How do you do mathhammer?

[Ravinsild]

Is there a formula or a chart somewhere I can find to start doing the maths myself? 

Apparently 3 to hit 3 to wound is a 45% chance. How do you arrive at this? What’s 3 to hit 4 to wound? Is 4 to hit 3 to wound the same probability to cause a wound? What about versus the save (6+, 5+, 4+) and how do you factor in rend? 

I feel like to really get good at the game I need to know what my average chance of dealing damage is versus how much saves my enemy has. 

Like a keeper of Secrets with a -2 to be hit takes all my guys up to a 5/6+ to hit with still a 3+ to wound which probably changes how many wounds would probably go through, so what’s my best unit to smash that to remove it, it has 10 wounds and a 4+ save, but it’s tricky to hit thanks to the Hellstrider escort always with it. 

How do I figure out my units odds of getting the winning trade? What’s mathhammer? 

[fued]

heres an example;

20 attacks hitting on 4s wounding on 3s with 1 rend and 2 damage. vs a 4+ armour, rerolling saves of 1

if you hit on 4s, you take your attacks(20) and times it by 0.5 (which is half, as 4/5/6 is half the dice rolls)

so with your 10 hits, you now times it by the amount you wound, which is 0.66666 (or 3/4/5/6, which is two thirds)

now with your 6.66 wounds, you take his armour saves (it would be 0.5(4/5/6), but you have rend 1, taking it to 0.3333 saved (only 5 and 6) but he rerolls ones, meaning you take 0.333 and times it by 7/6 for 0.3885, meaning he saves around 39% of the hits, so now taking 6.66 and multiplying it by 0.61(100%-39% is how many you will DEAL) means you will get through 4 times, you then times that by 2 for 2 damage, so 8 damage in total is dealt ON AVERAGE

now if you want to figure out a likely minimum (80% of the time this will happen), or potential maximum(0.001% of the time this will happen) you need to go more extreme, but averages tend to be enough to give you a good estimate 

[Ravinsild]

4 minutes ago, fued said:

heres an example;

20 attacks hitting on 4s wounding on 3s with 1 rend and 2 damage. vs a 4+ armour, rerolling saves of 1

if you hit on 4s, you take your attacks(20) and times it by 0.5 (which is half, as 4/5/6 is half the dice rolls)

so with your 10 hits, you now times it by the amount you wound, which is 0.66666 (or 3/4/5/6, which is two thirds)

now with your 6.66 wounds, you take his armour saves (it would be 0.5(4/5/6), but you have rend 1, taking it to 0.3333 saved (only 5 and 6) but he rerolls ones, meaning you take 0.333 and times it by 7/6 for 0.3885, meaning he saves around 39% of the hits, so now taking 6.66 and multiplying it by 0.61(100%-39% is how many you will DEAL) means you will get through 4 times, you then times that by 2 for 2 damage, so 8 damage in total is dealt ON AVERAGE

now if you want to figure out a likely minimum (80% of the time this will happen), or potential maximum(0.001% of the time this will happen) you need to go more extreme, but averages tend to be enough to give you a good estimate 

Hmmm I see. I wonder if there’s a chart that shows what the % of each dice face has somewhere (2+, 3+, 4+, 5+, 6+) etc... 

that way I can just plug in the % corresponding to the amount of attacks and damage and so forth. 

[EldritchX]

You don't really need a chart for this. It's simply the number of successful faces /6. Eg: 3+ means 4 successful faces (3,4,5 and 6), so it's 4/6 =2/3 or approximately 67%.

To understand how things like modifiers affect your damage output, you need to look at your original success chance and compare it to the success chances after modification. Eg: if you were hitting on 4 before (50%), -2 cuts that to 1/6, which is a third of 50%, so it has cut your damage output to a third of what it was before.

You don't necessarily need to know the numbers exactly to be good at the game; just general guidelines can be enough. For example, the better your chances to hit to begin with, the less you'll be affected by -to hit modifiers. It's the opposite with armour saves. The worse your saves are to start, the less your resilience will be affected by Rend, and vice versa: the better your opponent's armour saves, the more important for you to have Rend.

Applying such guidelines to the meta: in 2.0, -to hit has become significantly more common, while good armour saves have become less common, so good WS/BS has become relatively more important while Rend relatively less. 

[JackStreicher]

It‘s simple math:

a dice can show 6 numbers. If you want to know how likely it is to see ONE number if you roll the dice that would be one number out of 6 which is written 1/6 (~16% chance).

 

now let‘s say you want to know the chance of a Unit to wound an enemy:

10 Models, each 2 attacks. Hitting 4+, wounding 3+.

alright m, 4+ means that the following numbers are a success: 4,5,6.

that‘s three out of 6 numbers -> 3/6 (you can shorten that to 1/2).

multiply with the number of attacks:

20 Attacks * 1/2 = 10 attacks will hit.

now the 3+ -> 3,4,5,6 -> 4/6 (shortened to 2/3).

multiply this with the amount of attacks that did hit.

10 * 2/3 = 6,6666 

you will do 6,666 wounds

now you can do the same with the armour save though it‘s a bit different.

since you want to know how many wounds get through the armour you check the armour save (for example 5+). 5+ means that 5,6 -> 2/6 would be stooped by armour.

you want to know how many will NOT be stopped by armour. So you substract The chance of The armour save from The Maximum dice number:

6/6 (Max dice number) - 2/6= 4/6 will get through.

anount of wounds * 4/6 (shortened to 2/3)

6,6666 * 2/3 =~ 4,4

[Tiger]

3 hours ago, fued said:

meaning you take 0.333 and times it by 7/6

What does 7/6 represent?

[Ravinsild]

56 minutes ago, JackStreicher said:

It‘s simple math:

a dice can show 6 numbers. If you want to know how likely it is to see ONE number if you roll the dice that would be one number out of 6 which is written 1/6 (~16% chance).

 

now let‘s say you want to know the chance of a Unit to wound an enemy:

10 Models, each 2 attacks. Hitting 4+, wounding 3+.

alright m, 4+ means that the following numbers are a success: 4,5,6.

that‘s three out of 6 numbers -> 3/6 (you can shorten that to 1/2).

multiply with the number of attacks:

20 Attacks * 1/2 = 10 attacks will hit.

now the 3+ -> 3,4,5,6 -> 4/6 (shortened to 2/3).

multiply this with the amount of attacks that did hit.

10 * 2/3 = 6,6666 

you will do 6,666 wounds

now you can do the same with the armour save though it‘s a bit different.

since you want to know how many wounds get through the armour you check the armour save (for example 5+). 5+ means that 5,6 -> 2/6 would be stooped by armour.

you want to know how many will NOT be stopped by armour. So you substract The chance of The armour save from The Maximum dice number:

6/6 (Max dice number) - 2/6= 4/6 will get through.

anount of wounds * 4/6 (shortened to 2/3)

6,6666 * 2/3 =~ 4,4

Man, in 6th grade I spent almost all of math class out in the hall and fractions always never made much sense to me but I think I’m getting it. 

Mae started learning fractions in 6th grade at my school maybe a bit in 5th. 

Never been much of a math person but I want to know which list to bring for my game on Friday and how likely my guys are to actually successfully attack the enemy (Slaneesh with the Hellstrider -1 to hit aura). 

[JackStreicher]

1 hour ago, Ravinsild said:

Man, in 6th grade I spent almost all of math class out in the hall and fractions always never made much sense to me but I think I’m getting it. 

Mae started learning fractions in 6th grade at my school maybe a bit in 5th. 

Never been much of a math person but I want to know which list to bring for my game on Friday and how likely my guys are to actually successfully attack the enemy (Slaneesh with the Hellstrider -1 to hit aura). 

rule of thump also helps:

to hit and to wound (showing you how much you put through

6+ means ~ 16%  (16,666%)
5+ means ~ 30% ( ~ 33,32%)
4+ means     50% 
3+ means ~ 65% (66,64%)
2+ means ~ 80% (83,33%)

Amount of Misses = 100% - the above table at the according position

 

Against armour, showing you how much you get through (6+ etc being the armous save)

6+ means ~ 80% (83,33%)
5+ means ~ 65% (66,64%)
4+ means     50% 
3+ means ~ 30% ( ~ 33,32%)
2+ means ~ 16%  (16,666%)

 

Rerolls to hit and or wound and armour showing the additional hits you score with rerolling.

1s :  Misses * 1/6 (16%) * (to hit chance) 

1s and 2s: Misses * 2/6 (16%) * (to hit chance)

etc.

etc.

Means: With rerolling 1s one out of every six (1/6) of the missed attacks are ones, so you can reroll them. Then you multiply the amount of ones with your hit chance.

 

General rerolls, shwoing you how much hits you score INCLUDING rerolling:

(Attacks * hit chance) + (Attacks * (100% - hit chance) * (Hit chance)
....Actual Hits............... +  ............Missed attacks................... * Hit chance

 

 

[Satyrical Sophist]

Math hammer can definitely go too far, but I like to use it to have a rough idea what is a reasonable expectation of what's possible. An example would be knowing that a Gavespawn beastlord will on average kill a Stormcast hero in one phase. If he didn't, it wouldn't be worth going first with him. Or that your unit can probably kill or cripple the unit it charges, since your unit is a glass cannon.

If it's "easy" (simple numbers, only one type of attack etc) then I generally work it out in my head. If there are a lot of different attacks, or more complicated stuff, I tend to use a spreadsheet. 

[Dead Scribe]

Math hammer is essential if you want to do well, particularly at the upper end tables.  I don't know any really good players that don't utilize math hammer heavily.

Math hammer is how you know the probability of success for any given action and how you can target prioritize on the table.  You don't want to be doing things that are low chance moves unless you absolutely have to and conversely you want your opponent to only be able to do low chance moves if you can.

Before any given turn I math hammer out every potential charge and every action and have a success probability assigned to each action so that I can choose the best ones.

[Enoby]

Everything said on here is great, but if you want easy mathhammer on the fly, I've found this site really useful: http://tools.druchii.net/AoS-Simple-Calculator.php

 

It doesn't account for everything (there is a more complex version), but it can be useful to get a rough normal distribution of damage. 

[Nos]

Bear in mind that percentages are not a way of predicting the future. You could have 100 hits on 2+ and miss all of them. 

If you really want to win consistently at AOS you need to master the things you have complete reliable control of which is movement and placement. 

 

[Overread]

Like all things there is no one magic solution/strategy. Mathhammer helps people understand how to read the stats on units. Eg it helps them get that a 3+ is a 4/6 chance and a 4+ is a 3/6 chance. Those lines of thinking can be very important when it comes to making good movement and placement choices in the game.

 

Like many things its not about one big solution, but lots of little bits that all add up to the choices. By breaking it down into segments, like mathhammer, it starts to become easier to digest as a subject. 

[AaronWilson]

2 hours ago, Dead Scribe said:

Math hammer is essential if you want to do well, particularly at the upper end tables.  I don't know any really good players that don't utilize math hammer heavily.

Math hammer is how you know the probability of success for any given action and how you can target prioritize on the table.  You don't want to be doing things that are low chance moves unless you absolutely have to and conversely you want your opponent to only be able to do low chance moves if you can.

Before any given turn I math hammer out every potential charge and every action and have a success probability assigned to each action so that I can choose the best ones.

How long do your turns take out of interest? 

[Dead Scribe]

I play entire games under 2.5 hours because thats the tournament standard.

[Hankster]

9 hours ago, fued said:

heres an example;

20 attacks hitting on 4s wounding on 3s with 1 rend and 2 damage. vs a 4+ armour, rerolling saves of 1

if you hit on 4s, you take your attacks(20) and times it by 0.5 (which is half, as 4/5/6 is half the dice rolls)

so with your 10 hits, you now times it by the amount you wound, which is 0.66666 (or 3/4/5/6, which is two thirds)

now with your 6.66 wounds, you take his armour saves (it would be 0.5(4/5/6), but you have rend 1, taking it to 0.3333 saved (only 5 and 6) but he rerolls ones, meaning you take 0.333 and times it by 7/6 for 0.3885, meaning he saves around 39% of the hits, so now taking 6.66 and multiplying it by 0.61(100%-39% is how many you will DEAL) means you will get through 4 times, you then times that by 2 for 2 damage, so 8 damage in total is dealt ON AVERAGE

now if you want to figure out a likely minimum (80% of the time this will happen), or potential maximum(0.001% of the time this will happen) you need to go more extreme, but averages tend to be enough to give you a good estimate 

Thanks Feud that is quite helpful. It looks like my guestimations for my eels and king were about right.

...now I just need to get better a actual tactics and not getting sucked into charging too soon. 

[peasant]

I use python scripts of my own, is so fun!

import random

d6=random.choice([1,2,3,4,5,6])

and let the magic flow

[AaronWilson]

Maybe I should start doing this, though normally I do some quick maths on the spot roll the dice which is shortly proceeded by "bollocks". 

[Dead Scribe]

The more you do it the faster you get at it.

[Ravinsild]

4 hours ago, Enoby said:

Everything said on here is great, but if you want easy mathhammer on the fly, I've found this site really useful: http://tools.druchii.net/AoS-Simple-Calculator.php

 

It doesn't account for everything (there is a more complex version), but it can be useful to get a rough normal distribution of damage. 

I’ve tried using it but I don’t understand the results. 

[Drofnum]

I made an app that is on the play store that I use for mathhammer, I can do the math in my head but really dont see the point when its easier to just type numbers in to my phone.

I also only really find it useful for theorycrafting and dont tend to use it at all when playing.  Although I guess it does help knowing the potential damage of units, you have a better idea of where to send them if you know what they can kill reliably.

[Dead Scribe]

Heres an example that came up in my last game.

I have a unit that hits on 3s and wounds on 4s with -1 rend and 2 damage with at this point 2 attacks each.  I have eight models remaining.

They are parked near an objective with another unit.  My other unit holding the objective is largely only there to hold objectives.  It cannot fight very well without being babysat by a hero that had died at this point.

I can charge one of two targets, OR hold back.

Target 1:  2 wounds a piece, 4+ save - 5 of them left

Target 2:  1 wound a piece, 5+ save, 18 of them

8 models with 2 attacks = 16 attacks 3s hit 4s wound -1 rend
I'll hit 10.7 of them on average and do on average 5.4 wounds before they roll dice.

The 4+ save is a 5+ save and I will sneak in 3.6 wounds on average or do 7.2 damage
The 5+ save is now a 6+ save and I'll get in 4.5 wounds on average or do 9 damage

I won't kill either unit on average regardless of what I charge, but the 2 wound a piece unit will almost be destroyed where as target 2 will be at about half strength still.

Depending on where we are in the game, if I need the points I'll go after target 1.  Target 2 in a late game I'd likely ignore.  If I'm up in points and objectives, I'd sit back and do nothing except screen my objective better.

If you can't do the mathhammer on this then you're just as likely to always charge something since thats what "feels right".  But thats not always the best option and knowing the odds and probability helps you make better decisions.  
 

In my game it was the last turn and had I charged in I would have given him two guaranteed parts of the turn to beat on my unit and score secondary points off of me so since I didn't feel getting even more points was worth it and I wanted to make sure that the spread was as wide as I could (because the event put standings around how much you scored vs how much was scored on you) I opted to hold.

[Retro]

1 hour ago, Ravinsild said:

I’ve tried using it but I don’t understand the results. 

Have you tried this one?

http://cutitcustom.co.uk/kmh/aos.php

It was created by a tga user a while back and I just found his link to it in an old post

[Ravinsild]

8 minutes ago, Retro said:

Have you tried this one?

http://cutitcustom.co.uk/kmh/aos.php

It was created by a tga user a while back and I just found his link to it in an old post

Now that is exactly what I wanted. Thanks!

[Retro]

11 hours ago, Tiger said:

What does 7/6 represent?

If you have rerolling 1s, it is the effective modifier to work out the extra hits.

To expand it out, you work out the odds of hitting with reroll 1s:

Attacks*hit chance + Attacks*hit chance*1/6

If you take "attack*hit chance" out as the common factor you get:

Attacks*hit chance*(1+1/6)

Which is:

Attacks*hit chance*7/6