tag:blogger.com,1999:blog-2170237526012357403.post5493617984593194977..comments2021-01-19T21:53:14.145-05:00Comments on Delta's D&D Hotspot: Testing a Balanced DieDeltahttp://www.blogger.com/profile/00705402326320853684noreply@blogger.comBlogger40125tag:blogger.com,1999:blog-2170237526012357403.post-73396659817709880192016-03-07T10:41:26.277-05:002016-03-07T10:41:26.277-05:00My next guess was going to be that the "1&quo...My next guess was going to be that the "1" was coming up more often; the "6" side is probably shallowly engraved, so it's heavy on that side (and hence rolls to the bottom). Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-13305506033624144682016-03-05T22:56:18.463-05:002016-03-05T22:56:18.463-05:00This comment has been removed by the author.Anonymoushttps://www.blogger.com/profile/11917902569957515708noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-54133037502407324152016-03-03T22:42:03.227-05:002016-03-03T22:42:03.227-05:00Right; I'm just taking a stab at guessing why ...Right; I'm just taking a stab at guessing why it's so unbalanced. I'm guessing that the "6" side is coming up more than the others (or maybe it's coming up less). Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-64057634506913694872016-03-03T18:23:13.732-05:002016-03-03T18:23:13.732-05:00by special "6" side showing up more,do y...by special "6" side showing up more,do you meant it when rolling the dice 30 times? I have thrown away the calculation and I will try them all again. Anonymoushttps://www.blogger.com/profile/11917902569957515708noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-76449442659255003752016-03-02T18:01:04.829-05:002016-03-02T18:01:04.829-05:00"dub" -> "dug""dub" -> "dug"Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-44110487471423470952016-03-02T18:00:38.816-05:002016-03-02T18:00:38.816-05:00It seems like that data says yes, it does effect t...It seems like that data says yes, it does effect the balance of those dice -- that's pretty compelling evidence, actually. It may be that the army icon is larger/dub deeper than the other pips and makes that side unbalanced. (Similar to the dice that failed me <a href="http://www.madmath.com/2016/02/when-dice-fail.html" rel="nofollow">here</a> with a giant "1" pip.)<br /><br />That's kind of too bad, but having the test fail on your repeatedly like that is an extremely strong sign. Is that special "6" side showing up more commonly than the other sides (or something else)?Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-62560870317411099992016-03-02T17:55:35.733-05:002016-03-02T17:55:35.733-05:00Heya Delta,thanks for getting back to me.
well act...Heya Delta,thanks for getting back to me.<br />well actually those are custom dice from Chessex,I have the 6 sided pips to be changed to my army's icon. Does this affect the dice? I have done this before for a dice by chessex to but from 20 dice that I bought, 12 of them have the results of 55 Anonymoushttps://www.blogger.com/profile/11917902569957515708noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-16801696087803408742016-03-02T14:51:39.349-05:002016-03-02T14:51:39.349-05:00That definitely suggests that your die is unbalanc...That definitely suggests that your die is unbalanced! Is there anything visually, obviously wrong with it? If you try the test again (another 30 rolls), do you get another very high number at the end? Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-63606618843978826142016-02-29T00:25:20.854-05:002016-02-29T00:25:20.854-05:00hello there
I tried your formula but I hit some bl...hello there<br />I tried your formula but I hit some blocks on the way.<br /><br />I tried following the steps for the D6<br />I keep tabs on which the results of the die for 30 rolls.<br />Then I substrect each of those results with 5<br />then I square the result of each of the substraction<br />then I sum the result of the square.<br />in 1 dice I get the result of 122<br /><br />so is something wrong in the formula or the dice?Anonymoushttps://www.blogger.com/profile/11917902569957515708noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-40636821468411116552016-01-29T12:57:32.439-05:002016-01-29T12:57:32.439-05:00Interesting comment, and basically true, but I pro...Interesting comment, and basically true, but I probably wouldn't act on those suggestions for a couple reasons:<br /><br />One: Consider the "d20 rolls mostly below 10" case; it's pretty unlikely for that to be a hypothesis, because manufacturers post numbers of large differences next to each other (1 adjacent to 19, 2 next to 20, etc.) so this test doesn't appear on an unbalanced die. <br /><br />Second: Monday on my math blog (madmath.com) I'll post the first case I've ever found of dice failing the test. In this case it's a whole boxful of cheap, rather obviously unbalanced d6's; and in fact if I'd rolled less than about 500 dice I don't think it would have failed the test (at alpha = 0.05). <br /><br />This actually came up because I used those dice in a class experiment, effectively "how many hits can we get on armor value 5 [in Book of War]?", and the proportion was way less than expected. But if I'd asked for "armor 4" (i.e., proportion less than half, like the d20-below-10 thought experiment), I never would have noticed the difference, because likewise the "1" and the "4" faces are about equally overbalanced to mask this effect. <br /><br />But: Great intuition, and thanks for pinging me on this, because I've been working on writing up this failed test just the last day or so!Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-88768778221117339252016-01-29T10:01:41.339-05:002016-01-29T10:01:41.339-05:00While you (rightfully) cautioned readers about the...While you (rightfully) cautioned readers about the limitations of the chi-squared Goodness of Fit test in the follow-up article, I would like to say that as a statistician I do think there's still some practical usefulness to lower sample size tests like the ones you propose here. Not quite so low - I'd suggest about twice as many, so 60 rolls of a d6 or 300 rolls to test a d20 - but on the same order of magnitude.<br /><br />While this isn't extremely powerful, it's enough to find gross imbalances (e.g., a d20 that rolls below 10 three-quarters of the time) while being quick enough to test a large number of dice on a lazy Sunday afternoon. Making an analogy to professional statistical analysis, using a lower sample size keeps the "cost" of doing the test low, which is desirable if you don't require the extra precision granted by a larger sample. Also, bear in mind that if you're willing to discard a die more easily (say, alpha of .9 instead of .95) then the power increases - and after all, they're only plastic pieces in a game, so accidentally putting an "okay" die into the "unbalanced" pile isn't the end of the world.Danhttps://www.blogger.com/profile/14285793254382192231noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-42016707518506055032015-06-18T01:05:23.948-04:002015-06-18T01:05:23.948-04:00Search for where "d10" is referenced in ...Search for where "d10" is referenced in the original blog post above. Pick a per-side expectation E, minimum E = 5; so in this case roll the die at least 10*5 = 50 times and record the results. For a fair die, the SSE at the end should be no more than X*E = 16.919*5 = 85. <br /><br />* Noting again that this is a lower-power test; if the die fails, then you can be sure it's broken; but lots of biased dice will pass the test anyway. For a high-power tests you'd want to use lots of rolls, maybe around E = 100 (so roll the die 1,000 times and see if the SSE remains below 16.919*100 = 1692). <br />Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-46677601000083817362015-06-17T20:02:13.631-04:002015-06-17T20:02:13.631-04:00How can I translate this formula to another dice: ...How can I translate this formula to another dice: For example, what is the total expected for a D10Nayara Costahttps://www.blogger.com/profile/07695647762077332901noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-82904992848246538962014-12-20T12:43:21.862-05:002014-12-20T12:43:21.862-05:00Good question; pretty much the same except that th...Good question; pretty much the same except that the expectation of appearances now differs per value. Example: Say you roll this die 30 times. Keep a similar table of frequency appearances for 2-3-4-5; for 2 and 5 subtract 5, but for 3 and 4 subtract 10 (respective expectations); then square and do the rest as normal. Basically you tally the squared error in any case (difference of frequency and expectation, whatever that may be for each outcome).<br /><br />Alternatively, you could make a little mark to actually distinguish each of the 6 faces and do it normally (with equal expectations).Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-33216954291949155952014-12-05T11:55:04.720-05:002014-12-05T11:55:04.720-05:00How would this work for dice with non-uniform dist...How would this work for dice with non-uniform distribution, such as “average” dice which have sides 2-3-3-4-4-5 (to avoid the extreme 1 and 6 results)?Anonymoushttps://www.blogger.com/profile/16408174565756475668noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-3368079356440918472013-01-24T12:58:27.468-05:002013-01-24T12:58:27.468-05:00That's great, thanks for posting that!That's great, thanks for posting that! Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-31473341532790338922013-01-23T22:13:53.194-05:002013-01-23T22:13:53.194-05:00Thanks for this. I just built an Excel Spreadsheet...Thanks for this. I just built an Excel Spreadsheet for testing my D20's. I have uploaded a copy here if others want to play around with it as well.<br /><br />D20 Testing Spreadsheet (Google Docs) - https://docs.google.com/spreadsheet/ccc?key=0Aik7Xd__ctlTdE03ZkpqMXByQ1dkX1FEcnE4ajU3Ynclance.rangerbobhttps://www.blogger.com/profile/10349419066672725767noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-47103617437082548772013-01-07T12:56:19.416-05:002013-01-07T12:56:19.416-05:00And to follow-up: My understanding is if you care ...And to follow-up: My understanding is if you care about true-rolling polyhedral dice, the best bet is to just get the precision-edged Gamescience dice and leave it at that (on sale through gamestation.net).Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-19156834352296023052013-01-07T12:50:07.341-05:002013-01-07T12:50:07.341-05:00That particular comment is just silly and totally ...That particular comment is just silly and totally wrong in every respect. In fact, fewer dice rolls actually means more opportunity for the imbalance to make a difference (not less). Any save against poison shows that a single die-roll can have a monumental effect on the game. (It's a separate issue that it takes a large number of rolls to scientifically confirm that a die is biased).<br /><br />So as far as what action to take, it depends on how much you care about your game or its outcome. For D&D, I did test all eight of my d20's with 100-rolls each, and if they're not obviously biased, then I keep them. For <i>Book of War</i>, I actually did buy a set of casino d6's just last week, partly to show off the product to other people, and partly because the head-to-head competition gets people's dander up a little bit more when things go bad.<br /><br />Also keep in mind is that casino security doesn't do hundreds of trials of rolling, they just stack the d6's next to each other and visually confirm the corners are square and meet up evenly without visible gaps. For a die to be radically biased, it would likely need obvious cracking/chipping from the die. Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-83125250106351899022013-01-05T20:04:17.061-05:002013-01-05T20:04:17.061-05:00Hi, Delta! Thanks for this post! But I was reading...Hi, Delta! Thanks for this post! But I was reading through a post in boardgamegeek.com (http://boardgamegeek.com/thread/576612/testing-dice-for-fairness) and someone brought up the following point: "There are practically no games where the imbalance of a standard die would significantly influence the game. There are just too few die rolls." What do you think? Should I keep using my unbalanced die or buy cassino ones?News Casterhttps://www.blogger.com/profile/12176800543281660050noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-65282910287605056002012-07-11T01:07:24.181-04:002012-07-11T01:07:24.181-04:00@ starwed: What you're talking about is the &q...@ starwed: What you're talking about is the "power" of the test, as mentioned above. See the last link at the very end of the blog post for a complete treatment of that.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-26580919454717879232012-07-10T14:06:25.366-04:002012-07-10T14:06:25.366-04:00Hmm, I think this is actually a fairly meaningless...Hmm, I think this is actually a fairly meaningless test until you determine with what probability an *unfair* die will pass the test.<br /><br />You've shown how often a fair die will pass the test, but that doesn't directly translate into a confidence that the dice is fair -- a die with a very, very slight unfairness will pass the test only slightly less often. As the unfairness increases, it'll be less and less likely to pass, so the test can discriminate between a perfectly balanced die and a blatantly unbalanced one. But to be useful you definitely need to know what the sensitivity really is.starwedhttps://www.blogger.com/profile/16934356789996615781noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-29094669698226333162011-07-24T02:16:33.383-04:002011-07-24T02:16:33.383-04:00Actually, I think I was being flippant about the p...Actually, I think I was being flippant about the power-curve graphs, because (a) that's, like, real hard, and (b) I'm not sure how to do it immediately for a chi-squared test. I will continue to think about how to do that.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-25265977768383407462011-07-24T00:37:55.193-04:002011-07-24T00:37:55.193-04:00JohnF said: "If the number of test rolls were...JohnF said: "If the number of test rolls were to increase to 60 or 300 rolls then the SSE limit would increase proportionally to 110.7 and 553.5 respectively. Am I correct?"<br /><br />Hey JohnF, you have it exactly right. (Even though I embarrassingly forgot that myself up in my 6/27 comment.) And you're on-target that the usefulness of increasing the die-rolls is to make the test more sensitive, i.e., greater "power" which could be shown in a graph.<br /><br />At the moment, I don't have that graph. Let me think about that for a bit. Thanks for the kind words!Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-75163403349080294982011-07-23T23:48:36.591-04:002011-07-23T23:48:36.591-04:00As I look at the comments to your excellent Feb 4,...As I look at the comments to your excellent Feb 4, 2009 article I finally understand that for the d6 30 roll test that the SSE limit is 55.35. If the number of test rolls were to increse to 60 or 300 rolls then the SSE limit would increase proportionally to 110.7 and 553.5 respectively. Am I correct?<br /><br />Similarly, in the original article you mention a graph to show the possibility of a crooked dice. I would be glad to see it if readily available and you think useful.<br /><br />Great article!!JohnFarrishttps://www.blogger.com/profile/00065320394165810090noreply@blogger.com