paul_Harkonen
September 25th, 2008, 16:38
If anyone thinks there's a better location to post this, please feel free to move it, but I put it here as I thought it was the best location as it applies to both fantasy and 40k:
MathHammer for dummies:
I’ve found myself with a lot of free time and boredom during my classes at the start of this semester, and being the good engineer that I am, I set out to catalog the statistical probabilities of common situations in warhammer fantasy and 40k. I’ve always felt that a centralized location for the probabilities of events in Warhammer should be available on LO, so I’ve set out to make it so. From the very beginning I want to say I did all of these probabilities by hand during class, so if you find an error please point it out and I will be happy to correct it.
So, without further ado, probabilities of a successful cast at x cast level with y dice:
As a note, for abilities that add to your total (such as twin heads for chaos) simply subtract the value of the bonus from the target casting value to get an accurate prediction of your chances to cast.
2 dice
Cast chance to succeed
3+ 97%
4+ 92%
5+ 83.3%
6+ 72%
7+ 58.3%
8+ 41.6%
9+ don’t bother
3dice:
Cast Chance to pass
<5+ 93%
6+ 91%
7+ 89.3
8+ 83.8
9+ 76.9
10+ 67.1
11+ 49.1
12+ don’t bother
4 dice:
Cast Chance to cast
<7+ 86.8
8+ 86.5
9+ 86.0
10+ 83.3
11+ 79.6
12+ 73.0
14+ 41.5 (added for reference)
What do these tables show? They demonstrate two important things, namely when is it better to use fewer dice. If your cast is higher than a 5+ you want to be rolling 3 dice to have near certainty to pass, but 2 dice is still fairly probable for cast values up to 6+. In addition, for any cast value lower than 9+ it’s better to be using 3 dice. This is because of the drastic increase in the chance of blowing yourself up with 4 dice. Other than that, I think the tables are fairly self explanatory.
Now for the complicated ones. The tables below represent your chance to kill a target based on your ballistic skill against a relative toughness value. For example, if your weapon is str 5, x-2 means a target toughness of 3 and x+ 2 is a toughness 7. The different tables represent different armour saves. This is the odds that if you have one shot you will kill a model.
Converting my tables for use in close combat is fairly simple. A BS of 3 is a 4+ to hit, or a WS < or equal to the target. A BS of 4 is a WS> target. Use a BS of 2 is you’re hitting 5’s.
Adjusting armour saves is also quite simple, just use the table for the save your opponent will take and your probability will be accurate.
As of now I haven’t included a BS of 1 (hitting on 6’s) mostly because I’m a 40k player and the instances of that in 40k is limited, however, I intend to update the tables fairly soon and will include that possibility at that time.
No armour save:
BS -----T ---2------1------0-----+1----+2
2 -----------5.5----11-----17----22----27.8
3 ------------8------16 ---25----33---40
4 -----------11-----22----33----44---55
5 -----------14-----28----42----55---69
6+ armour save
BS-----T---- -2 -1 0 +1 +2
2 -----------4.6 --- 9.3-- 14 ---19 ---23
3 -----------6.9 ----14--- 21--- 28 ---35
4 -----------9.3 ----19--- 28--- 37--- 46
5 -----------12 -----23--- 35--- 46--- 58
5+ armour save
BS ----T- -2 ----- -1 -----0---- +1 ---+2
2 -------- 3.7---- 7.4 ---11--- 15 ---19
3 -------- 5.6 ----11 ----17--- 22 ---28
4 ---------7.4 ----15 ----22--- 30 ---37
5 ---------9.3 ----19 ----28--- 37--- 46
4+ armour save
BS -----T--- -2----- -1 ---- 0---- +1--- +2
2 ------------2.8--- 5.6 ---8.3--- 11--- 14
3 ------------4.2--- 8.3 ---13 ----17 ---21
4 ------------5.6--- 11 ----17 ----22 ---28
5 ------------6.9--- 14 ----21 ----28--- 35
3 armour save
BS ----- T--- -2 --- -1 ---- 0 ---- +1 --- +2
2 ----------- 1.9--- 3.8--- 5.6--- 7.4 ---9.3
3 ----------- 2.8--- 5.6 ---8.3--- 11 --- 14
4 ----------- 3.8--- 7.4 ---11 ----15 --- 19
5 ----------- 4.6--- 9.3 ---14 ----19 --- 23
2 armour save
BS ---- T --- -2 ---- -1----- 0 --- +1 ---- +2
2 ----------- .93 --- 1.8 ---2.8 -- 3.7 --- 4.6
3 ----------- 1.4 --- 2.7 ---4.2 -- 5.6 --- 6.9
4 ----------- 1.9 --- 3.7 ---5.6 -- 7.4 --- 9.3
5 ----------- 2.3 --- 4.6 ---6.9 -- 9.3 --- 15
For the future, a twin-linking adjustment, reroll to wound, and other less common modifiers. Also, probabilities of damaging a vehicle in 40k.
-Paul Harkonen
MathHammer for dummies:
I’ve found myself with a lot of free time and boredom during my classes at the start of this semester, and being the good engineer that I am, I set out to catalog the statistical probabilities of common situations in warhammer fantasy and 40k. I’ve always felt that a centralized location for the probabilities of events in Warhammer should be available on LO, so I’ve set out to make it so. From the very beginning I want to say I did all of these probabilities by hand during class, so if you find an error please point it out and I will be happy to correct it.
So, without further ado, probabilities of a successful cast at x cast level with y dice:
As a note, for abilities that add to your total (such as twin heads for chaos) simply subtract the value of the bonus from the target casting value to get an accurate prediction of your chances to cast.
2 dice
Cast chance to succeed
3+ 97%
4+ 92%
5+ 83.3%
6+ 72%
7+ 58.3%
8+ 41.6%
9+ don’t bother
3dice:
Cast Chance to pass
<5+ 93%
6+ 91%
7+ 89.3
8+ 83.8
9+ 76.9
10+ 67.1
11+ 49.1
12+ don’t bother
4 dice:
Cast Chance to cast
<7+ 86.8
8+ 86.5
9+ 86.0
10+ 83.3
11+ 79.6
12+ 73.0
14+ 41.5 (added for reference)
What do these tables show? They demonstrate two important things, namely when is it better to use fewer dice. If your cast is higher than a 5+ you want to be rolling 3 dice to have near certainty to pass, but 2 dice is still fairly probable for cast values up to 6+. In addition, for any cast value lower than 9+ it’s better to be using 3 dice. This is because of the drastic increase in the chance of blowing yourself up with 4 dice. Other than that, I think the tables are fairly self explanatory.
Now for the complicated ones. The tables below represent your chance to kill a target based on your ballistic skill against a relative toughness value. For example, if your weapon is str 5, x-2 means a target toughness of 3 and x+ 2 is a toughness 7. The different tables represent different armour saves. This is the odds that if you have one shot you will kill a model.
Converting my tables for use in close combat is fairly simple. A BS of 3 is a 4+ to hit, or a WS < or equal to the target. A BS of 4 is a WS> target. Use a BS of 2 is you’re hitting 5’s.
Adjusting armour saves is also quite simple, just use the table for the save your opponent will take and your probability will be accurate.
As of now I haven’t included a BS of 1 (hitting on 6’s) mostly because I’m a 40k player and the instances of that in 40k is limited, however, I intend to update the tables fairly soon and will include that possibility at that time.
No armour save:
BS -----T ---2------1------0-----+1----+2
2 -----------5.5----11-----17----22----27.8
3 ------------8------16 ---25----33---40
4 -----------11-----22----33----44---55
5 -----------14-----28----42----55---69
6+ armour save
BS-----T---- -2 -1 0 +1 +2
2 -----------4.6 --- 9.3-- 14 ---19 ---23
3 -----------6.9 ----14--- 21--- 28 ---35
4 -----------9.3 ----19--- 28--- 37--- 46
5 -----------12 -----23--- 35--- 46--- 58
5+ armour save
BS ----T- -2 ----- -1 -----0---- +1 ---+2
2 -------- 3.7---- 7.4 ---11--- 15 ---19
3 -------- 5.6 ----11 ----17--- 22 ---28
4 ---------7.4 ----15 ----22--- 30 ---37
5 ---------9.3 ----19 ----28--- 37--- 46
4+ armour save
BS -----T--- -2----- -1 ---- 0---- +1--- +2
2 ------------2.8--- 5.6 ---8.3--- 11--- 14
3 ------------4.2--- 8.3 ---13 ----17 ---21
4 ------------5.6--- 11 ----17 ----22 ---28
5 ------------6.9--- 14 ----21 ----28--- 35
3 armour save
BS ----- T--- -2 --- -1 ---- 0 ---- +1 --- +2
2 ----------- 1.9--- 3.8--- 5.6--- 7.4 ---9.3
3 ----------- 2.8--- 5.6 ---8.3--- 11 --- 14
4 ----------- 3.8--- 7.4 ---11 ----15 --- 19
5 ----------- 4.6--- 9.3 ---14 ----19 --- 23
2 armour save
BS ---- T --- -2 ---- -1----- 0 --- +1 ---- +2
2 ----------- .93 --- 1.8 ---2.8 -- 3.7 --- 4.6
3 ----------- 1.4 --- 2.7 ---4.2 -- 5.6 --- 6.9
4 ----------- 1.9 --- 3.7 ---5.6 -- 7.4 --- 9.3
5 ----------- 2.3 --- 4.6 ---6.9 -- 9.3 --- 15
For the future, a twin-linking adjustment, reroll to wound, and other less common modifiers. Also, probabilities of damaging a vehicle in 40k.
-Paul Harkonen