Troll Dice Calculator Rolls.

[Thunder_God]

Didn't know where to put it, so putting it here. The Troll Dice Probability Calculator has an online interface, a robust if very obtuse coding language, and I'll post some code here, that people could plug in to get various results. Code, explanation, maybe some thoughts.
Going to the site also gives you if you choose "Calculate probabilities" the curve.

I didn't create the calculator, and I am working on using better, more streamlined code for the figures/rolls, so it'd also be easier for people to use on their own.

[Thunder_God]

Manifest Destiny, Incite (Or any +2 effect), Calandra's feat, Ashlynn's feat used offensively, etc.:

Base statistics:
1d6, 3.5.
2d6, 7.
3d6, 10.5.
4d6, 14.
5d6, 17.5.

Calandra:
1d6, 4.166.
2d6, 8.33.
3d6, 12.5.
4d6, 16.66.
5d6, 20.83.

Ashlynn: This assumes you're going to pick highest, not crits.
1d6, 4.955.
2d6, 9.34.
3d6, 13.43.
4d6, 17.34.
5d6, 21.15.

Incite:
1d6, 5.5.
2d6, 9.
3d6, 12.5.
4d6, 16.
5d6, 19.5.

Manifest Destiny, Signs and Portents, Pin Cushion...
1d6, 4.47.
2d6, 8.45.
3d6, 12.24.
4d6, 15.93.
5d6, 19.56.

Conclusions:
I am going to disregard the curve, and just look at statistics here, also going to ignore crits. Too much headache otherwise.
Calandra never really matches Ashlynn, unless you go above 3d6 and Ashlynn's roll is extremely unlucky, that is, if she rolls 3 or more results of 1's or 2's.
At one or two dice Calandra's feat doesn't do as well as Incite, it matches it at 3 dice, and passes it afterwards. Calandra's is way better at ensuring no snake-eyes, but Incite can give you a lower minimum (5 instead of 3) and higher maximum.
Manifest Destiny, Signs and Portents... do slightly better at 2d6 or under, and at 3d6 Calandra passes them.

Calandra can also give re-rolls, in case that with 4-5d6's you didn't get a high enough roll.

Just some figures, which took a long time to come up with. Curse my curiousity :P


Code: Replace N with the number of dice.
Base Numbers:
Sum Nd6. Just adds together Nd6s.
Calandra:
x := Nd6;
y := (count 1=x) d6;
r := (count 2=x) d6;
sum {x,y,r, -(count y), -2*(count r)}
It says:
1. Roll N D6 and assign to pool x.
2. Count the number of 1's in x and roll that many more d6es, and assign to pool y.
3. Count the number of 2's in x and roll that many more d6es, and assign to pool r.
4. Build a total pool of x, y, and a negative offset die equal to (0 minus the count of 1's), and an additional negative offset die equal to (0 minus twice the count of 2's).
5. Sum it all up.

Ashlynn:
x := N;
sum largest x (x+2)d6
It says:
You pick the largest n results out of (N+2)d6. Want more dice, just have as "N" how many dice you would roll normally without the feat, and it'd pick those out of a number of dice larger by 2.

Incite:
x := N;
sum (x)d6+2
You can simply skip the first line and just write "sum Nd6+2"

MD/Pin Cushion/ Signs and Portents:
Same as Ashlynn, just with 1 more.:
x := N;
sum largest x (x+1)d6

Defensively:
Ashlynn, as pointed out only boosts attack rolls, not damage, but she also affects the enemy, so here's what she does for enemy attack rolls, just replace "largest" with "least" in the code. Also, Calandra can do the same with Star-Crossed, just replace "Largest" with "Least" in MD stats. You could also just take the difference from the positive and subtract to reach them...
Ashlynn, enemy to hit:
1d6, 2.04.
2d6, 4.65.
3d6, 7.56.
4d6, 10.65.
5d6, 13.84.

In other words, enemies need to boost to get to average 2d6 rolls, and 4 dice to get to boosted dice. Against Ashlynn's DEF of 17, this is major. Of course, when the enemy CRAs, they can negate this somewhat, so Ashlynn has her +2 versus ranged spell... but still. The enemy can do it on average with RAT 5 and 10-men CRA.
Calandra's Star-Crossed basically gives you +1.5 DEF, so pushes you to non-Trollkin defenses, and when they need to boost, it's effectively +1.7. Not great, but something.

BTW, for those who wonder, about Calandra's old FT feat atrocious "Re-roll 1-2, endlessly" feat, aside from making criticals about 25% with unboosted rolls, it amounted to:
x := N;
sum (x)d4+(x*2)
Simply, roll 1d4, add 2 to the score, simplest way of doing it, and I'm sure if they had D4s in the game, an easy way to mark it as well.

Anyway, for those curious about such things:
1d6, 4.5.
2d6, 9.
3d6, 13.5 (already passing Ashlynn).
4d6, 18.
5d6, 22.5.

P.S. for multi-player games, putting crits aside, with 6 dice and above, Calandra's feat beats Ashlynn's feat... wild.

[Thunder_God]

This is the brand new calculator code (April 3rd!), cleaner and leaner, to which adding different functions will be easier for you lot. It takes into account auto-miss on all 1s and auto-hit on all 6s (just when you have more than 1 die for the auto-hits).

Just replace the relevant lines with the number of attacks, MAT/RAT, power/ps, armour and enemy defense.
You can replace the last line ("q") with "hitcheck" to know how many attacks you will hit on average, and percentages.

Code:
function hit(t, wa) =
h := sum(t)d6; if h=t then 0 else if ((t*6)=h&t>1) then 1 else if (h>=wa) then 1 else 0
function damage(f, xr) =
h := sum(f)d6; if (xr>=h) then 0 else (h-xr)

n := 2; \number of attacks
sum n#
t := 2; \number of dice on attack rolls
f := 2; \number of dice on damage rolls.
x := 18; \ enemy armour
w := 14; \enemy defense
a := 8; \attack stat.
r := 12; \power of attacker's weapon

wa := w-a; \defense minus attack, in one variable.
xr := x-r;\ armour minus power, in one variable.
hitcheck := call hit(t, wa);
q := (if (hitcheck=1) then (call damage (f, xr)) else 0);
q

[Thunder_God]

Suppose you want to try and do some... more complicated things with your calculator, such as see what happens if you have Anatomical Precision or Blight Storm up (which means you always do at least one damage if you hit), or your damage when you auto-hit, or when you get to re-roll all missed attacks once (due to Combined Arms or Fortune)?

Well, you take the code from the original calculator and replace select lines as follows. If you want to modify it by several aspects, so long they modify different lines go ahead, if not, look at the "What I did" and modify as applicable, or post asking for help:

Auto-hit:
Replace:
q := (if (hitcheck=1) then (call damage (f, xr)) else 0);

With:
q := call damage (f, xr);

(What I did: Simply removed rolling the attack in the end. You can also remove the whole "Hitcheck..." line to speed things up.)

Anatomical Precision:
Replace:
function damage(f, xr) =
h := sum(f)d6; if (xr>=h) then 0 else (h-xr)

With:
function damage(f, xr) =
h := sum(f)d6; if (xr>=h) then 1 else (h-xr)

(What I did: You only get to this roll if you hit the enemy, so what I did was replace "Then 0" with "Then 1", because this is how much damage you do if you don't pass the armour.)

Anatomical Precision analysis (pMorghoul):
Assuming you hit all, then interesting results: (at this stage I suddenly remembered Maltreatment, so up to 14 attacks, not 12 anymore!)
For 14 attacks: ARM 18, 15.55 damage; ARM 17, 17.88; ARM 16, 21.77; ARM 15, 27.611.
For 12 attacks: ARM 17, 15.33; ARM 16, 18.66; ARM 15, 23.66.
For 10 attacks: ARM 16, 15.55; ARM 15, 19.722.

Once you take into account DEF, it drops down, but then it becomes more important to boost damage, especially with Savage, which I might work on...

[Sevwall]

I don't mean to ask more of you, but if you could post the chances to roll a 3 or less, 4 or less, 5 or less, 6 or less, and so on, for Calandra's feat, for 2 dice, 3 dice, and 4 dice, I would be very greatful.

I promise to put it into a nice chart for ease of reference for all the trollblood players out there.

If you could include crit likelyhood as well, I would appreciate it, though I don't really expect it. I myself will do the numbers when fate bound is included.

[Thunder_God]

Fate bound? You mean star-crossed?

I'll update in a couple of mins with what you asked for, minus crits. Crits will be done later, once I manage to wrangle the basic to-hit roll into working with functions and kicking some strangeness that is in my new code now but wasn't before :-/ TBH, crits are relatively simple, and I can copy them from elsewhere, but I want to try and get boosts first.

Calandra's feat (just added "-" in front of the sum in the code. As such, simply ignore the "-" sign): Personally, for small enough curves, I'd have just hit print-screen from that site, or downloaded troll, inputted my code, and asked for it to somehow print you the curve in ascii.
2d6:
Value % >=
-12 100
-11 95.0617283951
-10 85.1851851852
-9 70.3703703704
-8 50.6172839506
-7 33.3333333333
-6 18.5185185185
-5 8.64197530864
-4 3.7037037037
-3 0.925925925926
-2 0.308641975309

3d6:
Value % >=
-18 100
-17 98.90260631
-16 95.6104252401
-15 89.0260631001
-14 78.0521262003
-13 64.0603566529
-12 48.4224965706
-11 33.3333333333
-10 20.987654321
-9 11.7283950617
-8 5.89849108368
-7 2.60631001372
-6 0.960219478738
-5 0.325788751715
-4 0.0685871056241
-3 0.017146776406

4d6:
Value % >=
-24 100.0
-23 99.7561347356
-22 98.7806736778
-21 96.3420210334
-20 91.4647157446
-19 83.6610272824
-18 72.930955647
-17 60.0060966316
-16 46.3496418229
-15 33.3333333333
-14 22.2374638012
-13 13.7021795458
-12 7.72748056699
-11 3.99329370523
-10 1.85947264137
-9 0.777320530407
-8 0.289590001524
-7 0.0904968754763
-6 0.0257201646091
-5 0.00476299344612
-4 0.000952598689224

There you go. To clarify, the chances to get a roll of 14 or under on 4d6 is 22.22%, whereas it'd be 55.63% on regular 4d6.

[Thunder_God]

Suppose what you want to count is how many single wound models you want to kill? That is to say, how often you'll both hit and do at least one damage? Suppose you want to see what happens if you re-roll all failed attacks once?

Killing Single Wounders:
Replace:
function damage(f, xr) =

h := sum(f)d6; if (xr>=h) then 0 else (h-xr)

With:
function damage(f, xr) =

h := sum(f)d6; if (xr>=h) then 0 else 1

(What I did: Replace the "else__" with "else 1". because all you care for is that you passed the armour)

Re-roll Attacks (Once):
Replace:
hitcheck := call hit(t, wa);
With:
hitcheck := if (call hit(t, wa))=1 then 1 else call hit(t,wa);

(What I did: If the first attack roll misses, I try again. This allows me to also input changes into the hit function from stuff like Manifest Destiny and such)

Re-roll (Fortune with Scattergunners) Analysis:
Now, cause we are all curious about Scattergunners:
With RAT 5, against DEF 13, 1 shot without Fortune: 41.66% to hit. 10 shots (2 scattergunners shooting at 5 models each, or 5 at 2... of course, the figures are a little off here, because you may kill a model in the first shot.. but this also holds true if you spray 3 models with 2 of your own, right?). Anyway, 10 is interesting because that's what a normal melee unit can do.
MAT/RAT 5 against DEF 13, without Fortune: 4.166 hits out of 10.
MAT/RAT 5 against DEF 13, with Fortune: 6.59 hits on average, and actually, 54% to get at least 7 hits. The average begins to slightly lie here due to the curve being lop-sided.

If we had Trollkin Champions:
Trollkin Champions, so 10 attacks, MAT 7. Let's say enemy is DEF 14 nimble:
8.26 attacks will hit on average.
Against DEF 16 (caster level): 4.78 attacks will hit.
If you have a Fell-Caller or another +2 MAT buff:
DEF 14: 9.722 attacks will hit (out of 10!). DEF 16: 8.26.

[Thunder_God]

So, you want to adjust the regular calculator with Incite, Manifest Destiny, Calandra's feat or such? Well, look no further, assuming you are not looking for crits. Replace the relevant lines with the following, and if you want to add one of the other functions as well, then modify the relevant line HERE, not in the original calculator.


Replace:
function hit(t, wa) =
h := sum(t)d6; if h=t then 0 else if ((t*6)=h&t>1) then 1 else if (h>=wa) then 1 else 0
function damage(f, xr) =
h := sum(f)d6; if (xr>=h) then 0 else (h-xr)




For Manifest Destiny/Pin Cushion/Signs and Portents.
With:
function hit(t, wa) =
h := sum largest t (t+1)d6; if h=t then 0 else if ((t*6)=h&t>1) then 1 else if (h>=wa) then 1 else 0

function damage(f, xr) =
h := sum largest f (f+1)d6; if (xr>=h) then 0 else (h-xr)

For Incite (or any +2 to hit and +2 damage):
With:
function hit(t, wa) =
h := sum(t)d6+2; if h=t then 0 else if ((t*6)=h&t>1) then 1 else if (h>=wa) then 1 else 0
function damage(f, xr) =
h := sum(f)d6+2; if (xr>=h) then 0 else (h-xr)

For Ashlynn?s feat, for friendlies:
With:
function hit(t, wa) =
h := sum largest t (t+2)d6; if h=t then 0 else if ((t*6)=h&t>1) then 1 else if (h>=wa) then 1 else 0

function damage(f, xr) =
h := sum(f)d6; if (xr>=h) then 0 else (h-xr)

(What I did: Replaced just the to-hit)


Ashlynn?s feat, for enemies:
With:
function hit(t, wa) =
h := sum least t (t+2)d6; if h=t then 0 else if ((t*6)=h&t>1) then 1 else if (h>=wa) then 1 else 0

(For Calandra's defensive spell, just replace (t+2) with (t+1), also, keep the damage line intact, as above.)

Calandra?s feat:
With:
function calandra (n) =
x := (n)d6; y := (count 1=x) d6; r := (count 2=x) d6;
sum {x,y,r, -(count y), -2*(count r)}
function hit(t, wa) =
h := call calandra(t); if h=t then 0 else if ((t*6)=h&t>1) then 1 else if (h>=wa) then 1 else 0

function damage(f, xr) =
h := call calandra(f); if (xr>=h) then 0 else (h-xr)

(Had to add a new function to the top)

Trying to do Calandra's feat without a function, but just shoving her small dice calculator into both to hit and to damage in the main function made it work over 10 seconds for 3d6, and we don't want that.

[Thunder_God]

Ok, this one will be a bit messy, requiring some more efforts from those who want to use it, but I think it's worth it. I actually had a neat thing in less time and effort, when I only wanted damage output, but then I got to thinking, "They'll want to know if they hit for some effects", and that took several more hours to handle due to the crazy nature of "Sum n#" in this coding language.

The Code:
function hit(t, wa) =
h := sum(t)d6; if h=t then 0 else if ((t*6)=h&t>1) then 1 else if (h>=wa) then 1 else 0
function damage(f, xr) =
h := sum(f)d6; if (xr>=h) then 0 else (h-xr)

n := 1; \number of attacks
t := 2; \number of dice on attack rolls
f := 3; \number of dice on damage rolls.
a := 6; \attack stat.
r := 18; \power of attacker's weapon
x := 19; \ enemy armour
w := 10; \enemy defense

hitqa :=sum n# count 1 = call hit(t, w-a); \# of hits
qa := sum hitqa# (call damage (f, x-r)); \1st attack setup result

n := 2; \number of attacks
t := 2; \number of dice on attack rolls
f := 2; \number of dice on damage rolls.
a := 6; \attack stat.
r := 16; \power of attacker's weapon
x := 19; \ enemy armour
w := 10; \enemy defense

hitqb :=sum n# count 1 = call hit(t, w-a);
qb := sum hitqb# (call damage (f, x-r)); \2nd attack setup result

n := 4; \number of attacks
t := 2; \number of dice on attack rolls
f := 2; \number of dice on damage rolls.
a := 6; \attack stat.
r := 18; \power of attacker's weapon
x := 19; \ enemy armour
w := 10; \enemy defense

hitqc :=sum n# count 1 = call hit(t, w-a);
qc := sum hitqc# (call damage (f, x-r)); \3rd attack setup result

qa+qb+qc

Explanation:
Note the lines:
hitqb :=sum n# count 1 = call hit(t, w-a);
qb := sum hitqb# (call damage (f, x-r)); \2nd attack setup result
These stand for the second attack. You repeat each section that ends in them for each attack, and in the final line you add them all together. Each new attack should have all the "hitqX" and "qX" have their Xs replaced by the new letter - never a number, the coding language doesn't allow for numbers in variables' names!

In case you're curious, the figures here are for a Carnivean with a free charge on a Menite heavy jack. We'll assume it has "no shooting" on it, so no spray. The first attack is the charge attack, the second attack setup is the 2 claw attacks (note, the "n:=X" line at the beginning of each section), and then it buys 4 more maw attacks.

You can use this either for one model with several attacks, or to quickly compare different setups of one model. Take the Gorax for example; you can setup the first attack setup for 4 fury buying attacks, the second for 3 attacks with boosted attack rolls, the third for 3 attacks with boosted damage rolls, and the fourth setup for 2 fully boosted attacks.
Then, you just shift the last line to look at each setup's results in order (just qa, qb, qc, or qd).

This is also really good for things with one attack that really counts, like models with *Armor Piercing.

Finally, if you don't change the number of dice, your MAT, enemy's ARM or DEF between sections, you can omit the relevant lines, and end with a cleaner code.

Some Permutations:
I guess you could add a global number of attacks ("Big N!" of sorts), and then have your stated number of first type of attacks, and each following number of attacks will be equivalent to the global number minus the number used thus far, plus some number (say, number of double boosted attacks*2 due to fury?), but this is a bit of a headache.

What might be more useful, is "Damaged/Hit" effects, such as Baldur's debuff if he hits an enemy. Or an effect that triggers on damaging. For the time being, you can only use to check if you've hit/damaged in the previous section(s), and not if you hit in the middle of a section (such as, if you've only damaged the enemy in the middle of the third section with 4 attacks, it's a lost cause).

If you want to check if you've hit the enemy, say, for a def debuff, in the second section you'll replace the line:

w := 10; \enemy defense
with:

w:= if sum hitqa>=0 then 8 else 10;

That's for a -2 debuff
In the third section, we'll replace it with:

w:= if (sum hitqa+sum hitqb)>0 then 8 else 10;

If it triggered of off being damaged, just replace "Sum hitqX" with "qX" where applicable.

[Thunder_God]

07/07/2010. I managed to tackle Crit percentages, including under Signs and Portents, double S&P, and Calandra's Feat! Now, I can't do Ashlynn because of the "Choose" aspect. Rolling 3d6 on double SnP can lead to 3,3,4,5,6 which Ashlynn would get a crit from (assuming needing 12 or less to hit), but double Signs and Portents wouldn't.
Everything else works.

This is the simple critical hit calculator:
n:= 1; \number of attacks
sum t#
t := 2; \number of dice on attack roll
attack := 6; \your attack stat
defense := 12; \enemy's defense
h := (t)d6;
x := sum h;
diff := -(count different h)+t+1;
if x=t then 0 else if ((t*6)=x&t>1) then 1 else if ((diff>1)&((x+attack)>=defense)) then 1 else 0

For one attack, the % of getting "1" is your percentage of landing a hit that is also a critical hit. For multiple attacks, the percentage of say 3 is your percentage of landing 3 critical hits, on however many attacks you make. "0" lumps the chances of not only missing, but landing a non-critical hit together.

"t" is the number of dice we roll; "attack" is our MAT/RAT/Magic; and you should know what "defense" is. If you auto-hit, just use the calculator above, ok? this calculator also takes into account the auto-hit on all 6s and auto-miss on all 1s.

So long you only want to check the crit chances on a single attack, leave "t" alone. Change it to see your chances of getting at least X crits for T attacks.

"Hitting X" Code:
t := 2; \number of dice on attack
x := (t)d6;
q := sum x;
if ((-(count different x)+t+1)>1)&(q>t) then q else 0


This code is slightly different, it gives you the chances of landing a critical hit when you need X or above to hit, which saves you adjusting MAT/DEF one at a time. So for 2d6 it says (We as always care for the third row, the chances to get this or better):
4 -> 13.88%; 6 -> 11.11%; 8 -> 8.33%.
Or in other words, when you need 4 or better to land a hit, you'll get a critical hit 13.88% of the time, when you need 6 or better to hit, it drops to 11.11%. At 2d6 all criticals are a result of both dice being identical, so in order to get "5 or better", you'll need to look at the results for 6.

***

Now, we'll go onward and do the same codes for Calandra, Signs and Portents, and double Signs and Portents. Flat MAT modifiers simply go to either your attack stat, or reduce the number you need to hit.

Calandra:

"Hitting X" Code:
t := 2; \number of attack dice
x := (t)d6 drop {1,2};
y := (t-(count x))d6;
q := sum {x,y};
if ((-(count different {x,y})+t+1)>1)&(q>t) then q else 0



Attack Calculator:
n:=1; \number of attacks
sum n#
t := 2; \number of attack dice
attack := 8; \your attack stat
defense := 15; \enemy's defense
x := (t)d6 drop {1,2};
y := (t-(count x))d6;
q := sum {x,y};
r:= if ((-(count different {x,y})+t+1)>1)&(q>t) then q else 0;
if (t*6)=q then 1 else if ((r>0)&((attack+q)>=defense)) then 1 else 0


Signs and Portents:

Hitting X Code:
t := 3; \number of attack dice.
x := largest t (t+1)d6;
q := sum x;
if ((-(count different x)+t+1)>1)&(q>t) then q else 0

Attack Calculator:
n:=1; \number of attacks
sum n#
t := 2; \number of attack dice
attack := 8; \your attack stat
defense := 16; \enemy's defense
x := largest t (n+1)d6;
q := sum x;
r:= if ((-(count different x)+t+1)>1)&(q>t) then q else 0;
if (t*6)=q then 1 else if ((r>0)&((attack+q)>=defense)) then 1 else 0

***

For double signs and portents (Vlad and Drago) just replace the line:
"x := largest t (t+1)d6;" with: (minus the quotation marks) "x := largest t (t+2)d6;"
For reverse Signs and Portents (we'll assume Ashlynn always picks lowest for double) replace the same line with:
"x := least t (t+1)d6;" and again, t+2 instead of t+1 for double the whammy.

I'll post some thoughts on the results, and some of the really tasty results later. Suffice to say, invest in Calandra/Signs and Portents, and your crit chances are going to become better. Considerably so, even if you still can't rely on them under 4d6. Well, 50% on 3d6 for a crit sounds pretty good to me...

[Not Dice]

My head...

It spins...

[Thunder_God]

Well, you just need to click the link, copy-paste the relevant code, and input the parameters? If you have a specific question, feel free to post here/PM me and I'll give you the numbers. Hopefully it'll be something already covered, and I'll just act as an interpreter?

But yeah, at some point I'll also make this more readable... maybe, somehow.. I'll try?

[Thunder_God]

Ok, this post has the following: Number of dice on attack roll for each group. Then we have the chance to get a crit when you need "x to hit" or higher. Then we have the crit percentage for #-to-hit under Calandra's Feat, Signs and Portents, and Double Signs and Portents (2*S&P).

"Infinit" means this is your percentage to hit def=infinite, or in other words, all dice=6. I cut off the probabilities at 22, I thought that was more than sufficient. I also cut it off two digits after the period, I doubt the slight rounding up this resulted in is of much consequence.

Also, the file is available on Google Docs here.
I hope you guys enjoy it, and use it to see that once you roll 4d6, crits are not that hard Calandra/Signs and Portents make it pretty reliable (47%+) to get a crit with 3d6 when you need 10 or higher to hit.

2d6

# regular Caland S&P 2*S&P
3 13.89 20.06 23.15 30.48
4 13.89 20.06 23.15 30.48
5 11.11 19.75 21.30 29.63
6 11.11 19.75 21.30 29.63
7 8.33 14.81 18.06 27.08
8 8.33 14.81 18.06 27.08
9 5.56 9.88 13.43 21.91
10 5.56 9.88 13.43 21.91
11 2.78 4.94 7.41 13.19
infinit 2.78 4.94 7.41 13.19


3d6

# regular Caland S&P 2*S&P
4 43.98 52.25 53.63 62.44
5 42.59 52.19 53.32 62.37
6 39.81 51.94 52.55 62.18
7 37.96 51.71 51.85 61.91
8 33.80 50.48 49.85 61.01
9 29.63 49.25 46.91 59.34
10 26.39 47.12 44.52 57.84
11 22.22 42.80 39.74 54.12
12 18.06 35.39 34.80 49.42
13 14.81 30.18 30.25 45.04
14 10.65 22.77 24.38 38.16
15 6.48 15.36 16.67 28.19
16 4.63 10.97 13.04 23.42
17 1.85 4.39 5.79 11.39
infinit 0.46 1.10 1.62 3.55


4d6

# regular Caland S&P 2*S&P
5 72.15 80.25 79.15 85.34
6 71.84 80.24 79.09 85.32
7 71.06 80.22 78.90 85.28
8 69.52 80.16 78.45 85.16
9 66.82 79.96 77.53 84.87
10 62.50 79.47 75.86 84.27
11 58.18 78.75 73.87 83.38
12 52.01 76.99 70.46 81.65
13 46.06 73.98 66.14 78.97
14 38.97 69.84 60.03 74.74
15 33.26 64.59 54.57 70.47
16 26.16 56.42 47.04 63.99
17 20.22 46.33 38.86 55.70
18 14.04 34.14 30.05 45.87
19 9.72 27.07 23.69 38.55
20 5.40 16.34 15.07 26.83
21 2.70 8.54 8.50 16.60
22 1.16 3.66 4.06 8.70
Infinit 0.08 0.24 0.33 0.87


5d6

# regular Caland S&P 2*S&P
6 90.73 95.12 93.83 96.40
7 90.66 95.12 93.81 96.40
8 90.47 95.12 93.77 96.39
9 90.02 95.11 93.65 96.36
10 89.12 95.09 93.38 96.28
11 87.50 95.04 92.83 96.11
12 84.86 94.88 91.85 95.77
13 80.94 94.53 90.19 95.13
14 75.54 93.80 87.63 94.01
15 68.60 92.39 83.91 92.19
16 61.77 90.34 79.61 89.72
17 53.86 86.79 73.86 86.04
18 45.37 81.32 66.73 80.94
19 36.88 73.73 58.44 74.33
20 28.97 65.29 49.40 66.24
21 22.15 55.32 41.66 58.73
22 15.20 43.02 31.96 48.35
Infinit 0.01 0.05 0.07 0.20

[Thunder_God]

Almost all done with the new calculator, including auto-hit and auto-miss,just left organizing the first post with an index. Also, will clarify some of the critical hit stuff, still not boost or not to boost in it, but you can increase number of dice manually.

[PG_Agamemnon]

My head...

It spins...

It Hurts us......

[Thunder_God]

Big Error crept in and fixed, mostly noticeable for Ashlynn's feat.

The program used seems to round down, so a crit miss was had when 3d6 resulted in 3-5 and not merely 3. This had been fixed.

[PG_Gringo]

So would it be best to use the Ashlynn set for Drago and Signs and Portents (Double Signs)? I remember a thread in the old forum that had the curve for it. RingKichard did some amazing work on it, here's the link: http://old.privateerpressforums.com/...owtopic=165863

[Thunder_God]

Ashlynn for Drago would give you exactly the correct results. Better than they do for Ashlynn, because Ashlynn gets to pick, so Ashlynn has a chance to get crits not reflected in the calculator she uses, which only assumes she'll pick the highest dice.

Sevwall planned to do some graphics for the Troll Faction's statistics. I content myself with churning out the data, if not making it look pretty

[PG_Gringo]

Ashlynn for Dragon would give you exactly the correct results. Better than they do for Ashlynn, because Ashlynn gets to pick, so Ashlynn has a chance to get crits not reflected in the calculator she uses, which only assumes she'll pick the highest dice.

Sevwall planned to do some graphics for the Troll Faction's statistics. I content myself with churning out the data, if not making it look pretty

Sorry man, I can't find Ashlynn for Dragon. As it's 4d6 dropping 2d6 lowest rolling I can't find it in your opening posts. Care to post the tables?

Cheers for this, I really appreciate it.

[Thunder_God]

Second post has the average:
Ashlynn: This assumes you're going to pick highest, not crits.
1d6, 4.955.
2d6, 9.34.
3d6, 13.43.
4d6, 17.34.
5d6, 21.15.

It also has the code, for you to be able to calculate the chance of getting each number or higher than that number:
x := N;
sum largest x (x+2)d6
The third post has the basic calculator, and the ninth post has the modification required for Ashlynn/Signs and Portents. Ashlynn only does "To-hit" and signs and portents only adds 1 die, but it's easy to figure out from both what to do (just add 2 dice instead of 1 for signs and portents). The calculator you desire is as follows:

Code:
function hit(t, wa) =
h := sum largest t (t+2)d6; if h=t then 0 else if ((t*6)=h&t>1) then 1 else if (h>=wa) then 1 else 0
function damage(f, xr) =
h := sum largest f (f+2)d6; if (h-xr)>0 then h-xr else 0

n := 2; \number of attacks
sum n#
t := 2; \number of dice on attack rolls
f := 2; \number of dice on damage rolls.
x := 18; \ enemy armour
w := 14; \enemy defense
a := 8; \attack stat.
r := 12; \power of attacker's weapon

wa := w-a; \defense minus attack, in one variable.
xr := x-r;\ armour minus power, in one variable.
hitcheck := call hit(t, wa);
q := (if (hitcheck=1) then (call damage (f, xr)) else 0);
q

That's your average damage done. If you just want to find out "To hit percentage" then:
1. You could just use Ashlynn's code, since the damage part from Signs and Portents would be irrelevant. This is not necessary, just me explaining what could've been used.
2. replace the last line (which reads just "q") with: "hitcheck", without the quotation marks.

Change n to 1 if you want to find out one attack percentage, t to 3 if you boost the attack roll, and MAT/DEF (a/w).

[PG_Gringo]

By running the calculator I've noticed that the Ashlynn (or Drago+Signs) version has a better chance of rolling >=6 than just rolling 3d6. Ashlynn with boost rolls has a better chance of rolling >=12 than 4d6. Is that correct?

[Thunder_God]

The numbers are all correct.

The more dice you have, the more you get from MD/other such effects. You get +0.97 with 1d6 and nearly +2 with 4 or so. Ashlynn and MD and such are especially good at eliminating the lower side of the curve. If you will look, Ashlynn with 4d6 is only 0.16 less on average than simply rolling 5d6. Ashlynn with 5d6 is better than simply rolling 6d6.
Once you look for under-average numbers, it becomes earlier and earlier that MD/Ashlynn will beat simply rolling more dice. Yes.

Ashlynn also raises your chances of getting an auto-hit (all dice coming up as 6s) versus infinite defense, quite dramatically.

[PG_Gringo]

That's amazing. I'm truly impressed by the help this provides. I'd find eliminating the lower end of the curve much more useful. In a gaming sense, it's safer to roll using the MD/Ashlynn than using the usual method.

You sir, are a Mathemagician.

[Thunder_God]

LOL, I didn't create the Troll calculator, with its horrid documentation. I just try to make it work for Warmachine/Hordes.

And yeah, I often look at % to kill something, if it's a heavy Warbeast, then to do 32 damage to kill heavy jacks, and if aimed at assassination, roughly 17 damage. Average is nice, but it's far from everything, especially as the median (where half the results are over and half are under) and the average are often quite different.

[Thunder_God]

1. Apparently in May 14th there was some change made to the code of the language used. This resulted in several things which worked before not working.
2. Crit calculator doesn't work right now: It doesn't like my "t:=..." line for some mysterious reason...
3. Damage didn't work, I changed what was there to an entirely equivalent statement and changed all the posts to incorporate it. I don't know why what was there didn't work and this does, as they should yield identical results, but it works now...
4. Changed the thread so all my posts have identical text colour, font, and font size. Go "Automatic" and names and not having to guess!
5. ! If you see anything that doesn't work aside from the critical calculator, please let me know, and I'll try to fix it. I also made contact with the language's creator to gain more information, help, and to see if I can somehow get a program with a visual GUI of this tool on my computer, instead of the DOS window option.

Will try to get the critical calculator up and running again, and to incorporate the ability to see % of how many crits when you make multiple attacks.

EDIT: Speedy reply from the site's creator, apparently it's a bug caused by allocation optimization aimed changes introduced with the last update. He'll work on fixing it, at which time I'll revert the code back. Hopefully after that everything will work again and the new thing I wanted to add will be added.

Edit 2: Site creator fixed the bug, and I have returned the code to its old form, can't know what errors might have crept in with my changes. In 20 minutes or so, expect a more advanced critical hit calculator, that accounts for more than one attack.

[PG_Gringo]

In 20 minutes or so, expect a more advanced critical hit calculator, that accounts for more than one attack.

Now that is awesome.

[Thunder_God]

Currently on pause, but there's work being done (mostly by a friend of mine who also uses this forum) to create a java based program that'll spit out the statistics, and will have a GUI that just asks you to check boxes and enter numbers...

[MagnusDarkPrince]

Even with computer generated dice my rolls suck... this is 3d6 average for me
8 15 7 10 9 7 is it any wonder I use S&P LOL

[Thunder_God]

Ha! Yes, that's no good BTW, to get the statistics, you need to change it to "Calculate Probabilities" above the "Troll the Dice!" button.

[Thunder_God]

See post #10. Crits had been revised, I had finally figured out how to do critical percentage for Calandra. And while at it, I also did Signs and Portents crit chances.

Next I will look at the results of these comparisons, and how much we can rely on a crit, and when.

[Thunder_God]

Post #13 now has the percentages to land a critical hit with unmodified dice, under Calandra's feat, under signs and portents, and under double signs and portents.
Ashlynn's Feat will always fare better than double Signs and Portents. How good? I still can't tell.

[Verjigorm]

You're a good man

[Thunder_God]

Verjigorm, thank you kindly

Post #9 had been updated with a new thing that I can now calculate, how much damage a model with several different attacks, or a model that charges, for instance, can produce. Hope you find it useful.

[Sachiel]

Have you had a look at http://anydice.com/ ?

[Thunder_God]

I have. It doesn't seem to add anything, and will require translation, though I could be mistaken. Using it will necessitate me learning to learn a new language, even if simpler, though I am unsure why to go that route?

So I could post links to specific code instead of requiring people to copy-paste? That might be nice, but it'd lose out on all the possible permutations made available by copy-pasting, by gene-splicing the code, so to speak.

If anyone else wants to translate what I've done to AnyDice, and then send me the links to the specific "code", I'll be happy to make these available here as well. But as it does not seem to add anything, from my cursory glance and light playing around, I don't see why to go there myself. I am more than willing to be persuaded.
The UI is better, that's true.

[lastspartacus]

So, what is the point of this? I'm missing it.

[Thunder_God]

Letting people know the chances of something occuring. Such as Rhyas critting and killing a caster, expected damage of one heavy against another, effects of some buffs...? Knowledge. Run it for aiming CRAing Nyss Archers, and be surprised.

[The Happy Anarchist]

Can you do some Star Crossed numbers? It would be nice to get a chart like you guys did for Calandra's feat for the effects of star crossed. My coding skills are sub par!

[Thunder_God]

These are the numbers, percentage to roll X or higher on Yd6. 31% to get a 7 on 2d6, 11% less to roll 6 with Star Crossed than 7 without (thinking of the lower Troll DEF).

If you want it prettified, talk to Sevwall. I can send him the excel chart.

-- 1d6 2d6 3d6 4d6 5d6
1 100.00 ---- ---- ---- ----
2 69.44 100.00 ---- ---- ----
3 44.44 92.59 100.00 ---- ----
4 25.00 80.09 98.38 100.00 ----
5 11.11 64.35 94.21 99.67 100.00
6 2.78 47.69 86.96 98.51 99.93
7 ---- 31.94 76.85 95.94 99.64
8 ---- 19.44 64.51 91.50 98.86
9 ---- 10.65 51.23 84.93 97.25
10 ---- 5.09 38.35 76.31 94.47
11 ---- 1.85 26.93 66.09 90.20
12 ---- 0.46 17.52 54.96 84.31
13 ---- ---- 10.49 43.70 76.84
14 ---- ---- 5.71 33.09 68.04
15 ---- ---- 2.78 23.77 58.34
16 ---- ---- 1.16 16.11 48.29
17 ---- ---- 0.39 10.25 38.47
18 ---- ---- 0.08 6.07 29.41
19 ---- ---- ---- 3.31 21.51
20 ---- ---- ---- 1.63 14.99
21 ---- ---- ---- 0.72 9.92
22 ---- ---- ---- 0.27 6.20
23 ---- ---- ---- 0.08 3.63
24 ---- ---- ---- 0.01 1.98
25 ---- ---- ---- ---- 0.99
26 ---- ---- ---- ---- 0.45
27 ---- ---- ---- ---- 0.18
28 ---- ---- ---- ---- 0.06
29 ---- ---- ---- ---- 0.02
30 ---- ---- ---- ---- 0.00

[The Happy Anarchist]

Sweet, that is exactly what I am looking for. Would be great to get that all diagramed up for the Calandra thread.