Interesting mathematical dice rolling I came across.

Evenglare · Jul 20, 2012

If you roll 3d6 you get an average of 10.5, also if you roll 3d20, and take the middle roll you also get an average of 10.5 . This has no relevance to most people, but some GMs out there may like to know this fact, if you play GURPS or HERO, or use the 3d6 variant for d20 system. They are indeed interchangeable .

This is using an excel sheet which simulated over 100,000 different rolls and averaging the sum of each type of rolling .

prosfilaes · Jul 20, 2012

Evenglare said:
If you roll 3d6 you get an average of 10.5, also if you roll 3d20, and take the middle roll you also get an average of 10.5 .

If you roll 1d20, the average is 10.5, too. I'm pretty sure if you take any nd20 and take the middle one (for odd), or average the middle 2 (for even), or average them all, the average will still be 10.5.

Cor Azer · Jul 20, 2012

Evenglare said:
If you roll 3d6 you get an average of 10.5, also if you roll 3d20, and take the middle roll you also get an average of 10.5 . This has no relevance to most people, but some GMs out there may like to know this fact, if you play GURPS or HERO, or use the 3d6 variant for d20 system. They are indeed interchangeable .

This is using an excel sheet which simulated over 100,000 different rolls and averaging the sum of each type of rolling .

Not really interchangeable.

1. Minimum on 3d6? 3. Minimum on one out of 3d20? 1
2. Maximum on 3d6? 18. Maximum on one out of 3d20? 20
3. Probability of 10.5 on 3d6 or one out of 3d20? Nada.
4. Probabiliy of 10 on one out of 3d20? 1:20. On 3d6? Higher

Essentially, you're missing the whole bell curve thing.

Evenglare · Jul 20, 2012

Cor Azer said:
Not really interchangeable.

1. Minimum on 3d6? 3. Minimum on one out of 3d20? 1
2. Maximum on 3d6? 18. Maximum on one out of 3d20? 20
3. Probability of 10.5 on 3d6 or one out of 3d20? Nada.
4. Probabiliy of 10 on one out of 3d20? 1:20. On 3d6? Higher

Essentially, you're missing the whole bell curve thing.

I respectfully disagree, heres the distribution of 20,000 points with my 3d20 method. Not exactly a bell curve like 3d6, but I do think it is interchangeable. Infact with this method you get the benefit of a bell-like curve with the fact that you do not have to change any numbers when dealing with a d20 system. You can ALSO add some cool additions like take the best of 3 rolls or worst of them, and other things like that.

Argyle King · Jul 20, 2012

I'm not so sure I'd agree that your method is interchangeable with 3d6. Picking to keep one die out of a pool of three (in my opinion) is not interchangeable with rolling three dice and using them to get a bell curve in actual play.

If I were playing a d20 game and wanted to keep a range of numbers which more closely matched a d20, I'd probably go with 2d10.

Evenglare · Jul 20, 2012

Johnny3D3D said:
I'm not so sure I'd agree that your method is interchangeable with 3d6. Picking to keep one die out of a pool of three (in my opinion) is not interchangeable with rolling three dice and using them to get a bell curve in actual play.

If I were playing a d20 game and wanted to keep a range of numbers which more closely matched a d20, I'd probably go with 2d10.

Eh... 2d10 leaves you with a 2-20 value range which would make rolling 1's irrelevant , but of course you could tweak it. I guess it's usable though, it gives a linear pick of numbers unlike the parabola of my 3d20 pick middle and the bell curve. It also favors an 11 over a 10.5 which makes a difference , however slight. Eh, I figured it was interesting information, apparently no one else does though since I have only gotten dissenters replying, anyway here's a pic of all 3, overlayed. 100k data points on each of these now. I probably wont post any more in this topic, since everything that has needed to be said is said.

Dannyalcatraz · Jul 20, 2012

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the Jester · Jul 22, 2012

Did you run fewer trials with 3d6? From your image, it looks like it.

TwoSix · Jul 22, 2012

Evenglare said:
Eh... 2d10 leaves you with a 2-20 value range which would make rolling 1's irrelevant , but of course you could tweak it. I guess it's usable though, it gives a linear pick of numbers unlike the parabola of my 3d20 pick middle and the bell curve. It also favors an 11 over a 10.5 which makes a difference , however slight. Eh, I figured it was interesting information, apparently no one else does though since I have only gotten dissenters replying, anyway here's a pic of all 3, overlayed. 100k data points on each of these now. I probably wont post any more in this topic, since everything that has needed to be said is said.

Not sure why you needed a Monte Carlo simulation of a dice combination that only has 8000 combinations. You can do an exact model.

Interesting mathematical dice rolling I came across.

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