ATTACK! MCDM's new rpg and removing the to-hit roll


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rmcoen

Adventurer
HAckmaster did exploding dice, but had teh bigger weapons do multiple d4s instead of single big dice. So the greataxe was doing like 3d4 (actually I feel like it did 4d4?), and any individual die could explode - or all of them could! So your 7pt hit might be 1, 2, 4, and the single 4 explodes for a little more damage. But ranged weapons did bigger dice - they didn't explode as often, but when they did, ouch!

Anyway, I'd love to see your system, of course. I like the elegance of smaller-die-weapons exploding more being balanced by larger-die-weapons have more impactful effects. I was just reviewing some shipboard combat rules, for example, and noting that PCs could always outperform the shipmounted ballista in terms of raw ranged damage... but against a DR10 ship, they do nothing and the ballista bolt punches through. Again - lots of little dice vs. single larger attack having its place. [This would work with an armor/DR system too -- a dagger will rip an unarmored person apart with exploding dice, and might hurt the armored person on good hits; the greataxe will punch through the armor every time though.]
 


Does it? It always boils down to roughly 0.6 points more, doesn't it? So 3d6 will be better than 3d4, exploding or not.

I can see wanting say 6d4 over 4d6 (or whatever gets the same average without exploding), but unless you make it up in numbers...

An individual d4 has a 25% chance to roll its max value, while a d6 only has a rough 16% chance to fo so, and it gets lower from there.

And that percent chance should, unless I am completely misunderstanding math (possible, I am an english major not a mathmetist), stay constant no matter how many dice you're rolling.

24 possible options in 6d4 with 6 being the target 4. 6/24 = 25%

Likewise, 36 options on 6d6, 6 being the target 6. 6/36 = 16%

Now granted i believe that only really says thats the chance of getting just one die with max value, but even so, intuitively the less undesired values there are to roll the more likely you are to roll max.

Now possibly there will be edge cases, where say having 6d4 might not actually be better than 2d6 for example, but that might not even be an issue, given theres other factors in weapon choice at play, in particular ones that will ideally integrate with and feedback into the kinds of playstyles a character might want for Momentum play versus raw effects and damage.
 

pemerton

Legend
An individual d4 has a 25% chance to roll its max value, while a d6 only has a rough 16% chance to fo so, and it gets lower from there.
They're infinite series.

For a d4, the expected value is 2.5 + 1/4 * 2.5 + . . . , = 10/3 (= approx 3.3). Exploding is adding just over .8 to the average.

For a d6, the expected value is 3.5 + 1/6 * 3.5 + . . . , =4.2. Exploding is adding exactly .7 to the average.

For a d8, the expected value is 4.5 + 1/8 * 4.5 + . . ., = 36/7 (= approx 5.14). Exploding is adding over .6 to the average.

For a d10, the expected value is 5.5 + 1/10 * 5.5 + . . ., = 55/9 (= approx 6.1). Exploding is adding just over .6 to the average.

For a d12, the expected value is 6.5 + 1/12 * 6.5 + . . ., = 78/11 (= approx 7.1). Exploding is adding just under .6 to the average.

Exploding is interesting in the way that it creates the possibility of low probability unlimited results. But it doesn't really change the balance between dice.
 

They're infinite series.

For a d4, the expected value is 2.5 + 1/4 * 2.5 + . . . , = 10/3 (= approx 3.3). Exploding is adding just over .8 to the average.

For a d6, the expected value is 3.5 + 1/6 * 3.5 + . . . , =4.2. Exploding is adding exactly .7 to the average.

For a d8, the expected value is 4.5 + 1/8 * 4.5 + . . ., = 36/7 (= approx 5.14). Exploding is adding over .6 to the average.

For a d10, the expected value is 5.5 + 1/10 * 5.5 + . . ., = 55/9 (= approx 6.1). Exploding is adding just over .6 to the average.

For a d12, the expected value is 6.5 + 1/12 * 6.5 + . . ., = 78/11 (= approx 7.1). Exploding is adding just under .6 to the average.

Exploding is interesting in the way that it creates the possibility of low probability unlimited results. But it doesn't really change the balance between dice.

Note that by exploding Im referring explicitly to just rolling the max value, not any additional damage rolled or anything like that.
 


Nikosandros

Golden Procrastinator
I thought that by exploding you mean on a 4 on d4, you get to roll again and add, and if that is a 4 you get to roll again and add again. And similarly for the larger dice.

That's what I've calculated.
Yes, that's what is commonly called exploding dice. Interestingly (at least to me), Hackmaster has slight variation. If a N-sided dice explodes, you roll a (N-1)-sided dice for all successive rolls. This avoids a "jump" in the distribution by not skipping "N" as a possible result. With this mechanism, the expected value rises exactly by 0.5 for all values of N.
 
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mamba

Legend
An individual d4 has a 25% chance to roll its max value, while a d6 only has a rough 16% chance to fo so, and it gets lower from there.

And that percent chance should, unless I am completely misunderstanding math (possible, I am an english major not a mathmetist), stay constant no matter how many dice you're rolling.
yes, the chance obviously gets lower, but unless the goal is to just roll the highest number, that does not matter.

Exploding dice means that you roll again when you do roll the maximum number, and that is what evens things out.

Simply put, the chance of rolling the highest number on an n-sided die is 1/n, the average roll is (n + 1) / 2. So your second roll on average is (n + 1) / (2 * n) or an increase of roughly 0.5 over your first roll. Repeat for additional maximum rolls.

This is close to the series (1/2)^x, the sum of that is 1. So no matter what sided dice you use, having it explode increases the average roll by essentially 1. A d4 then has an average of 3.5, a d6 of 4.5 and so on. The increase is essentially constant, the smaller die does not increase the average result more (by much, there is a little bit of rounding here)
 
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but unless the goal is to just roll the highest number

That is precisely the goal. You roll a 4 on a d4, that gives you "Boons" which you can spend to x,y,z.

Obviously not accurate to what exploding dice traditionally do but afaik theres no other term for what Im doing.
 


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