Question for the math nerds re: 3d6

[Pielorinho]

So I have a question for the math nerds. Let's say I roll 3d6 29 times. What are the chances that none of those rolls will be less than 8?

(I was teaching a lesson on probability to some fourth graders, focusing on medians and modes of different data sets; the group rolling 3d6 gave me these results, which smell fishy to me).

Daniel

 

[MerricB]

So I have a question for the math nerds. Let's say I roll 3d6 29 times. What are the chances that none of those rolls will be less than 8?

(I was teaching a lesson on probability to some fourth graders, focusing on medians and modes of different data sets; the group rolling 3d6 gave me these results, which smell fishy to me).

The chance of rolling 7 or less on one 3d6 roll is 35/216. or 16.2%
The chance of rolling 8 or more on one 3d6 roll is 181/216 or 83.8%
The chance of rolling 8 or more on 29 3d6 rolls is (181/216)^29 = 0.59% or 1 in 169
The chance of not rolling 7 or less on 29 3d6 rolls is the same: 0.59% or 1 in 169.

Cheers!

 

[Crothian]

This is fast, so I may be off. My way of doing it might be wrong to, it's been a while. Chances of rolling 8 or higher is 181/216

For that to happen 29 times we multiple that by itself 29 times which is about .6%

Now for others to do it and see if I actually did it right.

 

[Pielorinho]

Awesome--thanks! I'll probably find a dice simulator and show them the difference between their results and expected results.

Daniel

 

[MerricB]

(I was teaching a lesson on probability to some fourth graders, focusing on medians and modes of different data sets; the group rolling 3d6 gave me these results, which smell fishy to me).

I would advise you to immediately use those fourth graders to roll up the stats of your next character.

My knowledge of probability and statistics is quite limited, but I've spent a lot of time working out dice probabilities for some reason...

Cheers!

 

[LiquidBlue]

Just remember at these probabilities you can expect to see such results about once every 169 times you run this demonstration.

 

[Crothian]

(I was teaching a lesson on probability to some fourth graders, focusing on medians and modes of different data sets; the group rolling 3d6 gave me these results, which smell fishy to me).

How many groups did you have doing this? 1/169 is the odds of one group doing it. If you have more then one group the chances of it happening once increase.

 

[Pielorinho]

How many groups did you have doing this? 1/169 is the odds of one group doing it. If you have more then one group the chances of it happening once increase.

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

 

[Vrecknidj]

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

Dave

 

[The Lost Muse]

And, unfortunately, bell curves are an ideal abstraction, not what you'll actually get most of the time.