are not taken into account. This first step is solely a judgment of the first roll (without choosing dice, without rerolling). This is why I don't consider the reroll for six dice and why I don't consider the utility implications of the amount you already have banked. The full analysis will take all of that into account, although it is taking a lot longer than I thought, searching through so many cases.Leadhyena Inrandomtanhttp://www.blogger.com/profile/00597365838412115319noreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-65392725490674805182008-11-12T12:03:00.000-05:002008-11-12T12:03:00.000-05:00Great results so far!One thing that needs to be ta...Great results so far!<BR/><BR/>One thing that needs to be taken into account is the amount you're risking. I mean, if you have a thousand points on the board you'll want to bank it straight away, even if there's a good chance you won't zilch the next round. <BR/><BR/>What's important in many considerations is not what you stand to gain but what you stand to lose in relation to it - for instance, if you've got a very low score (say, 350 or so) and the opportunity to roll the sixth die, I'd intuitively say you'd do it even if it's just a 1/3 chance because the potential gain is so high.Birdseedhttp://www.blogger.com/profile/01161105277182690887noreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-37548513838235217922008-11-12T10:01:00.000-05:002008-11-12T10:01:00.000-05:00Does the estimated score per dice rolled account f...Does the estimated score per dice rolled account for the roll again if you use all six dice? I understand the odds of zilching on one die are 2/3rds but shouldn't the payoff matrix (even in its approximate form) include the 6 dice payoff?<BR/><BR/>I.e. if you roll one die you a 1/3 chance of scoring, but if you do score you get to roll again and get an additional average 426.60?<BR/><BR/>Or is this what the next part of the study will cover? Sorry if I'm being dense.Patricknoreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-23352757221606704652008-11-10T21:17:00.000-05:002008-11-10T21:17:00.000-05:00this game is so one sided it is fucking terrible. ...this game is so one sided it is fucking terrible. the maker should have coded it better so that the computer doesn't get all the good rolls.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-11532213610618004052008-11-10T00:17:00.000-05:002008-11-10T00:17:00.000-05:00Thanks for the kind words. And it's looking like a...Thanks for the kind words. And it's looking like a lot more work than I realized. :D But I'm thrilled at the prospect of flexing my math muscles, so it's a labor of love.Leadhyena Inrandomtanhttp://www.blogger.com/profile/00597365838412115319noreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-8964588278072330972008-11-09T22:20:00.000-05:002008-11-09T22:20:00.000-05:00Awesome, I had no idea that Zilch would generate t...Awesome, I had no idea that Zilch would generate this kind of response. Keep up the good work!Gabyhttp://www.blogger.com/profile/10840373257458791333noreply@blogger.comtag:blogger.com,1999:blog-4081946784040239088.post-58253596871930691202008-11-09T17:52:00.000-05:002008-11-09T17:52:00.000-05:00Loved your post and can't wait for the next instal...Loved your post and can't wait for the next installment!<BR/><BR/>In fact i was just about to find some spare time to implement the score-evaluation code myself when i saw your post linked from the game page.<BR/><BR/>Great work so far! Kept me from wasting more time on Zilch than i already did ;)Bartolomewnoreply@blogger.com