Dice math help?

[Grod_The_Giant]

Can anyone help me find dice combinations that will give me a bell curve around 15? Preferably with a maximum result of less than 25?

[Lord Torath]

How much of a Bell do you want?

6d4 has an average of 15, max of 24, and with six dice will have a pretty good curve.
4d6 has an average of 13 14, but you could add two one to it for a less 'curved' bell curve that averages 15, but and puts the max up to 26 25.

More dice results in more common 'middle' results and less common 'end' results.

[Satinavian]

How much of a Bell do you want?

6d4 has an average of 15, max of 24, and with six dice will have a pretty good curve.
4d6 has an average of 13, but you could add two to it for a less 'curved' bell curve that averages 15, but puts the max up to 26.

More dice results in more common 'middle' results and less common 'end' results.
4d6 averages to 14, not 13.


So yes, i would recommend 4d6+1, which has an average of 15 and a span from 5-25. The extreme ends have a probability of 1/1296 or slightly less than a tenth percent.

If the span is too much, you could do 4d4+5, also with an average of 15 and a range of 9-21.

[Lord Torath]

4d6 has an average of 134d6 averages to 14, not 13.:redface:

Whoops. Good catch! I think I somehow turned 4d6 into 2d12, which are obviously not the same.

[SpyOne]

If you want something steeper, there's 3d8+1, though that has an average of 14.5.

Or we can get really crazy and start mixing dice. 2d8 + 2d4 +1 has an average of 15 and a max of 25, but a much weirder curve.

Or we could have no curve at all: 1d20 + 5.

I think the weird combos need to get used a lot more, but YMMV.

[Stonehead]

Are you cool with static bonuses? Mathematically, as was pointed out earlier, 6d4 gives you exactly what you're looking for. Personally I don't like d4s though, because they're harder to roll than the other dice, and I don't think everyone has 6 of them laying around.

3d8 gets you kinda close (13.5). 4d6 is better (14.0) and everyone and their mother has enough d6s for each player to have 4.

If you're cool with mixing dice, 3d6+1d8 averages 15 exactly, and ranges from 4 to 26. 1d8+3d6 is my favorite, because it fits the mathematical constraints, and everyone is going to have enough dice for it. It's also fun to roll a bunch of different dice.

[Grod_The_Giant]

Are you cool with static bonuses?
In this case, no-- there will be other static bonuses added to the total, so I'd rather not make people roll, say, (3d4+4)+7.

It sounds like the best candidates for single die types are 6d4, 4d6, and 3d8. For mixed dice, we've got 3d6+1d8, 2d6+2d4... any other candidates?

[Socksy]

In this case, no-- there will be other static bonuses added to the total, so I'd rather not make people roll, say, (3d4+4)+7.

It sounds like the best candidates for single die types are 6d4, 4d6, and 3d8. For mixed dice, we've got 3d6+1d8, 2d6+2d4... any other candidates?

From silliest to least silly:

Do your dice have to have discrete integer values on them?

If you're using a dice bot to generate them, own a handful of d5, or you don't mind halving a d10 and rounding up, 5d5 would be a great candidate for a symmetrical bell curve with an average of 15 and a maximum of 25.

2d6+2d4 has an average of 12, so won't be much use to you. I think the suggestion was 2d8+2d4+1. If you don't want a +1, you could instead roll d10+d8+2d4, although that could go up to 26.

Edit: You could also use a table and assign probabilities yourself, then roll d1000. So for example, if you wanted it to be, the chance of getting a 15 could be 100/1000, but the chance of getting a 1 could be 1/1000. As long as your probabilities add up to 1, you're good.

[Khedrac]

if you want silly remember you can use negative dice.

For example, 1d4 - 1d4 has a maximum of 3 but an average of 0

So 5d4+1d6-1d4 is max 25 average 13.5

[Socksy]

if you want silly remember you can use negative dice.

For example, 1d4 - 1d4 has a maximum of 3 but an average of 0

So 5d4+1d6-1d4 is max 25 average 13.5

Can I steal this for educational purposes? I have some students who love cancelling things which cannot cancel.

The worst I've had would probably be "d/dx cancels to 1/x" from someone who really should have known better.

[Khedrac]

Can I steal this for educational purposes? I have some students who love cancelling things which cannot cancel.

The worst I've had would probably be "d/dx cancels to 1/x" from someone who really should have known better.

Be my guest. it's fun when people actually manage to get their brains undestanding maths.

Probablility is one of the classics - it is simple and logical, but unless you have been taught the basics everyone gets it wrong.
(I admit it is decades since I did anything complex so I cannot rememebr how the harder stuff works, but at least I still understand the basics.)

[Telok]

The worst I've had would probably be "d/dx cancels to 1/x" from someone who really should have known better.

You owe me a piece of cheese. Its been at least five years since I dealt with a derivative and that made me drop my cheese.

[Thane of Fife]

How about 9dF to get a distance from 15?

That is, fudge dice, each marked with two minus signs, two blank sides, and two plus signs.

[Stonehead]

While we're talking silly, 1d20+1d8 hasn't been mentioned yet. The bell curve is noticeably flattened, but it does average 15 exactly. If you just look at the average value for each die (1d4:2.5 1d6:3.5 1d8:4.5 1d10:5.5 1d12:6.5 1d20:10.5) it's pretty easy to put together all the different combinations.

Personally, I think 4d6 or maybe 3d6+1d8 are your best bet, depending on how important averaging exactly 15 is. Do we get to know what this is for, or is that a secret?

[Socksy]

While we're talking silly, 1d20+1d8 hasn't been mentioned yet. The bell curve is noticeably flattened, but it does average 15 exactly. If you just look at the average value for each die (1d4:2.5 1d6:3.5 1d8:4.5 1d10:5.5 1d12:6.5 1d20:10.5) it's pretty easy to put together all the different combinations.

Personally, I think 4d6 or maybe 3d6+1d8 are your best bet, depending on how important averaging exactly 15 is. Do we get to know what this is for, or is that a secret?

We can't have the top of the distribution go above 25, though.

[Grod_The_Giant]

While we're talking silly, 1d20+1d8 hasn't been mentioned yet. The bell curve is noticeably flattened, but it does average 15 exactly. If you just look at the average value for each die (1d4:2.5 1d6:3.5 1d8:4.5 1d10:5.5 1d12:6.5 1d20:10.5) it's pretty easy to put together all the different combinations.

Personally, I think 4d6 or maybe 3d6+1d8 are your best bet, depending on how important averaging exactly 15 is. Do we get to know what this is for, or is that a secret?
A variant/spinoff rule for this insane project (https://forums.giantitp.com/showthread.php?641560-Behold-I-give-you-the-d20-Exalted-it-is-the-lightning-it-is-the-madness)-- a giant system hack built from M&M 3e rules. In the original project I used hit points, but I'd like to bring back a simplified version of M&M's Toughness save mechanic as an optional thing.

Rolling 1d20+[damage] against [Toughness+5] and counting degrees of success is roughly equivalent to rolling 1d20+[Toughness] against [Damage+15] and counting degrees of failure, which is a variant I've used extensively. But for this, I'd like the roll to be against [Toughness+10], to keep things consistent with everything else in the system. Since I already was using different d20-equivilents for different weapon types, I thought simply shifting them to a d25-equivilent would be the most graceful solution.


We can't have the top of the distribution go above 25, though.
A bit above or below is okay. I'd rather have a nice clean set of damage dice than be super-precise.

[Lvl 2 Expert]

We can't have the top of the distribution go above 25, though.

Which I think demonstrates the main "problem" of this question well. Assuming we're only adding up several different dice and not using any dice with a distribution other than 1, 2, ..., x, then to have an average of exactly 15 and a maximum of exactly 25 you need to use 5 dice, which also gives you a minimum roll of 5. Then to actually fit those parameters perfectly you'll have to use 5 dice whose top values add up to 25, which isn't really possible with standard dice since those all have an even number of sides, so given that a maximum below 25 was also fine we'll have to settle with using 6 dice whose top values add up to 24, the easiest solution being the 6d4 given earlier. This gives a pretty steep curve with almost 96% of all results falling between 10 and 20. That's all good and well from a simulationist standpoint, but for a game I'd argue that both using less dice in itself ánd a less steep curve usually make for more fun.

I really shouldn't be one to speak here, because I myself have worked on a d3 system that included "half dice" and even "quarter dice" (custom d6's with different numbers on them, including 0). This gave great curves, I just don't think it was a realistic idea for a game.

All in all, I think OP is probably better off using a two or three dice system, allowing either the average to drop a bit lower then 15 (say 3d8, minimum 3 average 13.5 maximum 24) or allowing the maximum to go over 24. (like 1d20+1d8, minimum 2, average 15, maximum 28). Try a bunch of them out on anydice.com or in model them in Excel, see what looks good.

[Stonehead]

Which I think demonstrates the main "problem" of this question well. Assuming we're only adding up several different dice and not using any dice with a distribution other than 1, 2, ..., x, then to have an average of exactly 15 and a maximum of exactly 25 you need to use 5 dice, which also gives you a minimum roll of 5. Then to actually fit those parameters perfectly you'll have to use 5 dice whose top values add up to 25, which isn't really possible with standard dice since those all have an even number of sides, so given that a maximum below 25 was also fine we'll have to settle with using 6 dice whose top values add up to 24, the easiest solution being the 6d4 given earlier. This gives a pretty steep curve with almost 96% of all results falling between 10 and 20. That's all good and well from a simulationist standpoint, but for a game I'd argue that both using less dice in itself ánd a less steep curve usually make for more fun.

I really shouldn't be one to speak here, because I myself have worked on a d3 system that included "half dice" and even "quarter dice" (custom d6's with different numbers on them, including 0). This gave great curves, I just don't think it was a realistic idea for a game.

All in all, I think OP is probably better off using a two or three dice system, allowing either the average to drop a bit lower then 15 (say 3d8, minimum 3 average 13.5 maximum 24) or allowing the maximum to go over 24. (like 1d20+1d8, minimum 2, average 15, maximum 28). Try a bunch of them out on anydice.com or in model them in Excel, see what looks good.



A bit above or below is okay. I'd rather have a nice clean set of damage dice than be super-precise.

OP said the center and range was a guideline, rather than an absolute mathematical necessity.

And bell curve vs flat distribution is definitely a preference, rather than one just being more fun than the other. I personally think it's incredibly unfun to fail 1 in 5 checks in a skill the character hard specced into, and they're supposed to be experts at in-fiction. 3d6 vs 1d20 is about consistency vs unpredictability, not realism vs fun.

[ross]

10d2
minimum post lengths are dumb

[Lvl 2 Expert]

And bell curve vs flat distribution is definitely a preference, rather than one just being more fun than the other. I personally think it's incredibly unfun to fail 1 in 5 checks in a skill the character hard specced into, and they're supposed to be experts at in-fiction. 3d6 vs 1d20 is about consistency vs unpredictability, not realism vs fun.

Sure, but 3d6 is not 6d4. I actually advocated for "a two or three dice system" in that post.

And if you are going to use something like 6d4 I'd probably prefer a dice pool system, where you only throw and add a lot of dice for the skills you're actually good at. Because for those rolls it sort of makes sense to both want to put in the extra work for the roll and get the stat distribution that sorta mostly prevents easy failures.

[Stonehead]

Sure, but 3d6 is not 6d4. I actually advocated for "a two or three dice system" in that post.

And is you are going to use something like 6d4 I'd probably prefer a dice pool system, where you only throw and add a lot of dice for the skills you're actually good at. Because for those rolls it sort of makes sense to both want to put in the extra work for the roll and get the stat distribution that sorta mostly prevents easy failures.

True, 6d4 is noticeably steeper than 4d6, I'd still argue it's just more consistency though. I don't like it because how many people have 6 d4s for each player? It's not that different than Fate's 4 fudge dice though, and a lot of people like that game.

Now that I'm thinking about it, a dice pool system is basically nd2-n. Although it's slightly different if the number that separates successes from failures can change.