Question for the math nerds re: 3d6

[Whisper72]

The odds depend entirely upon whether the person rolling the 29 rolls is lucky or unlucky, as all seasoned D&D players know.

Dave

On top of that, it matters whether you use your own dice, or those of someone else....

 

[Nadaka]

That's a pretty good point, actually. I had nine groups rolling dice. I love you guys, because instead of writing out the groups longhand like I had to do for my prof and my classroom teacher, I can tell you there was one group each rolling:
1d6
2d6
3d6
1d8
2d8
3d8
1d10
2d10
3d10

I wanted them to see that the 1dx groups got a random distribution, but that the 2dx and 3dx groups got bell curves. Unfortunately, I only got one beautiful bell curve out of the bunch--the 2d6 group came out exactly right. I want to find a way to convince them that on average, most curves for multiple dx will look like the 2d6 group's curve.

Daniel

keep them rolling. Get a sample space of a few hundred or thousands of rolls and you will see that nice sweet bell curve. That our you could simply plot every possible combination of dice that result in a specific number and that will give you the exact distribution.

 

[Catavarie]

Bah all you got o do is Freeze your dice in a block of ice for 1 month and day and then you'll be a crit rollin fool...trust me I worked for my dice. I'm a players worst nightmare as a DM and a DMs worse nightmare as a player

 

[Umbran]

So I have a question for the math nerds. Let's say I roll 3d6 29 times.

There's your problem right there. Statistical expectations start clearly kicking in when the sample size is large when compared to the number of possible outcomes. There are 18 results, but only 29 in the sample set - that's not even twice, and so certainly not large.

You have 9 groups. Have all of them roll 3d6 twenty times, and pool the results. Then you'll get your bell curve. In addition, you'll probably also get to show that the individual small samples often deviate from expectation, while large samples don't...

 

[Drawmack]

First, statistics do not tell us what will happen on a given event, they tell us what will happen as the occurances of an event approach infinity. So I concure that 29 rolls is not enough as that is not even begning, to begin to approach infinity. There are 18 possible results stemming from 216 combinations. So if you used 3,888 (216 * 18) rolls that would probably be a descent sample set.

Another neat thing you can do is the probably of any given number coming up. This makes a bell curve.

Also on a set as small as 1 or 2 hundred rolls you should be able to trendline the results with a 2nd degree polynomial you should get a bell curve for the trendline eventhough the rolls will be all over the place.

 

[billd91]

There's your problem right there. Statistical expectations start clearly kicking in when the sample size is large when compared to the number of possible outcomes. There are 18 results, but only 29 in the sample set - that's not even twice, and so certainly not large.

You have 9 groups. Have all of them roll 3d6 twenty times, and pool the results. Then you'll get your bell curve. In addition, you'll probably also get to show that the individual small samples often deviate from expectation, while large samples don't...

And if you build on the original 29 trials, you can show them how increased numbers of trials will tend to push the distribution toward the bell curve.

 

[orsal]

I wanted them to see that the 1dx groups got a random distribution,

I'm assuming that by "random" you mean "uniform". All of the distributions are random.

but that the 2dx and 3dx groups got bell curves. Unfortunately, I only got one beautiful bell curve out of the bunch--the 2d6 group came out exactly right.

Not quite. 2d6 will give you a pyramidal distribution -- if you roll them enough times (29 is not enough) and graph the results, you should see something close to two striaght lines, sloping up to the peak at 7, and then down. It's only with 3 dice that you start seeing the bell features (curved, dome at the top and tapering off at the ends), and the more dice you use, the closer you get to the normal distribution (which is the technical name for *THE* bell curve, as opposed to *A* bell or bell-like curve).