Some random d20 that rolls tons of 20s. True?

[randomhero00]

Or is it kind of an urban myth.

The myth: I hear of people buying those grab bags of dice for cheap and then rolling each a ton of times to see which roll the best. And every once in a while someone will find the "perfect" d20 that rolls 20 about 40% of the time and almost never lands on 1.

So is that fake or fact?

PS I am NOT talking about weighted dice. Talking about although cheap, legit dice.

[valadil]

Doubtful, but I've got a dicebag full of "perfect 2" d20s.

[RndmNumGen]

Though I expect people find dice like these every now and then, they're not a 'perfect' d20 in any way; rather, they are accidentally 'weighted' or perhaps have one side that is larger than the other. In this case, the dice is no more legit that buying a weighted one would be, as the only difference is the way the die was obtained.

[Tyndmyr]

Cheap dice are often substantially non-random. I once did a very large statistical study(tens of thousands of rolls, IIRC) on games workshop D6s to prove that they were highly biased. Crappy manufacturing led to air pockets in the dice.

If you've got patience, you can find the ones that happen to be biased in certain ways. It does work. It would be unlikely to find one biased enough to roll 20s 40% of the time though. That kind of bias would require noticeable differences in weight or corner rounding.

[randomhero00]

You know its sad I may do this...not to cheat, just to collect them...and because I like rolling dice that much

[Tyndmyr]

You know its sad I may do this...not to cheat, just to collect them...and because I like rolling dice that much

Meh, not sad at all.

The guy who does it to cheat comes across as more sad than the guy who just likes dice, IMO.

[Sillycomic]

This will explain why some dice roll 20's more often than others.

http://www.youtube.com/watch?v=bR2fxoNHIuU

That being said, I bought some Game Science dice and they are awesome. They're random, but awesome.

[Binks]

Or is it kind of an urban myth.

The myth: I hear of people buying those grab bags of dice for cheap and then rolling each a ton of times to see which roll the best. And every once in a while someone will find the "perfect" d20 that rolls 20 about 40% of the time and almost never lands on 1.

So is that fake or fact?

PS I am NOT talking about weighted dice. Talking about although cheap, legit dice.

Yes, you are talking about weighted dice. Weighted means the die isn't statistically average, and any d20 that hits a certain number more than 1/20 times isn't statistically average and is weighted.

As for finding one, that I don't know. There are plenty of statistical methods you can use to analyze a die, but I don't know of any way to divine how it'll roll beforehand. That said it's as others have said, the cheaper the better, as higher quality dice tend to be more statistically average.

[dsmiles]

I recently bought a set of steampunk-themed dice, and the d20 seems to roll an inordinate number of 20s. I just hope I'm not using them all up.

[Delwugor]

Our old AD&D GM had a d6 he always used for initiative and it was always rolling 5s and 6s. We mention the die was biased. Next week he shows up with a sheet of 300 rolls fairly even distribution. We don't quite believe it and make him roll it 100 times again nice and even. Then we play and he rolled 6 for all 3 initiatives that night, we mentioned stealing that die after that.

[Shyftir]

I have a d20 that seems to roll a 17 slightly more often than other numbers. I value it highly...

[The Dark Fiddler]

Our old AD&D GM had a d6 he always used for initiative and it was always rolling 5s and 6s. We mention the die was biased. Next week he shows up with a sheet of 300 rolls fairly even distribution. We don't quite believe it and make him roll it 100 times again nice and even. Then we play and he rolled 6 for all 3 initiatives that night, we mentioned stealing that die after that.

That sounds more like proper rolling technique than a biased die. That way he can roll high when he wants, and roll random when he needs to prove the die isn't rigged.

Not to accuse him or anything.

[Seb Wiers]

As for finding one, that I don't know. There are plenty of statistical methods you can use to analyze a die, but I don't know of any way to divine how it'll roll beforehand. That said it's as others have said, the cheaper the better, as higher quality dice tend to be more statistically average.

With a 20 sided die, you are gonna need to make a LOT of rolls to have any statistically valid evidence that a die has a bias- and even then, the bias might not be at all meaningful in terms of game balance Good or bad). Consider rolling a 20 sided die 200 times; you'd expect each side to come up 10 times. If 20 comes up 15 times, does it really mane anything? No, because with that small a sample, you SHOULD get at least one side coming up 50% more often than "normal"!

Also, while cheap dice do tend towards bias, expensive dice often aren't any better.

Anyhow, I chalk 99.9% of "lucky dice" stories up to confirmation bias.

[Delwugor]

That sounds more like proper rolling technique than a biased die. That way he can roll high when he wants, and roll random when he needs to prove the die isn't rigged.

Not to accuse him or anything.

Good point but I knew him for 10 years and he wasn't the cheating type.
My own thinking is that dice are good randomizers ... except when they aren't.

[OracleofWuffing]

Consider rolling a 20 sided die 200 times; you'd expect each side to come up 10 times. If 20 comes up 15 times, does it really mane anything? No, because with that small a sample, you SHOULD get at least one side coming up 50% more often than "normal"!

Oh, hey, there was an XKCD relevant to this!

[The Dark Fiddler]

Also, while cheap dice do tend towards bias, expensive dice often aren't any better.

Well, more expensive dice are usually more expensive for a reason, such as being extra-precise. So if they're just more expensive for no reason, then yeah, not likely to be better, but if they're precision made then they best be better, since that's the whole point.

[Seb Wiers]

Oh, hey, there was an XKCD relevant to this!

Pretty much. Grabbing a few dozen d20's, chucking them around a bunch, and keeping the one that comes up 20 the most is probably even less meaningful.

Wish I knew how to do the math to figure out how many rolls you'd need on each d20 to prove actual bias with a 95% confidence, but my guess is "a hell of a lot".

Well, more expensive dice are usually more expensive for a reason, such as being extra-precise. So if they're just more expensive for no reason, then yeah, not likely to be better, but if they're precision made then they best be better, since that's the whole point.

What you say holds true if you are purchasing casino dice, yes. But afaik there's only ONE manufacturer of rpg gaming dice that puts effort towards making them extra precise (Gamescience).

[Mystic Muse]

How many times should you roll a die to find what numbers it's biased towards?

[The Dark Fiddler]

How many times should you roll a die to find what numbers it's biased towards?

Infinitely.

Or, as many times as you can, really. The more you roll the die, the less likely outside factors (table tilt, rolling technique) are to become a factor. Over 100 at least, if you want a good test, and something where you're supposed to get a nice even number for each side (600 rolls = 100 on each side, hypothetically), should be good as well.

[Solaris]

That sounds more like proper rolling technique than a biased die. That way he can roll high when he wants, and roll random when he needs to prove the die isn't rigged.

Not to accuse him or anything.

My brother does that with pretty much any dice he touches. I've seen him roll a set of six eighteens using 3d6 before.

[Seb Wiers]

How many times should you roll a die to find what numbers it's biased towards?

I can't do the math, but discussions I've seen by those who can say something like 20 x number of sides. If a specific number comes up more than 30 times, there's a good chance its not just due to random variation, and then you should repeat the whole process for that die.

So yeah, for a d20, its a lot of work.

[Volos]

I've tested my DMing and my PCing dice, finding that I only had one die that held a substatial bais. Then I had my friend roll it for me and it turned out that it was that die with my rolling style that made the bais. We tried it on several surfaces, many temperatures, and during different times of day. It seemed that whenever I touched the d20, it wanted to roll high. Whenever he touched it, it rolled low. Then I offered my friend icecream if he completed the last set of rolls, and suddenly his rolls were high. The conclusion? Don't wast a weekend testing your dice.

[manyslayer]

I had a die that rolled an inordinate number of 20s and 1s. Called it the die of death since (using fumbles as well as crits) someone was dieing (even if it was me or an ally).

[Noedig]

Mine is a d6 story, but the it's in the spirit of rolling "nat 20's" if you will. I was playing in my first SR3 game, and came up against a bank vault door that had been welded shut. He called for a strength test, and I rolled my considerable amount of dice. I had one 6 come up, and then proceeded to roll a 6 on that same dice for the next 17 rolls. As a result, I one inch punched the door clean off its hinges.

[Conners]

Well, you do occasionally hear stories about bad luck curses, and places that are unlucky.... I guess it could extend to dice which are lucky/unlucky?

[Vladislav]

Among a large number of random results, you are bound to find one that looks non-random.

For example, if you take about 1000 completely fair coins, and flip each ten times, you will almost certainly find one that will produce ten heads in a row. Why? Statistics.

Same goes for rolling a large number of dice a large number of times. You are bound to get an abnormal number of 20's with one of the dice. Doesn't necessarily mean the die is skewed.

[Tyndmyr]

Rolling hundreds of times is a slow way to test dice.

Instead, drop it in a tall cup of water a few times. If it has significant weight, the heavy side will end up on bottom.

[Jay R]

Rolling hundreds of times is a slow way to test dice.

Instead, drop it in a tall cup of water a few times. If it has significant weight, the heavy side will end up on bottom.

Unfortunately, with most uneven dice, the weight isn't the problem, the differences in the edges is. A rolling die is more likely to stop when the edge it has to roll on next is sharp that when it's rounded, for the same reason that round wheels roll better than square ones.

The way cheap dice are made these days leaves some edges more complete that others, and the water test doesn't catch this.

[Tyndmyr]

Unfortunately, with most uneven dice, the weight isn't the problem, the differences in the edges is. A rolling die is more likely to stop when the edge it has to roll on next is sharp that when it's rounded, for the same reason that round wheels roll better than square ones.

The way cheap dice are made these days leaves some edges more complete that others, and the water test doesn't catch this.

Yeah. That one isn't as obvious, but you can often just feel the corners for any difference.

[Jay R]

How many times should you roll a die to find what numbers it's biased towards?

Wish I knew how to do the math to figure out how many rolls you'd need on each d20 to prove actual bias with a 95% confidence, but my guess is "a hell of a lot".

That depends on how biased the die is. It should be clear that if the die always rolls a twenty, it doesn't take that long to be sure. If it rolls a 20 10% of the time rather than 5% like it ought to, that takes more time.

It also depends on what level of assurance you need. This is called alpha, and is the probability you're willing to accept of mistakenly deciding that a fair die is biased. Let's assume alpha = 5% for now.

The statistical test used is a Chi squared test. If the die rolls a 20 50% of the time, 8 rolls should be enough to convince you of it.

If it rolls a 20 25% of the time, it should take at least 36 rolls.
If it rolls a 20 10% of the time, it should take at least 573 rolls.
If it rolls a 20 8% of the time, it should take roughly 1,600 to find out.
If it rolls a 20 6% of the time, it should take roughly 14,300 to find out.

And remember that "find out" means you're wrong 1 time in 20. This means that using this test, you'll catch (virtually) all the biased dice, but you'll also throw out 5% of all your fair dice. To reduce that to 1 time in 100 would change the results to the following:

If it rolls a 20 50% of the time, it should take at least 10 rolls.
If it rolls a 20 25% of the time, it should take at least 43 rolls.
If it rolls a 20 10% of the time, it should take at least 688 rolls.
If it rolls a 20 8% of the time, it should take roughly 1,912 to find out.
If it rolls a 20 6% of the time, it should take roughly 17,200 to find out.

[These are quick calculations, unchecked, made very roughly. If you want better answers, my billing rate is $100 / hour, and I can complete an excellent report for you in about 4 hours. This one took roughly an hour, done because I felt like it.]

[To calculate these, I made several simplifying assumptions of interest only to other statisticians.]

But afaik there's only ONE manufacturer of rpg gaming dice that puts effort towards making them extra precise (Gamescience).

Correct. The quickest solution to getting the most accurate dice possible is to throw out all non-Gamescience dice, replace everything but 6-siders with Gamescience dice, and replace all 6-siders with casino dice.