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RAWR! KROXIGOR!!
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Discussion Starter · #1 · (Edited)
I have made an interesting discovery. Portent of Far will improve the number of wounds caused by your unit by 36.11% no matter what your "to hit" and "to wound" rolls require (on both a shooting unit or a unit in combat).

I've edited this after I made a more formal proof.



Previously I believed that casting Portent of Far when only rolls of 1 fail made its effect better (after all, you can't "waste" the spell by rolling a 2 and failing anyway). Oh boy was I wrong. 36.11%?! I'm going to be casting Portent a whole lot more.
 

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i am da Wahhchief
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i think theres a tiny error in this calculation... (just trying to help)
when you reroll and then throw a 1, it is still a failure.

andum.. 1/2 = 1/2 x 1/6 : 2
what are you basing this on exactly? (my math is very very rusty)


shouldnt the number just be

normal: 1/2 x 1/2 = 0,25 = number of wounds per dice (x100 to make it look like %)
portent: 2/3 x 1/2 = 0,3333 number of wounds per dice


ok this doesnt add up >.< wow i need to get back in the books

would like to see how you made that calculation though :D
 

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RAWR! KROXIGOR!!
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Discussion Starter · #3 ·

shouldnt the number just be

normal: 1/2 x 1/2 = 0,25 = number of wounds per dice (x100 to make it look like %)
portent: 2/3 x 1/2 = 0,3333 number of wounds per dice


ok this doesnt add up >.< wow i need to get back in the books

would like to see how you made that calculation though :D
OK. So lets us the hit on 4+ wound on 4+ example.

Normally the probabaility of attack becoming a wound is 1/2 x 1/2 (thus 1/4).


With portent, the chance to hit/wound is now 1/2 + 1/6x1/2 (the chance of rolling a straight up 4+, or rolling a 1 THEN rolling a 4+).

So the probability of an attack becoming a wound is then (1/2 + 1/6x1/2)x(1/2 + 1/6x1/2)
=(1/2 + 1/6x1/2)^2
= 49/144
 

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I decided to do some quick maths to find a pattern. After spending a while wrestling with excel so it would give me a graph I gave up but here's the stuff I got:

Attacks | With portent | Without portent | Improvement
5--------|2.5-------------|1.25----------------|100%
10------|3.75------------|2.5------------------|50%
20------|6.25------------|5--------------------|25%
50------|13.75----------|12.5-----------------|10%
500----|126.25---------|125------------------|1%

When you double the attacks, the improvement halves. If you multiply the attacks by ten the improvement divides by 10. This assumes that every time at least 3 ones are rolled. Intrestingly the portent always improves the wounds by 1.25. That around an extra wound against most infantry saves. With 3s to hit and wound the improvement percentages where greatly decreased falling to only 10% for 5 attacks and the improvement was only 0.222222... wounds. This means the improvement fell by 90% with 500 attacks only having an improvement of 0.1%! The ratio of percentage increases stayed the same. So I would use this spell on hard to hit and wound enemies for the maximum improvement. Sometime I may test 5s to hit and wound to see what that does.
 

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For 4+ to hit and wound I'm using:=((B5-3)/4)+2
B5 being number of attacks, -3 for the portented attacks and +2 for the portented attacks that will hit and wound (Its effectively 5 up on D12, six up without portent count half of ones as wounds and that gives 5+, which means out of 3 2 wound)
For 3+ to hit and wound I'm less confident of my formula but its:=((((B12-3)/3)*2)/3)*2+((((3+3/6)/3)*2)/3)*2 :D
Which is complicated :D but B12 is attacks. /3*2 and its done once for to hit and once for to wound which gives the wounds caused without portent. The second half is for the effect of portent, I'm not sure if its right maybe: =(((((B12-3)/12)*8)/12)*8)+(((3/12)*9)/12)*9) that seems better actually when I think of it as D12 it makes more sense :D

Argh, when I plug that in the numbers get ugly! Everything has improved slightly, 10% increase on 5 attacks has gone to 15.random and the rest have all gone up by roughly half as well! The increase in wounds caused has gone to 0.35416666... so a slight improvement there.

Does that answer the question?

EDIT: OMG I just realised its reroll all ones! oops... I'll go fix that :D

EDIT2: Okay fixed, your 36.11 was correct for 4+ to hit and wound but seemingly wrong for 3+ to hit and wound, I get 26.5625.

Now getting table:
Attacks Portent No portent Improve (%) Change in wounds
5 1.701388889 1.25 36.11111111 0.451388889
10 3.402777778 2.5 36.11111111 0.902777778
20 6.805555556 5 36.11111111 1.805555556
50 17.01388889 12.5 36.11111111 4.513888889
500 170.1388889 125 36.11111111 45.13888889

Attacks Portent No Portent
5 2.8125 2.222222222 26.5625 0.590277778
10 5.625 4.444444444 26.5625 1.180555556
20 11.25 8.888888889 26.5625 2.361111111
50 28.125 22.22222222 26.5625 5.902777778
500 281.25 222.2222222 26.5625 59.02777778

Which means a bigger % improvement for harder to hit and wound but a smaller increase in wounds caused, so cast it on those 3+ combats! Or better the 2+ combats, that'll be my next table :D

First is for 4s second for 3s
Formulas are:
4+: =((((B5/12)*7)/12)*7)
3+:=((((B12/12)*9)/12)*9)

Are those right?

EDIT3: 2+ improves even more! Improvement of 0.729166667 with 5 attacks!

EDIT4 :D : Okayies, I have made a table which you can put any to hit or to wound roll in and it gives you all the stats. I can plug in any numbers you guys need. It seems that the easier it is to hit and wound the more the spell will improve you wounds so there you have it, cast it on the combats where you're easily causing wounds but are against lots of static CR to get a extra wound or two, for example 10 attacks with 4s to hit and 2s to wound will gain an extra 1.32 wounds before saves but with 4s to hit and 6s to wound you only get an additional 0.625 wounds.

Phew :D
 

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RAWR! KROXIGOR!!
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Discussion Starter · #8 · (Edited)
I'm not sure what you are saying Sturen.

My numbers for hit on 3s, wound on 3s are:

Normal - (2/3)^2 = 4/9 attacks become wounds
Portent - (2/3 + 1/6*2/3)^2 = 49/81 attacks become wounds

49/81 divided by 4/9 = 1.36111

Ergo, 36.111% improvement.


I think I'm going to come back later and attempt a formal mathematical proof later.

EDIT: Here we go... hope its not to blurry

 

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Okay, I made another mistake :( I for some reason forgot that if you got a 1 and rerolled you still needed to roll a 3+,5+,6+ ect and made it always a 4+ :(
Will fix my spreadsheet in a minute and then give you the correct result for any to hit and to wound rolls :)

EDIT: now its working and you where right all along :), there is always a 36.11% increase and the easier it is to hit and wound the better the improvement. So cast it on your strong troops for an improvement of over 1 wound :)
 
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