How to do Dice and Damage calculations?

[Biblofilter]

Mage Wars damage dice:
2 blanks
1 normal hits
1 critical hits
2 normal hits
2 critical hits

So if we roll 4 dice we will roll 4 damage on average (2 normal and 2 critical?)

But if i want to know how big is the chance of rolling 5+ damage.

And how do you make calculations when armor is envolved: like to take down a Mana Crystal (2 armor 6hp)
How likely am i to take it Down in how many rounds with
3 dice attack
4 dice attack
5 dice attack
6 dice attack

Most importantly i want to be able to do rough estimates at the table. Any advice/recomendations?

[Schwenkgott]

http://joechip90.batcave.net/MageWars/damCalc.html

[lukard]

It's more complex than that.

In short, if you do not consider armor; then, a die is likely to cause one damage:

Average Damage per Die = {blank, blank, 1normal, 1critical, 2normal, 2critical} = (0+0+1+1+2+2)/6 = 1

However, when you add Armor, Resilient, Incorporeal, Veteran's belt, Piercing, etc; then, the calculation becomes far more complex as you can read here:
http://forum.arcanewonders.com/index.php?topic=13562.msg29141#msg29141

[lukard]

http://joechip90.batcave.net/MageWars/damCalc.html

Cool! I did not see it before

[fas723]

In the link lurkad refers to you can download a printable version of the table (you need Ms Excel though) which answer all your questions and which you can bring to the table when you play.

http://forum.arcanewonders.com/index.php?topic=13562.msg29141#msg29141

[Biblofilter]

Txs all

[echephron]

well this needs a sticky or to be referenced in the sticky. damage calculators rock.

[Sailor Vulcan]

I just started trying to use the damage calculator. Why doesn't it have the option of defenses? I want to calculate the probability of 10+ damage on a 4 dice doublestrike melee+3 piercing 1 attack against an unarmored target with a defense of 7+. It doesn't let me, and I haven't been able to figure out how to do it on my own. Could somebody update this to include defenses please? Thanks!

[DaveW]

Either an attack will be avoided or not... so if a defense is able to be used, just multiply the result by (n-1)/12, where n = the defense number or higher to avoid, to get the modified result.

[Sailor Vulcan]

Either an attack will be avoided or not... so if a defense is able to be used, just multiply the result by (n-1)/12, where n = the defense number or higher to avoid, to get the modified result.

Except the attack has double strike. The defense only works for the first strike. I'm trying to figure out the damage probabilities for the whole attack, not just the first strike.

[Halewijn]

Either an attack will be avoided or not... so if a defense is able to be used, just multiply the result by (n-1)/12, where n = the defense number or higher to avoid, to get the modified result.

Except the attack has double strike. The defense only works for the first strike. I'm trying to figure out the damage probabilities for the whole attack, not just the first strike.

don't use the doublestrike calculations but use the probabilities of each attack, add the damage values up and multiply their chances.

As DaveW mentioned: for the first attack you multiply each value given by the program with (n-1)/12 and for zero you additionally add (12-(n-1))/12.
The calculations are easy, but take some time to do and you should probably use excel.

For an extremely simple case: 1 die, no bonuses, doublestrike, 1 armor, defence 8+ (1 time use)

without defence:

0 damage --> 50%
1 damage --> 33,33%
2 damage --> 16.67%

For the first attack with defence this becomes:

0 damage --> 5/12 + 7/12*(0.5) = 70.833%
1 damage --> 7/12*(0.3333) = 19.444%
2 damage --> 7/12*(0.1667) = 9.7222%

Thus the chance for the entire attack:
Px(y): probability of attack x having y damage

0 damage: P1(0)*P2(0) --> 0.70833*0.5 = 35.4166%
1 damage: P1(0)*P2(1) + P1(1)*P2(0) --> 0.5*0.19444 + 0.3333*0.70833 = 33.33%
2 damage: P1(1)*P2(1) + P1(2)*P2(0) + P1(0)*P2(2) --> 0.3333*0.1944 + 0.1667*0.70833 + 0.5*0.09722 = 23.14%
3 damage: P1(1)*P2(2) + P1(2)*P2(1) --> 0.3333*0.09722 + 0.1667*0.19444 = 6.48%
4 damage: P1(2)*P2(2) --> 0.1667*0.09722 = 1.62%

35.4166 + 33.33 + 23.14 + 6.48 + 1.62 = 99.9866%. The difference is there due to bad rounding of the probabilities.

Average: 1.055 damage
variance: 0.593