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Again, I just don't really trust that article.

I'm open to being proved wrong, but I've read it and think the "science" used left quite a bit to be desired...

That explanation certainly could be true, but if I rolled thousands of dice, I'd be more shocked if I actually got completely even (16.6%) results for each face.

If it's random, shouldn't some faces end up with higher percentages? You can do a much smaller scale test and get very skewed results... how many dice do you need to roll until you get the "perfect" random result?

Imho, if the result is "perfectly random" then it's no longer random at least as far as the realm of rolling dice.

Just my $0.02, of course!

Sit down and watch a group of 10 year olds play monopoly. Within 20 minutes, their little brains are already figuring out how to subconsciously cheat via dropping the dice, palming the dice and how to roll. And with the white square-edged dice, they can begin to control the outcome or at least influence it.

Give them rounded dice and very quickly they figure out they can't exploit the dice and just play the game. May not be equal results of 16% per side, but if all players suffer the same fate and can't influence the dice, it is FAIR even if it is not statistically average.

Kids are just following the laws of natural selection and like life, doing what they do to 'win'. Adults should know better because it becomes malicious cheating when they know they are knowingly manipulating the dice or knowingly are getting better odds than their opponent.

That being said... Casino dice cannot be rolled on a wargaming surface and be randomized, especially when rolled with a single or pair of dice. They require a bank.

Most square dice require a dice cup in order to be randomized because dice rolling techniques can easily manipulate hard-edged dice especially when rolling 2 or less dice. Dice cups are the only way to eliminate any and all of the issues with palming which is why most serious dice games like backgammon and yahtzee require a DICE CUP. If you are not using a dice cup, you are not randomizing.

True randomization of balanced dice require a controlled surface a bank and a dice cup. If you are not using them, then you are entering a place where the roller will be consciously or unconsciously controlling the outcome of the dice roll. IE: cheating.

Rounded dice may not be balanced and as some claim may not give statistically average random results, but the results are not influenced by the roller and if both players use the same dice, then it is FAIR.

And if you think that is garbage and you are morally justified to your special casino dice for LD rolls and square edged dice for your 12% less 1s, I will introduce you to my friend who can roll a 4+ on a white boardgame dice close to 99% of the time through a simple rolling technique and he will play an army who takes a ton of cover saves. He will roll each cover save 1 by 1 and never miss a single roll. If you can knowingly manipulate the game to your personal advantage and not see it as unfair or cheating then both sides can do it right?

Krak_kirby wrote:No, I did not pick the ones that rolled highest on more than average. I compared half a cube (18) of chessex dice to 18 koplow dice, and the koplow dice rolled better, so now I play with koplow dice. I did not buy large amounts of koplow dice and roll each one till I could cherry pick the high rollers, I simply bought several different colors of koplow and I use them all. If that sounds like cheating to you, you are welcome to your opinion. You should consider your words before you accuse someone directly or by inference of being a cheat or a liar. Please don't put me in with the crowd that loads dice, microwaves them, fast rolls, picks up successful rolls instead of fails, adds extra movement, or anything else that actually is cheating.

So you got two sets of dice, rolled them 1000 times. Then picked the ones that rolled better? I'm sorry but the only difference between doing that and doing it with 1000s of dice is just a matter of scale. Obviously the ways of cheating you mentioned are more obvious, and seen as 'worse' ways of cheating. But in my view, what you did is still cheating. Again it's just a matter of scale.

Oshova

Oshova wrote:So you got two sets of dice, rolled them 1000 times. Then picked the ones that rolled better? I'm sorry but the only difference between doing that and doing it with 1000s of dice is just a matter of scale. Obviously the ways of cheating you mentioned are more obvious, and seen as 'worse' ways of cheating. But in my view, what you did is still cheating. Again it's just a matter of scale.

Oshova

I bought some koplow dice, and use them exclusively (rather than my chessex dice), without having compared the two before selecting. Does that make me a cheater?

By you logic, someone who rolls poorly, then switches to different dice for their next set of rolls would also be considered to be cheating. /rollseyes/

No, by my logic someone who either buys a set of dice knowing they will roll better than their current dice, or who rolls dice excessively to test them out before using them is a cheat.

Did you roll your dice excessively? Did you roam the internet looking for the dice that rolled the best? If yes to either, then you fall in the bad area in my eyes.

Oshova

nkelsch wrote:*everything relevant remains*

We're talking about backgammon dice

While those are a lot harder to control the outcome of than the larger square-edged dice, nkelsch mentioned backgammon dice and how a cup is used to roll them, despite their small size...

RiTides wrote:While those are a lot harder to control the outcome of than the larger square-edged dice, nkelsch mentioned backgammon dice and how a cup is used to roll them, despite their small size...

Which can equally be applied to chessex dice. Dude, not everything that moron Stelek says is accurate.

oni wrote:I'd like to buy some precision dice. I know GameScience seems to be the place to go, but they don't seem to have what I want. All I'm looking for are some white and black opaque dice with pips and no bigger than 1/2". I've looked at Backgammon dice, but can bring myself to spend $10 for a single D6. Any ideas?

Yeah, by a whole box of dice for $10, then stop complaining because Warhammer sucks due to their shoddy d6 requirements... Just play the %$@#%#@ game!

I'm surprised that no one has linked to this article yet:

http://www.dakkadakka.com/wiki/en/That%27s_How_I_Roll_-_A_Scientific_Analysis_of_Dice

I guess it just goes to show how ignored the Dakka articles are !

Anyway, I find that the standard GW/Chessex dice work just fine for me, and since that is what a majority of the people I play with use, then both sides are equally biased. One thought that article raises that wasn't very well expounded upon was the notion that GW games were actually designed to use less than random dice. I would tend to think that this wasn't so much by design, but rather it is just a product of play testing and rules tweaking using chessex style rounded dice.

If we accept the premise of the article, namely that rounded dice with pips are roughly twice as likely to roll 1's than a theoretical "perfect" die, then using precision dice would suddenly make thinks with a 2+ save even more survivable!

RiTides wrote:Again, I just don't really trust that article.

I'm open to being proved wrong, but I've read it and think the "science" used left quite a bit to be desired...

That explanation certainly could be true, but if I rolled thousands of dice, I'd be more shocked if I actually got completely even (16.6%) results for each face.

If it's random, shouldn't some faces end up with higher percentages? You can do a much smaller scale test and get very skewed results... how many dice do you need to roll until you get the "perfect" random result?

Imho, if the result is "perfectly random" then it's no longer random at least as far as the realm of rolling dice.

Just my $0.02, of course!

Randomness is reasonably predictable.

In a trial of 1,000 rolls, if a number varies by more than 23 off the expected mean of 167 (144-190, 14%-19%) then you can say with 97.5% confidence that the dice are flawed.

For the result to be 29% you can say with much greater accuracy than 99.9999% confidence that the dice are not 1/6th per side. The degree to which you can say this, if the trial was well-performed, is staggering. 24% would assure any reasonable person that the dice were very bad. 29% is ridiculous.


At the 36,000 roll level they did for testing pip variance, the result of 19% also reveals nonrandomness at 99.7%+ confidence


These dice should have a variance of well under 1%: http://www.michellibackgammon.com/dice.php

My conclusion to that article is . . . Wow what a great way to use your job to gain an advantage in wargaming

I must say all the statistics etc interest me as a scientific prospect. But in the eyes of my wargaming I must say that testing dice for advantage should still be frowned upon. Testing dice for scientific discovery, and to give you an excuse for bad rolling however

The human mind is programmed to always find external reason for personal failure. If you always find internal reasons for your failure you will end up going insane, or being depressed. So I don't blame anyone who blames their dice for losing a game. Or even just that one roll going badly losing the entire game for you. It's a perfectly natural thing to do.

Oshova

I dont understand why using BALANCED dice as opposed to UNBALANCED dice would be frowned upon? Why would you *want* to play with a disadvantage. Sounds like an excuse to use when you lose

Also, dont call Kirby a cheater just because he tests his dice. Thats like saying a runner is cheating because he tests different running shoes and uses the one that performs the best

He didnt make the dice, nor did he alter them.. Its the exact same thing as saying people should just use flawed chessex dice. Both sets of dice are bought at a retail store, sorry Im using the better set

Will it help me win vs someone who uses flawed dice? Sure.. is it my fault? No.

Lots of things help you win in wargaming that you influence such as army lists and the tools you use.

I use a laser leveler to determine LOS and lots of things, I guess im cheating because its superior to someones eye sight. Personally I dont test dice, because thats insanely time consuming.. I simply just refuse to use small rounded dice for reasons stated previously

Well basically I don't see why people should be that bothered by apparent low rolling on apparent unbalanced dice. If you're that bothered then go ahead, but if I knew that the person I was playing against had done this to gain an advantage I would ask to use their dice, or them to use mine. As obviously both using the same dice excludes the balance problem. But I know that in a tournament most people would refuse this, as people get personal over their dice.

Basically I'm again raising the point of, have tournament dice supplied by the tournament organisers. It's expensive yes, but it gets rid of these problems. And you can always cover the costs by an increase in ticket price, but include the cube of dice along with the ticket or something. It's going to make things a lot fairer.

Oshova

Personally, I would have no problem if everyone used supposedly balanced dice.

As long as everyone had access to them and every roll was made with the same types of dice.

I do have problems when people buy special dice because they *KNOW* they get 12% less 1s and feel they are entitled to that advantage because they am smart and their opponent is dumb.

I do have problems when people will not share dice especially when they are using dice that actually impact the odds of the game in one persons favor.

I do have problems when people use a pair of special segmented dice which are different from what they roll for everything else for special saves, especially when they are using larger dice that are known to be easily manipulated like Casino dice.

If it bothers you that chessex dice roll 50% 1s, then bring good dice, inform your opponent how these dice will have better results and your opponent has the option to shar eyour dice to keep things fair. If he then refuses, you can't say he didn't know and that you refused to share. But if I see you are doing dice tricks and then get gakky when I want to roll on your special casino AV save dice then prepare for problems.

(This is why I like how most tourneys mandate dice sharing. I purposefully try to diceshare to see the reaction when I suspect dice shenanigans. The simple act of sharing usually means the person is not trying to maliciously gain an unfair advantage)

Well on that point I agree, I think everyone should use the same dice (IE non-small rounded dice).. I let people use my dice all the time since I have like 200 or something in a bag. They are completely random and based on whatever I find at a store

I really only care about those kind of dice during 2nd round of 'ard boyz :p Any other time Ill use whatever is available if for some reason I dont have mine..

Ive met a lot of people who constantly blame their dice for rolling too many 1s (they all use small rounded dice) and I explain to them if they use larger dice or non-rounded ones their odds will improve. I show them mine and even say that I roll better because of that. Yet virtually everyone refuses to listen and doesnt even seem to care that my dice roll better. I can only assume they dont believe me and/or WANT to continue being able to bitch about their dice when they perform poorly. Also I suppose the small dice are cheaper and stores carry a wide selection

If you want to share my dice, fine. Keep your hands clean (If I see you using the bathroom and walking right past the sink, no go) and we don't have problems.

If you want to pull a Stelek and cry like a little girl because you think someone else is using 'better' dice when the dice have 16.6% chance of hitting each face, then go whine at Yes The Truth Hurts, that's what that fail location is for.

Oshova wrote:*Stuff About Cheating* Oshova

I have personally played against Krak at ArdBoys and I will vouch that he is not a cheat, or any of the other things that you accuse him of. He was one of the best opponents I have played with in a long time. He was friendly, courteous, even when he was beating me with his ork list. Afterwards he was able to talk and give advice in a non-prickish manner. As far as picking better dice more power to him. I should of done the same. His tactics were sound, my tactics were sound, but if my dice had rolled more consistently I think I could of stopped the beating, not win mind you his list was tough, and I was playing Mechdar.

If you are playing at a tournament and not trying to minimize your weaknesses while trying to bolster your strength then you are wasting everyone's time crying about how unfair everything or everyone is, or how all the evil WAAC players are ruining the hobby. Dice aren't perfect. After rolling any block of dice, unless you purposely blind yourself, you will notice how that block will generally roll. The Pretty Chessex dice are some of the worse dice to use in competition. The Solid color dice tend to roll higher averages. The Koplow square dice are more dependable. Before the next tourney I'm in I'll be getting some squared dice myself.

As far as testing dice, why not? Unless you are a masochist no one likes to be punished every game. Saves are the one thing you have that it all relies on those dice being truly random. With To-Hits and Wounds there is a sliding scale that helps, but with saves there is only the save and that's it.

Personally I wouldn't pay money just to make my dice more random. A bunch of normal dice is good enough for me and I refuse to believe any statement that it is 'cheating' because I did not spend an extra 40 bucks on dice.

Right so now 40k is like mtg where everything must be standardised and regulated and we play for 1000's of $£€¥ in prizes and its ALL SO SERIOUS!

Also if someone was rolling each cover save individualy I'd be suspect. MASS DICE ROLLING!

Phototoxin wrote:Right so now 40k is like mtg where everything must be standardised and regulated and we play for 1000's of $£€¥ in prizes and its ALL SO SERIOUS!

Also if someone was rolling each cover save individualy I'd be suspect. MASS DICE ROLLING!

For reference, we got to this post from here:

oni wrote:I'd like to buy some precision dice. I know GameScience seems to be the place to go, but they don't seem to have what I want. All I'm looking for are some white and black opaque dice with pips and no bigger than 1/2". I've looked at Backgammon dice, but can bring myself to spend $10 for a single D6. Any ideas?

I don't want to say the 40k community has more than its fair share of whiny babies who panic whenever anyone does anything that they themselves don't do, but... it does.

Phloop wrote:Back to the original question: Oni, you live in the states, yeah? I heard Vegas casinos only use their dice for like, 3 hours before they chuck them. Can't you find a site that sells second-hand casino dice? Surely they must be producing these things at a prodigious rate...

Casino dice are HUGE (3/4") and I'm looking for something small (no larger than 1/2") plus they're just as expensive as the backgammon dice.


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hungryp wrote:

Phloop wrote:Back to the original question: Oni, you live in the states, yeah? I heard Vegas casinos only use their dice for like, 3 hours before they chuck them. Can't you find a site that sells second-hand casino dice? Surely they must be producing these things at a prodigious rate...

Not a bad idea if you could find them, but could be hard to get. Put simply, casinos wouldn't want exact copies of their dice rolling around (pun only kinda intended ) all over town. Same with cards, you can get the slightly used casino decks, but they punch them so they can't be slipped into play at the table without being spotted. At least that's they way it goes around these parts.

Retired casino dice have a hole drilled through the middle so they can not be reused.

You can ignore what I say all you like, or extrapolate it to the extremes of MTG, but I'm just trying to make it fair. If I'm playing with a set of Chessex dice that I enjoy playing with, and you're playing with another set of dice that you've tried and tested to ensure they roll closer or better than average, then how am I going to enjoy the game when I can't kill anything and all my stuff dies?

And I can completely understand that Krak is a good opponent to play with. And I'm not putting you in the same group as serious cheaters (using loaded dice ro whatever) but I still wouldn't find it fun if every time I played you I got wiped off the table because you always rolled better than me. Hence the one set of dice between players. Or a tournament set of dice supplied by the organisers.

Oshova

Oshova wrote:You can ignore what I say all you like, or extrapolate it to the extremes of MTG, but I'm just trying to make it fair. If I'm playing with a set of Chessex dice that I enjoy playing with, and you're playing with another set of dice that you've tried and tested to ensure they roll closer or better than average, then how am I going to enjoy the game when I can't kill anything and all my stuff dies?

If someone is playing with dice that mathematically roll each result 1/6th of the time because they did their research and found actual dice, and you're playing with cheap dice that are uneven (and thus cheating), you're mad because someone else went through the trouble not to cheat?

I... don't even know what to say. The closest analogy I can think of is that there's a person who went through time and effort to make sure every single model is WYSIWYG and you are fielding a pile of counts-as crap, and you start complaining he has an unfair advantage because he can look at his models to see what weapons he can fire, whereas you keep forgetting about all your non-modeled pintle mounted bolters and sponsons and stuff.

I wouldn't say Chessex or GW dice are cheap. And how can I be cheating if I didn't know about the statistcally low rolling of said dice?

Also using WYSIWYG models is a part of the rules. Whereas using cheap dice isn't. So I'm not going to spend a lot of money on 'perfect' dice, when I can buy lovely looking dice that to the naked eye look fine, and roll fine.

Oshova

RisingPhoenix, you seem to have something against Stelek- which is fine, a lot of people do. However, it's not on-topic here. No one has mentioned his name apart from you, as far as I can tell, and I personally have never read his blog and didn't even know he had an opinion about dice. So, you're off-base there... you seem to be reacting against something none of us have said.

Secondly, I'm not sure where you're getting your percentages from. The site you linked to is simply a site that sells backgammon dice. Interestingly, these are rounded edge dice as well. They do, however, have the pips filled in rather than drilled, making them perfectly weighted.

Thirdly, my point stands about randomly rounded dice being skewed towards random numbers. Anyone can tell you that they have found dice that roll particularly high or low. I'm not proud of it, but in high school I bought a bag of Chessex "Pound o' Dice" and found two that rolled particularly low. We used them for Axis and Allies where 1's are favorable. Of course, everyone was using them, but still- it was picking a dice based on it not rolling average.

Perhaps I will test my cube of GW dice to prove my point. Honestly, from what I've seen, and everyone I've gamed against as well, they roll high. I've stopped using them. My point wasn't that chessex (or any mass-produced dice) roll perfectly average. My point was that they can be skewed towards any number with an equal likelihood. My particular cube of dice rolled high. Others, roll low. However, the only ones you're going to hear about on the net are the ones that roll low.

It's not a crime to be skeptical of and question research, is it? I've said before that I don't really believe the science behind that article, and in your post you've listed percentages with nothing to support them, other than a site that sells dice and makes no mention of testing or percentages.

It's OK to disagree, but really, you need to back up what you are saying... as does our side of the argument, which is why I may test my cube of dice to demonstrate what I'm talking about (as I'm really sick of that article coming up every time we have this conversation on Dakka... meaning about every month )

Again, not sure why you're so worked up about this... people are entitled to disagree with you and believe that mass produced dice don't magically favor "1's" over other surfaces. It seems a little too nefarious to be true, imho, and from my experience a mass-produced item is much more likely to be randomly off than to favor one particular side over another.

As always, just my $0.02!

Be a REAL tfg, go get yourself a frictionless vacuum and roll your fresh-out-the-foil vegas dice in that!

RiTides wrote:RisingPhoenix, you seem to have something against Stelek- which is fine, a lot of people do. However, it's not on-topic here. No one has mentioned his name apart from you, as far as I can tell, and I personally have never read his blog and didn't even know he had an opinion about dice. So, you're off-base there... you seem to be reacting against something none of us have said.

Secondly, I'm not sure where you're getting your percentages from. The site you linked to is simply a site that sells backgammon dice. Interestingly, these are rounded edge dice as well. They do, however, have the pips filled in rather than drilled, making them perfectly weighted.

Thirdly, my point stands about randomly rounded dice being skewed towards random numbers. Anyone can tell you that they have found dice that roll particularly high or low. I'm not proud of it, but in high school I bought a bag of Chessex "Pound o' Dice" and found two that rolled particularly low. We used them for Axis and Allies where 1's are favorable. Of course, everyone was using them, but still- it was picking a dice based on it not rolling average.

Perhaps I will test my cube of GW dice to prove my point. Honestly, from what I've seen, and everyone I've gamed against as well, they roll high. I've stopped using them. My point wasn't that chessex (or any mass-produced dice) roll perfectly average. My point was that they can be skewed towards any number with an equal likelihood. My particular cube of dice rolled high. Others, roll low. However, the only ones you're going to hear about on the net are the ones that roll low.

It's not a crime to be skeptical of and question research, is it? I've said before that I don't really believe the science behind that article, and in your post you've listed percentages with nothing to support them, other than a site that sells dice and makes no mention of testing or percentages.

It's OK to disagree, but really, you need to back up what you are saying... as does our side of the argument, which is why I may test my cube of dice to demonstrate what I'm talking about (as I'm really sick of that article coming up every time we have this conversation on Dakka... meaning about every month )

Again, not sure why you're so worked up about this... people are entitled to disagree with you and believe that mass produced dice don't magically favor "1's" over other surfaces. It seems a little too nefarious to be true, imho, and from my experience a mass-produced item is much more likely to be randomly off than to favor one particular side over another.

As always, just my $0.02!

1) You don't read Stelek, you talk about 'research' and 'background' and somehow you echo his stupid, misguided opinions to the letter? The thing about that is, people don't actually reach dumb conclusions this way. Your conclusions are the same as his, you are using the same logic, and it's dumb for the exact reasons I laid out. The logic is too torturous and silly for two people to follow it independently. This isn't about Stelek? Fine. Support your statements using your own logic, not Stelek proxy bs.

2) The percentages are from basic math. Anyone can calculate them, given the number of trials. Fire up Excel, I gave you all the data sources I used, you'll discover that I rounded to 2 sig figs, and everything is exactly accurate. There is no chance at all that the results reached were reached because of 'dumb luck' as you put it. I have a better shot of winning the lottery today than I would of duplicating those results with dumb luck - a MUCH better shot. Standard devs on 1000 iterations is SQRT(N*P*(1-P)), this is obviously 11.8 for 1000 iterations, which is 1.18% on 16.6%. 29% is quite a bit too many standard devs. Maybe you used 50%? But that would still produce 16, which is still 1.6% and that's the coin flip worse case for deviations, and anyway dice have more than two sides, it would be a silly mistake

3) They do tend to be randomly skewed on rock tumblers. But the small dice are skewed because of the material hollowed out for the pips - which is consistent (all 6s have 6 pips, 3s have 3 pips, etc.). Large dice are too, but the pips are a lower percentage of the mass.

Oshova wrote:

Krak_kirby wrote:No, I did not pick the ones that rolled highest on more than average. I compared half a cube (18) of chessex dice to 18 koplow dice, and the koplow dice rolled better, so now I play with koplow dice. I did not buy large amounts of koplow dice and roll each one till I could cherry pick the high rollers, I simply bought several different colors of koplow and I use them all. If that sounds like cheating to you, you are welcome to your opinion. You should consider your words before you accuse someone directly or by inference of being a cheat or a liar. Please don't put me in with the crowd that loads dice, microwaves them, fast rolls, picks up successful rolls instead of fails, adds extra movement, or anything else that actually is cheating.

So you got two sets of dice, rolled them 1000 times. Then picked the ones that rolled better? I'm sorry but the only difference between doing that and doing it with 1000s of dice is just a matter of scale. Obviously the ways of cheating you mentioned are more obvious, and seen as 'worse' ways of cheating. But in my view, what you did is still cheating. Again it's just a matter of scale.

Oshova

The way I understood it is that he was choosing the dice that rolled more randomly.

That is what dice are supposed to do.

Dice which roll less randomly are "worse".




Automatically Appended Next Post:

RisingPhoenix wrote:

RiTides wrote:Again, I just don't really trust that article.

I'm open to being proved wrong, but I've read it and think the "science" used left quite a bit to be desired...

That explanation certainly could be true, but if I rolled thousands of dice, I'd be more shocked if I actually got completely even (16.6%) results for each face.

If it's random, shouldn't some faces end up with higher percentages? You can do a much smaller scale test and get very skewed results... how many dice do you need to roll until you get the "perfect" random result?

Imho, if the result is "perfectly random" then it's no longer random at least as far as the realm of rolling dice.

Just my $0.02, of course!

Randomness is reasonably predictable.

In a trial of 1,000 rolls, if a number varies by more than 23 off the expected mean of 167 (144-190, 14%-19%) then you can say with 97.5% confidence that the dice are flawed.

For the result to be 29% you can say with much greater accuracy than 99.9999% confidence that the dice are not 1/6th per side. The degree to which you can say this, if the trial was well-performed, is staggering. 24% would assure any reasonable person that the dice were very bad. 29% is ridiculous.


At the 36,000 roll level they did for testing pip variance, the result of 19% also reveals nonrandomness at 99.7%+ confidence


These dice should have a variance of well under 1%: http://www.michellibackgammon.com/dice.php

The suspicion towards the article is more because it is not listed in the literature, only mentioned on a few wargame forums, than because of the accuracy of the maths.

Another area of probability research is in the shuffling of cards. There are several respected papers in this area, which can be referenced, so the claims made in them are far from outlandish or unbelievable.

The thing about maths is you can work it both ways. It would be easy to work backwards from the confidence limits to a set of deliberately skewed results.

I am not saying that is what happened.

For me, the fact that casinos, who trade many millions of dollars a year on their dice, use precision dice, confirms that the non-precision dice are not fully random.

As other people have pointed out, there are various ways to roll dice properly -- dice cups and towers, for example.

If a set of dice is genuinely not random, the unfairness can be mitigated by having both players use the set.

RisingPhoenix, not really sure what you're getting at...

You're talking about points I've never made. Regardless of your (rather amusing) assertion otherwise, I haven't read Stelek's blog. Do a search on my posts on Dakka and you can easily see my take on him. You're beating your head against a brick wall, here...

I also never used the phrase "dumb luck"... and the percentages I was referring to were the 97.5% / 99.999% that you included in your previous post (as the chances that the dice were unbalanced).

I also was referring to the randomly rounded edges since that's what we'd been talking about...

Anyway, a good thing from this thread is it has gotten my curiosity up to check the data in that article. I actually just found a sweet 24-compartment container at work which I'm going to borrow and try out my dice in. Will post up the results here... in a less charged thread, hopefully!