Dumb Questions
Re: Dumb Questions
As far as my understanding goes modifiers simply increase a given step.
Is that the case with Flameweapon and similar spells as well or is the additional damage rolled as a separate dice?
Is that the case with Flameweapon and similar spells as well or is the additional damage rolled as a separate dice?

 Posts: 359
 Joined: Mon Nov 28, 2016 12:04 am
Re: Dumb Questions
Two possible rules, both correct. Modifiers either can increase the Step, and you roll that new Step, or they can be added as a flat bonus to the original Step's roll.PiXeL01 wrote:As far as my understanding goes modifiers simply increase a given step.
Is that the case with Flameweapon and similar spells as well or is the additional damage rolled as a separate dice?
However, Flameweapon specifically states it adds an extra D6 to the damage roll, with this bonus damage being fire.
If a spell specifically calls out a "Bonus Die" then it's not a modifier (not in the traditional sense, anyway).The wielder adds a D6 Bonus Die to the fiery weapon’s Damage test.
 The Undying
 Posts: 696
 Joined: Sun Nov 27, 2016 11:25 pm
Re: Dumb Questions
Sr. Rags provided the answer. You'd have to start digging through probability tables, but my gut tells me that an extra die is usually going to provide better results, statistically, versus a Step bonus. However, I really don't think it's insanely meaningful  if your table just treats it as a Step bonus, probably not a huge deal. Keep in mind, you get the same kind of issue with Karma "dice".
Re: Dumb Questions
A d6 is the equivalent to a +4 Step Bonus (d6 is step 4 on the chart).
While it is no longer important, the Flameweapon die used to cause the wielder 1 damage if it's result was greater than 4 (1st ed had a d4 Flame die, so "if it exploded"). This is no longer the case in 4E, but there is an artifact left in the description from the old effect. It is no longer important.
While it is no longer important, the Flameweapon die used to cause the wielder 1 damage if it's result was greater than 4 (1st ed had a d4 Flame die, so "if it exploded"). This is no longer the case in 4E, but there is an artifact left in the description from the old effect. It is no longer important.
Re: Dumb Questions
Personaly I would never put an "=" sign between Karma d6 and +4 Step.
Re: Dumb Questions
Well, for the statistics purpose: I made myself a program for Earthdawn Gamemastering and did a section for statistics. The program really rolls a million rolls with a given step and here are some numbers:
Step 3 / D4 > Average Roll 3.335, highest roll: 45
Step 4 / D6 > Average Roll 4.197, highest roll: 57
Step 5 / D8 > Average Roll 5.143, highest roll: 71
Step 6 / D10 > Average Roll 6.114, highest roll: 59
Step 7 / D12 > Average Roll 7.091, highest roll: 77
Step 8 / 2D6 > Average Roll 8.400, highest roll: 56
Step 15 / D12+2D6 > Average Roll 15.494, highest roll: 87
Step 20 / D20+2D6 > Average Roll 20.394, highest roll: 111
Step 30 / 2D20+2D6 > Average Roll 30.523, highest roll: 142
Step 40 / 2D20+D12+D10+D8 > Average Roll 40.468, highest roll: 162
Step 50 / 3D20+D12+2D8 > Average Roll 50.510, highest roll: 165
Don't spend too much attention to those highest rolls, they differ greatly between several sets of one million rolls. Hope that helps a bit to clarify.
I thought the 'dice explosion' would add much more to the average roll with increasind steps, but the average results always are very close to the step.
Step 3 / D4 > Average Roll 3.335, highest roll: 45
Step 4 / D6 > Average Roll 4.197, highest roll: 57
Step 5 / D8 > Average Roll 5.143, highest roll: 71
Step 6 / D10 > Average Roll 6.114, highest roll: 59
Step 7 / D12 > Average Roll 7.091, highest roll: 77
Step 8 / 2D6 > Average Roll 8.400, highest roll: 56
Step 15 / D12+2D6 > Average Roll 15.494, highest roll: 87
Step 20 / D20+2D6 > Average Roll 20.394, highest roll: 111
Step 30 / 2D20+2D6 > Average Roll 30.523, highest roll: 142
Step 40 / 2D20+D12+D10+D8 > Average Roll 40.468, highest roll: 162
Step 50 / 3D20+D12+2D8 > Average Roll 50.510, highest roll: 165
Don't spend too much attention to those highest rolls, they differ greatly between several sets of one million rolls. Hope that helps a bit to clarify.
I thought the 'dice explosion' would add much more to the average roll with increasind steps, but the average results always are very close to the step.
Re: Dumb Questions
Well you could do a million runs of a million rolls to get the average highest over a million times, that should flatten it out. That's a pretty cool set of numbers though.CPFCPF wrote:Well, for the statistics purpose: I made myself a program for Earthdawn Gamemastering and did a section for statistics. The program really rolls a million rolls with a given step and here are some numbers:
Step 3 / D4 > Average Roll 3.335, highest roll: 45
Step 4 / D6 > Average Roll 4.197, highest roll: 57
Step 5 / D8 > Average Roll 5.143, highest roll: 71
Step 6 / D10 > Average Roll 6.114, highest roll: 59
Step 7 / D12 > Average Roll 7.091, highest roll: 77
Step 8 / 2D6 > Average Roll 8.400, highest roll: 56
Step 15 / D12+2D6 > Average Roll 15.494, highest roll: 87
Step 20 / D20+2D6 > Average Roll 20.394, highest roll: 111
Step 30 / 2D20+2D6 > Average Roll 30.523, highest roll: 142
Step 40 / 2D20+D12+D10+D8 > Average Roll 40.468, highest roll: 162
Step 50 / 3D20+D12+2D8 > Average Roll 50.510, highest roll: 165
Don't spend too much attention to those highest rolls, they differ greatly between several sets of one million rolls. Hope that helps a bit to clarify.
I thought the 'dice explosion' would add much more to the average roll with increasind steps, but the average results always are very close to the step.
Todd Bogenrief
Noble Armada Line Developer, U18 Rules Guru
Noble Armada Line Developer, U18 Rules Guru
Re: Dumb Questions
Well, you could just calculate the expected values exactly...CPFCPF wrote:Well, for the statistics purpose: I made myself a program for Earthdawn Gamemastering and did a section for statistics.
Re: Dumb Questions
Well, tell me how to calculate the expected highest roll?
Re: Dumb Questions
Each die is a convergent infinite series. If algebra isn't your thing, you can set your program to perform the summation to an arbitrary degree of accuracy.CPFCPF wrote:Well, tell me how to calculate the expected highest roll?
EV(D6) = 1*1/6 + 2*1/6 +3*1/6 + 4*1/6 + 5*1/6 + (6+1)*1/36 + (6+2)*1/36 + (6+3)*1/36 + (6+4)*1/36 + (6+5)*1/36 + ...
And if algebra is your thing...
EV(D6) = 15/6 + (15+30)/(6^2) + (15+30*2)/(6^3) + (15+30*3)/(6^4) + ... = sum from n=0 to infinity of (15+30*n)/(6^(n+1)) = 21/5 or 4.2
In general,
EV(Dk) = sum from n=0 to infinity of ((k(k1)/2)+k*(k1)*n)/(k^(n+1)))
And, then for the sum of two Distributions, the Expected Value is conveniently equal to the sum of the Expected Values of the individual dice.
EV(D4)=3.3...
EV(D6)=4.2
EV(D8)=5.142857...
EV(D10)=6.111...
EV(D12)=7.09...
EV(D20)=11.053 (approximately)
EV(Step 15)=7.09...+4.2+4.2=15.491 (approximately)
EV(Step 20)=11.053+4.2+5.142857...=20.396 (approximately)
EV(Step 50)=11.053+11.053+11.053+7.09...+5.142857...+5.142857...=50.535 (approximately)
This is due to the fact that the D4 is the most likely to explode, so even though the larger dice explode with higher numbers, they explode with greatly reduced frequency, which averages out to a lower remainder over the Step number. Exploding the d4 adds .833 to the expected value, whereas exploding the d20 only adds .553. Eventually you will be rolling so many dice that the EV is more than one above the Step, but at that point the dice are so volatile, it doesn't really matter.CPFCPF wrote: I thought the 'dice explosion' would add much more to the average roll with increasind steps, but the average results always are very close to the step.