Dumb Questions

Discussion on playing Earthdawn. Experiences, stories, and questions related to being a player.
PiXeL01
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Re: Dumb Questions

Post by PiXeL01 » Tue Nov 29, 2016 11:06 pm

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?

Tattered Rags
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Re: Dumb Questions

Post by Tattered Rags » Tue Nov 29, 2016 11:51 pm

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?
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.

However, Flameweapon specifically states it adds an extra D6 to the damage roll, with this bonus damage being fire.
The wielder adds a D6 Bonus Die to the fiery weapon’s Damage test.
If a spell specifically calls out a "Bonus Die" then it's not a modifier (not in the traditional sense, anyway).
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The Undying
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Re: Dumb Questions

Post by The Undying » Wed Nov 30, 2016 12:46 am

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".

Telarus
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Re: Dumb Questions

Post by Telarus » Thu Dec 01, 2016 6:43 am

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.

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Kosmit
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Re: Dumb Questions

Post by Kosmit » Thu Dec 01, 2016 10:20 am

Personaly I would never put an "=" sign between Karma d6 and +4 Step.

CPFCPF
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Re: Dumb Questions

Post by CPFCPF » Thu Dec 01, 2016 11:24 am

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.

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Re: Dumb Questions

Post by Bogie » Thu Dec 01, 2016 1:17 pm

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.
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.
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etherial
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Re: Dumb Questions

Post by etherial » Thu Dec 01, 2016 2:02 pm

CPFCPF wrote:Well, for the statistics purpose: I made myself a program for Earthdawn Gamemastering and did a section for statistics.
Well, you could just calculate the expected values exactly...

CPFCPF
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Re: Dumb Questions

Post by CPFCPF » Thu Dec 01, 2016 4:07 pm

Well, tell me how to calculate the expected highest roll? :roll:

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etherial
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Re: Dumb Questions

Post by etherial » Thu Dec 01, 2016 4:34 pm

CPFCPF wrote:Well, tell me how to calculate the expected highest roll? :roll:
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.

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(k-1)/2)+k*(k-1)*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)
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.
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.

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