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Dkoz
27-09-2015, 18:13
I'm not sure if this is the right place to post this so if it needs to be moved feel free.

I haven't had to do the kind of math it take to figure out the percentages for dice rolling in 40K in sometime. Does anyone know of a good YouTube video or website that could explaine how to do the math so I could brush up and improve my army building skills?

wyvirn
27-09-2015, 20:16
I find it easier to deal with fractions than pure percentages. After a while it becomes fairly easy to work through a scenario. The trick is to multiply the chance to succeed to wound.

For example, a marine versus a chaos marine in CC. ( S4 versus T4)
To hit-3/6=1/2
To wound - 3/6= 1/2
Armor - 2/6 = 1/3
1/2*1/2*1/3= 1/12
So you need 12 attacks to deal a wound *on average*.

Now a Space Marine firing a bolter to Hive Tyrant (T6):
To hit BS 4- 4/6=2/3
To wound S4 versus T6-1/6
Save 2/6 = 1/3
2/3*1/6*1/3=2/54=1/27

Hive Tyrant Ws5 S6 versus a marine in combat:
To hit = 4/6= 2/3
To wound -5/6
Save-X
2/3*5/6=10/18= 5/9

Sent from my iPhone using Tapatalk

mightymconeshot
27-09-2015, 20:41
Actually the math above is incorrect. But basically to do the math is chance to hit times chance to wound times chance to fail a save which will give you the percent to cause wound.

So a tactical marine firing against a T3 model with a 4+save
(2/3)(2/3)(1/2) gives a rough 20% chance to cause a wound. So 5 bolter shots would "guarantee" a wound. If the model only had one that is all it would need. If it had two wounds, 10 shots should kill it. 3 wounds needs 15 bolter rounds. And so on.

AFnord
27-09-2015, 21:16
Actually the math above is incorrect. But basically to do the math is chance to hit times chance to wound times chance to fail a save which will give you the percent to cause wound.

It looks correct to me, what do you think look wrong? Wyvirn is doing exactly the same kind of calculation as you are, but is using fractions all the way through.

Much like Wyvirn, I find fractions easier to deal with as well. The fractions are not easily converted to % in your head (and even then you don't get an exact number), but multiplying the fractions is quite easy to do on the fly. When multiplying fractions, remember that (2/3)*(2/3)*(1/3)=(2*2*1)/(3*3*3)=4/27
Converting 4/27 or (2/3)*(2/3)*(1/3) to % is not fun to do in your head.

Now if you want to simplify that (and here it's getting a bit trickier to do straight up in your head, so consider this an advanced course), take a look at the two and see if the top & bottom part have anything in common, in this case they don't.
Now let's take another example:
(2/3)*(1/2)*(4/6)*(3/6)=(2*1*4*3)/(3*2*6*6). You can see that there is a 2 in both in the numerator (top) and denominator (bottom) Remove those and you get (1*4*3)/(3*6*6). Want to simplify it further? Well 6=3*2 and 4=2*2 so you get (1*2*2*3)/(3*3*2*3*2)=1/(3*3)=1/9 (~11%)
Makes it easier to compare two units when you do this.

We could go into the difference between having 10 10% chance to hit things and 1 100% chance to hit thing. On average they'll deal as much damage, but it does impact gameplay in a different way. But I think that's for another thread.

mightymconeshot
27-09-2015, 21:26
Space Marines hits on 2/3 not 1/2 in the first example. Which changes the math. But otherwise is correct.

AFnord
27-09-2015, 21:27
Space Marines hits on 2/3 not 1/2 in the first example. Which changes the math. But otherwise is correct.
But it's in CC, not a shooting attack, against another WS4 opponent.

27-09-2015, 21:54
Personly i would find the bell curve to be much more intressting then just the basic chance to do a wound. But i gues they are all alike since it is mostly 1/3 or 2/3 chances.

Snake Tortoise
27-09-2015, 22:26
Some of the principles have been described. Imagine in a simple case of a BS4 space marine shooting a bolt pistol at a termagant. 2/3 chance to hit. 2/3 chance to wound. No armour save. The odds of the bolt pistol killing the termagant require both events to happen at the same time, which would be 2/3 (the chance to hit) multiplied by 2/3 (the chance to wound). 2/3 is approximately 0.667, so then 0.667 multiplied by 0.667 will give the probability of the shot both hitting and wounding, and it comes out to be 0.445. In other words that space marine has about a 45% chance of killing a termagant

In the case of an armour save you have to remember to use the probability of the wounded model failing their save, and not passing. Imagine this termagant had a 6+ cover save. To know how many wounds we could expect a single bolt pistol shot to cause we'd multiply the chance of hitting and wounding (we know this is 0.445) by the chance of the termagant failing its cover save (5/6 or 0.833). The answer is about 0.371, so just over a third. That tells us we should expect to shoot with three bolt pistols to kill a single termagant with a 6+ cover save.

Where mathhammer becomes more complicated are situations involved 2D6 (or 3D6 etc.), but you can google '2D6 probability' and you'll find a chart listing every result (2 to 12) and the probabilities of rolling; a specific number, a number or less than that number, a number or more than that number etc.

Other tricky situations are times when rending attacks are being calculated. You usually have separately calculate the amount of wounds caused by attacks that roll a 6 to wound, and the attacks that still wound but don't roll a 6 so an armour save can still be taken. I'd be happy to go through that if anybody is interested. Maybe in the case of a genestealer charging a tactical marine.

I like statistics so mathhammer is fun to play around with, but I usually prefer the simpler approach of just rolling dice to simulated a scenario. Like a bloodthirster of insensate rage on full wounds charging an imperial knight errant with all of its hull points. It feels a bit more real that way!

mightymconeshot
27-09-2015, 23:06
Then that is my reading comprehension skills failing me. The math would be right.

papabearshane
28-09-2015, 04:59

Yes knowing the math is sometimes a good thing, but as in any game there are things in warhammer that will drive you crazy if you let them.

30 Shootaboyz boyz 60 shots vs 5 Marines
2/6 hit (so 20 hits) 1/2 wound (so 10 wounds) fail 2/6 saves (just over 3 dead Marines)......

The math is easy, don't confuse yourself by trying to make it perfect.

Fenrisulv
29-09-2015, 20:35
2D6 is not that hard to calculate, on 1D6 there are 6 possible outcomes, with 2D6 there are 6*6=36 possible outcomes, and their probability is:
Result | Probability
2 |1
3 |2
4 |3
5 |4
6 |5
7 |6
8 |5
9 |4
10|3
11|2
12|1
The chance of rolling 7' is 6/36 which is the same as 1/6.
Failing a Ld10 test for example is (1+2)/36 = 3/36 = 1/12.

bittick
29-09-2015, 21:48

Yes knowing the math is sometimes a good thing, but as in any game there are things in warhammer that will drive you crazy if you let them.

30 Shootaboyz boyz 60 shots vs 5 Marines
2/6 hit (so 20 hits) 1/2 wound (so 10 wounds) fail 2/6 saves (just over 3 dead Marines)......

The math is easy, don't confuse yourself by trying to make it perfect.

Math is just a good guideline. It doesn't "guarantee" results. A good player has to keep in mind that just because the odds say something is the average result, this doesn't mean that's what is going to happen.

The example was given of a marine shooting a termagaunt with a 6+ cover save. The odds are .371 that a bolt pistol shot will kill a termagaunt. So you need about 3 shots to kill one, on average. But remember that's just the average. Don't get upset if you shoot 3 times and don't kill him. The odds that you won't kill him are actually pretty good. You know how we got those odds that you'd kill him? Chance to hit, times chance to wound, times chance that he fails his save? Well, a .371 chance you kill him means there's also a .629 chance that he doesn't die from that shot. Shoot him 3 times, and he's got a .629 (chance of living first time) x .629 (chance of living second time) x .629 (chance of living third time) = .24885 chance that he'll live. That's basically one in four. 25% of the time, he'll live.

Understanding the math helps you to not make mistakes. Keep it in mind next time you're gonna charge in and you think "oh yeah I'm totally gonna kill this guy". It might make you decide to not charge.

Marshal
30-09-2015, 04:07
Math is just a good guideline. It doesn't "guarantee" results. A good player has to keep in mind that just because the odds say something is the average result, this doesn't mean that's what is going to happen.

Nothing is guaranteed when dice are involved. I watched an Imperial Knight charge a Wraithknight which just got hit with grav guns (concussed) with 1 wound left (Imperial at 6 HP) and watched the Wraithknight not only come out of the first round of combat, but kill the Imperial Knight in the second round. Strange things happen in the game of dice and when dealing with them, no matter how much the odds favour one outcome over another, you just have to roll with it. (yay, dice pun!)

Snake Tortoise
30-09-2015, 07:42
To simulate scenarios with dice I like this app

https://www.random.org/dice/

Running through scenarios with dice definitely reminds me that Sod's Law should be taken into account

2D6 is not that hard to calculate, on 1D6 there are 6 possible outcomes, with 2D6 there are 6*6=36 possible outcomes, and their probability is:
Result | Probability
2 |1
3 |2
4 |3
5 |4
6 |5
7 |6
8 |5
9 |4
10|3
11|2
12|1
The chance of rolling 7' is 6/36 which is the same as 1/6.
Failing a Ld10 test for example is (1+2)/36 = 3/36 = 1/12.

That's a good way of working out 2D6 probabilities, and the table seems easy to remember if you remember there is 1/36 chance of a 2 or 12 and 6/36 of a 7. Even still, I don't think there have been times I've been figuring out 40k probabilities without an internet connection, so I'd still find it faster just to bring up a 2D6 probability table and plug the number provided into a calculation

Fingers
30-09-2015, 20:20
Chance to roll a 1 on a 2+ save model with 1 wound remaining, 100%.