# Why your d20 only rolls low.. explained !

### #22

Posted 28 November 2008 - 09:33 AM

Don't ask me the meaning of life, though, because I haven't got a clue myself.

So it looks like we're all stuffed.

My theory is I'm making you all up in my head because I'm going insane being sensory deprived floating on my own in the void.

But to be honest that probably isn't true.

### #23

Posted 28 November 2008 - 02:31 PM

Believe it or not, I am actually God.

Don't ask me the meaning of life, though, because I haven't got a clue myself.

So it looks like we're all stuffed.

My theory is I'm making you all up in my head because I'm going insane being sensory deprived floating on my own in the void.

We all know you are not God. You sound more like Vladamir Harkonen. And everyone knows the meaning of life is 42. :lol:

### #24

Posted 28 November 2008 - 04:26 PM

You are quite right. He is not Bob. Bob's number on his high school football team was 42--thus the circle is complete. Glad I could explain things to you.We all know you are not God. You sound more like Vladamir Harkonen. And everyone knows the meaning of life is 42. :lol:

Embrace Bob. Be one with Bob. Bob is your friend. The cake is a lie...

:idea:

### #26

Posted 12 May 2009 - 01:36 PM

I have a Gamescience die that players long ago dubbed the 'vorpal die'. Much like a good Gamescience die It has sharp edges and a nub...and rolls 9,10,19 and 20 far too often (chi square test confirmed with 1% significance).

Sorry to dredge this topic, but I thought that more investigation into this topic was needed. I also have a statistics project due for the end of school and this gives me a very good reason to buy really expensive dice. (Thanks for the idea formenel.)

I am going to take 1000 rolls of a d20 with game science dice and use a chi squared goodness of fit test to see if they are random. Then I will use a chi squared test of homogeneity to see if there is a difference between this type of die and a normal 'rounded' and cheaper die. I will post my results here when I finish.

### #27

Posted 12 May 2009 - 03:57 PM

I have a Gamescience die that players long ago dubbed the 'vorpal die'. Much like a good Gamescience die It has sharp edges and a nub...and rolls 9,10,19 and 20 far too often (chi square test confirmed with 1% significance).

Sorry to dredge this topic, but I thought that more investigation into this topic was needed. I also have a statistics project due for the end of school and this gives me a very good reason to buy really expensive dice. (Thanks for the idea formenel.)

I am going to take 1000 rolls of a d20 with game science dice and use a chi squared goodness of fit test to see if they are random. Then I will use a chi squared test of homogeneity to see if there is a difference between this type of die and a normal 'rounded' and cheaper die. I will post my results here when I finish.

How many of each type of die are you using for your test?

### #28

Posted 12 May 2009 - 04:29 PM

The reason I am only doing d20s is because those dice seem like they would have the most problems resulting from being egg shaped.

EDIT:

My first few groups of 1000 rolls are done and the analysis is here:

http://spreadsheets....6Cx_3X4y242XKng

I did a chi square goodness of fit test just for each dice individually to determine if it was random. My alpha level is 5% and two of my dice are much lower than that for the probability value. My Teal chessex dice which is rounded seems to be random though. The probability value or p-value means: this is the probability of this set of data occurring due to sampling variation alone. In other words:

This is the probability that this would happen if the die was truly random. A P-value of 0.07 is good enough for that die to be considered random, but the other two are definitely not random.

No game science dice just yet though, still waiting for them to arrive.

Also, this does not mean that teal chessex dice are random, or that orange chessex dice aren't. It simply means that 1/3 of the 20 sided dice that I have from chessex are random and that isn't even a strong statistic.

### #29

Posted 14 May 2009 - 06:25 AM

You're not the first to think so; but I'm sure you'll enjoy this one:My theory is I'm making you all up in my head...

A man knocks on a door. When the door is opened, he says: "Hello, would you like to donate some money to help starving orphans in the Third World?" And the man who opened the door says: "No thanks, I'm a solipsist."

### #30

Posted 14 May 2009 - 08:15 AM

A broken idea-assuming you had nothing to do in your life- create a sample cumulative probability distribution that shows the likelihood of each die rolling at or above a particular number. Figure out for each number which die has the highest sample probability of exceeding (you could even weight it by expected damage since in D20 crits do more) your target number and then roll that one...

"Hmmm, I need a 13 to hit this Kobold Shamen. Beating a 13 is the purple D20 with gold print...

I believe that is how statisticians roll...

### #31

Posted 14 May 2009 - 12:09 PM

**You Tube**and on the strength of them I invested in two of the smaller set of

**Gamescience**polyhedral dice.

I do think poor initial manufacturing of dice has something to do with the superstitions that role-players have about dice (dice training, unlucky and lucky dies etc.).

Even if they are just as random as other dice – he does say they are made of a higher quality of plastic than other manufactures dice and the crisp edges do mean they stop rolling faster.

I bought the inked

**Gamescience**glow-in-the-dark set and the saffron yellow dice. I don’t think I have the time to roll a d20 a thousand times and compare it to another manufacturer’s dice. But I would be interested to hear the results of anyone else’s experiments. Perhaps it would be simpler just to give Neil of the Bradford Players some of them and see if they make any difference! :lol:

I must admit I’m a sucker for glow-in-the-dark things. And the

**Gamescience**dice were the only glow ones I could find that had plain numbers on. I’ve got about six blocks of glow-in-the-dark

**Fimo**and I’ve still to make up my mind what I’m going to make out of it all!

### #32

Posted 14 May 2009 - 02:00 PM

Gotta love unfair dice. The '20' frequency looks good, but not so much the '1'. Definitely dice to avoid if there are critical failures on a D20.

Well, I'm thinking that since the die has 20 opposite 1 that means that the 20 and 1 are the flat parts of the die and the rest of it is slightly egg shaped causing it to land on one of those two sides or adjacent sides more often than it should. I hope I will get my game science dice soon. I was really surprised by this result though. Maybe chessex does have a problem here. As always, I need more data.

With that data I could easily do that cumulative chart though. Although wouldn't you want a reverse cumulative chart? (Start at 20 and have 1 be 100%.)

EDIT:

I made the tables for the reverse cumulative chart and ... hm... These might prove useful...

I don’t think I have the time to roll a d20 a thousand times and compare it to another manufacturer’s dice.

For some reason that comment bothers me, Sinister...

I guess I have time because it is a stats project and stats requires a lot of data. My first 3000 rolls are linked to in an earlier post on page two of this thread.

I did most of my rolling at school on a flat hard surface next to a computer so I could enter the data immediately. It only took about 5 hours to do, three at a time.

### #33

Posted 14 May 2009 - 05:36 PM

Maybe chessex does have a problem here. As always, I need more data.

With that data I could easily do that cumulative chart though. Although wouldn't you want a reverse cumulative chart? (Start at 20 and have 1 be 100%.)

It does appear that way. However, just as a 'what if" if I were selling dice to D20 users there would be that temptation to engineer dice to roll a 20 somewhat more often than normal as a way to get that dice used by superstitious players and potentially generate more business. As long as no one used nonparametric statistics on the dice rolls then the higher probability would be ascribed to luck...

As far as the distribution, that is what I was trying to say although in a rather confusing way. Find the probability of rolling at or above a certain number so, for instance, rolling at or above 1 is 100%

I do statistics therefore I am, with a 99% probability

### #35

Posted 17 May 2009 - 01:19 PM

For some reason that comment bothers me, Sinister...

I guess I have time because it is a stats project and stats requires a lot of data. My first 3000 rolls are linked to in an earlier post on page two of this thread.

I did most of my rolling at school on a flat hard surface next to a computer so I could enter the data immediately. It only took about 5 hours to do, three at a time.

Sorry, I didn't mean to cause any offense.

I just imagined a gamer with a huge bag of dice just rolling ALL his or her dice just to find out if they had any bias. I suppose I should have taken notice of your use of those impressive terms such as 'reverse cumulative chart', and 'chi square goodness of fit test' and realise it was a scientific investigation. I shouldn't skim read threads...

### #36

Posted 25 May 2009 - 04:10 PM

Sorry, I didn't mean to cause any offense.

Oh, don't worry. You didn't, I will just look at you weirdly from now on as I go and roll all of my dice to figure out which is best for each situation.

And I'm finished with 1000 rolls on three dice and 500 on five others.

There are three dice with 1000 rolls each and three with 500 rolls each are rounded dice and two with 500 rolls each are gamescience dice.

So far only two of the rounded dice are random and four are not.

The Gamescience dice made the smallest chi^2 values causing their p-values to be much, much higher than the rounded dice.

This essentially means that the gamescience dice produced the values on each side of the die more equally than the rounded chessex or D20 dice.

I was very surprised how low a chi^2 value these gamescience dice produced. I guess there may be something to this after all.

My data can be found at http://spreadsheets....0AygOD8xLD_wQSg.

Twenty-sided dice:

Null hypothesis: The dice produce each side randomly with equal weight.

Alternate hypothesis: The dice do not produce random values with equal weight.

To be considered random a dice's p-value must be above my alpha-value of 0.05.

So, final result:

Chessex Brand

2 random dice p-values are 0.070519 and 0.070519.

2 not random dice with p-values very near 0.

D20 Brand (I got them in D&D 3rd Ed. starter kits)

2 not random dice with one p-value very near 0 and one at 0.002384.

Gamescience

2 random dice with p-values of 0.57632 and 0.67851

The Gamescience dice have very high p-values which leads me to believe strongly that they are indeed random.

Oh, ahem sorry.

With a p-value of 0.57632 and 0.67851 we fail to reject the null hypothesis for both these dice. The null hypothesis was that these two dice produce the values of each side evenly or each side has an equal chance of being rolled.

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