Well, this is my system for finding out how likely X is to wound Y. It works awesomely for me, and doesn't even require a calculator if you're decent at math. So, here's how it's done:
Creatures:
As we all should know, when you are shooting or assaulting an enemy non-vehicle model, you need to roll to hit, to wound, and then your opponent rolls to save. Thus, on any given attack, there will be (up to) 3 dice rolls. Each of these rolls have 6 possibilities, and this is where we get our perfect number:
216
216 is 6x6x6, or six times six times six, representing all three dice rolls. You start with your basic roll to hit, divide, roll to wound, divide, and roll to save, divide, and you get your fraction. That might've been hard to understand, so I'll do an example:
Tau Pulse Rifle fire versus Tactical Space Marines:
216 shots... Tau Fire Warriors roll a 4+ to hit, which is essentially a 50%. So, divide your number of shots in half, thus, reducing your 216 to...
108
Tau Pulse Rifles have one more point of Strength than Tactical Space Marines have Toughness. Thus, Pulse Rifles get a 3+ to wound. 3+ is 2/3 of a d6, so, divide your number by 3 and multiply by two... 108/3=36... times 2=...
72
Pulse Rifle AP does not beat Tactical Space Marine armour saves, so the Marine will get to roll his save. With the saves, your numbers are inverted. So, for your purposes, a 3+ is a 5+, and a 2+ is a 6+, and vice versa. 1's are the nonexistant save, and thus, don't come into effect. Okay, so, the Marine gets his 3+ save, meaning that 1/3 of your 72 wounds inflicted will be deflected by his armour. 72/3=...
24
So, now you have your final fraction. 24/216. This fraction can, and should, be reduced. 216 will always be divisible by any factor of the smaller number, so go by the smaller number's factors. Let's start with 2. 24/2=12. 216/2=108, as we already know. These numbers can be divided by 2 again, so... 12/2=6. 108/2=54. We can divide by 2 again... 6/2=3. 54/2=27. Now we can divide both of these numbers by 3. So... 3/3=1. 27/3=9. And thus, your final fraction is...
1/9
1/9 pulse rifle shots will successfully hit, wound and kill a space marine. This system can be applied with any attacks, shooting or close combat, against any unit.
Vehicles:
Against vehicles, you need to use a slightly different system. Since the Armour Penetration Table has 6 different effects in each section (glancing, penetrating, ordnance), you need to multiply your perfect number by 6, which can start to give you a headache. The Vehicle perfect number is 1200+60+36=1296. Big, scary number, but you may find it useful. So, I'll do a more brief example with the armour values. In this situation, I'll use two popular items: The Krak Missle (available to most races), and the Space Marine Dreadnought (front/side armour).
So, we start with our Vehicle perfect number. 1296. Let's say I'm shooting with and Eldar Dark Reaper Exarch, who has a 2+ to hit. For the 2+, I prefer to find the number and subtract it from my perfect number, rather than multiply the number by 5. So, 1296/6=216. 1296-216=1080. Now, things get a touch complicated. A krak missle will damage a vehicle on a 4+, but one of these will be a Glancing hit, where two are Penetrating hits. So, 1/6 will be glances, and 1/3 will be Pen.s. 1080/6=180. 1080/3=360. So, out of our initial 1296 Krak Missiles, 180 will glance, and 360 will penetrate. Then, we divide this number by 6 again, for each of the effects. 180/6=30, 360/6=60. Thus, each glance will have 30 occurences of each damage, and each pen will have 60. So, now it is time to reduce.
30/2=15, 60/2=30, and 1296(your base number)/2=648.
15/3=5, 30/3=10, and 648/3=216(hey!)
Now, understanding 5/216 and 10/216 will be a bit tough, let's reduce 10/216:
10/2=5, 216/2=108.
So, after all is said and done, out of 216 shots from an Eldar Dark Reaper Exarch Krak Missle, you will get 5 of each glance damage, and 10 of each pen. This seems like a small number, but it really isnt. If do not include the damage charts, you will have 30/216 glances, and 60/216 Penetrates, making 90/216 shots effective after rolling to hit and to "wound". 90/216=45/108=15/36=5/12. 5/12 doesn't seem too bad, does it? To find the fine specifics, you will probably need a calculator and a codex or two. I would cite all the occurences that would happen, but I am currently in Japan and separated from my books, so I am unable to do this.
So, for a wrap-up, when rolling against infantry, make a fraction out of 216 and reduce, and against vehicles, use the same if you want to know how often you will damage, or use 1296 if you want to know the rate of occurrence of each individual effect. I hope this has been useful/interesting for all of you who have read, and I hope I will see people using this system in the forums to compare units and the like. Thanks for reading.
Creatures:
As we all should know, when you are shooting or assaulting an enemy non-vehicle model, you need to roll to hit, to wound, and then your opponent rolls to save. Thus, on any given attack, there will be (up to) 3 dice rolls. Each of these rolls have 6 possibilities, and this is where we get our perfect number:
216
216 is 6x6x6, or six times six times six, representing all three dice rolls. You start with your basic roll to hit, divide, roll to wound, divide, and roll to save, divide, and you get your fraction. That might've been hard to understand, so I'll do an example:
Tau Pulse Rifle fire versus Tactical Space Marines:
216 shots... Tau Fire Warriors roll a 4+ to hit, which is essentially a 50%. So, divide your number of shots in half, thus, reducing your 216 to...
108
Tau Pulse Rifles have one more point of Strength than Tactical Space Marines have Toughness. Thus, Pulse Rifles get a 3+ to wound. 3+ is 2/3 of a d6, so, divide your number by 3 and multiply by two... 108/3=36... times 2=...
72
Pulse Rifle AP does not beat Tactical Space Marine armour saves, so the Marine will get to roll his save. With the saves, your numbers are inverted. So, for your purposes, a 3+ is a 5+, and a 2+ is a 6+, and vice versa. 1's are the nonexistant save, and thus, don't come into effect. Okay, so, the Marine gets his 3+ save, meaning that 1/3 of your 72 wounds inflicted will be deflected by his armour. 72/3=...
24
So, now you have your final fraction. 24/216. This fraction can, and should, be reduced. 216 will always be divisible by any factor of the smaller number, so go by the smaller number's factors. Let's start with 2. 24/2=12. 216/2=108, as we already know. These numbers can be divided by 2 again, so... 12/2=6. 108/2=54. We can divide by 2 again... 6/2=3. 54/2=27. Now we can divide both of these numbers by 3. So... 3/3=1. 27/3=9. And thus, your final fraction is...
1/9
1/9 pulse rifle shots will successfully hit, wound and kill a space marine. This system can be applied with any attacks, shooting or close combat, against any unit.
Vehicles:
Against vehicles, you need to use a slightly different system. Since the Armour Penetration Table has 6 different effects in each section (glancing, penetrating, ordnance), you need to multiply your perfect number by 6, which can start to give you a headache. The Vehicle perfect number is 1200+60+36=1296. Big, scary number, but you may find it useful. So, I'll do a more brief example with the armour values. In this situation, I'll use two popular items: The Krak Missle (available to most races), and the Space Marine Dreadnought (front/side armour).
So, we start with our Vehicle perfect number. 1296. Let's say I'm shooting with and Eldar Dark Reaper Exarch, who has a 2+ to hit. For the 2+, I prefer to find the number and subtract it from my perfect number, rather than multiply the number by 5. So, 1296/6=216. 1296-216=1080. Now, things get a touch complicated. A krak missle will damage a vehicle on a 4+, but one of these will be a Glancing hit, where two are Penetrating hits. So, 1/6 will be glances, and 1/3 will be Pen.s. 1080/6=180. 1080/3=360. So, out of our initial 1296 Krak Missiles, 180 will glance, and 360 will penetrate. Then, we divide this number by 6 again, for each of the effects. 180/6=30, 360/6=60. Thus, each glance will have 30 occurences of each damage, and each pen will have 60. So, now it is time to reduce.
30/2=15, 60/2=30, and 1296(your base number)/2=648.
15/3=5, 30/3=10, and 648/3=216(hey!)
Now, understanding 5/216 and 10/216 will be a bit tough, let's reduce 10/216:
10/2=5, 216/2=108.
So, after all is said and done, out of 216 shots from an Eldar Dark Reaper Exarch Krak Missle, you will get 5 of each glance damage, and 10 of each pen. This seems like a small number, but it really isnt. If do not include the damage charts, you will have 30/216 glances, and 60/216 Penetrates, making 90/216 shots effective after rolling to hit and to "wound". 90/216=45/108=15/36=5/12. 5/12 doesn't seem too bad, does it? To find the fine specifics, you will probably need a calculator and a codex or two. I would cite all the occurences that would happen, but I am currently in Japan and separated from my books, so I am unable to do this.
So, for a wrap-up, when rolling against infantry, make a fraction out of 216 and reduce, and against vehicles, use the same if you want to know how often you will damage, or use 1296 if you want to know the rate of occurrence of each individual effect. I hope this has been useful/interesting for all of you who have read, and I hope I will see people using this system in the forums to compare units and the like. Thanks for reading.