Probability in Warhammer Underworlds - Part 1 Attacking

-

Checkout my Warhammer Underworlds - Contents Page for more articles.
 
This is part 1 of a little series on Probability in Warhammer Underworlds.

I have always been fond of a little bit of Math-hammer. For those not in the know Math-hammer is working out the probability of a particular role in Warhammer games. Getting to grips with probability allows, you to plan you attacks to improve their efficiency. Clearly, this can also be applied to non-Warhammer games.

Underworlds has its own unique dice, although they are still 6 sided (d6). So we can use some simple maths to work out the probability of a particular roll.

Attack Dice


The 'white' (they are different colours in different season, but in the starter box they are white) attack dice in Underworlds have 6 sides and 5 unique symbols. The Smash symbol, or 'hammer' is the symbol that appears on two sides of the die. All the other symbols only appear once.

With a single die attack and no support, the most accurate attack is with 'hammers'. So how do we calculate this success.

Let us consider all of the possible option with one die.


When a single die is rolled there is a 1/6 chance of any particular face being rolled.

So, there is a 1/6 chance (16.67%) of a Crit being rolled. There is also a 5/6 chance that Crit will not be rolled. This is really important for calculating the chance of success with multiple dice.

A 1/6 chance (16.67%) of a Fury 'Swords' being rolled.

There is a 2/6 chance (33%) of a Smash 'Hammer' being rolled because it appears twice on the die.

So to calculate success (with a single dice), we need to count the number of sides that would be successful and divide it by the number of faces on the die.

What is the chance a fighter with a single Smash attack with a single supporting fighter would successfully hit?

This fighter would therefore be successful if they rolled: Smash, Crits or Single Supports. In total, these symbol cover four of the six sides of the dice.

 A single dice smash attack with a single supporting fighter would therefore have a 4/6 chance (66.67%) of success. The is also a 2/6 chance (33.33%) of failure.

In other words this fighter should hit two out of three times.

So who has a more accurate attack, a 2 dice Smash attack or a 3 dice Fury attack?

We will assume first of all that neither attack has any supports. 

Bahannar. The 2 dice Smash attack.

As discussed, each attack dice has two Smash and a single Crit on it. Therefore, there are 3 chances for failure (3/6). Then there are two dice, so 3/6 x 3/6 = 9/36. The percentage for failure for this attack is (9/36) 25%.  The chance of success is (27/36) 75%.


Slakeslash. The 3 dice Fury attack.

Each dice has one Sword and one Crit on its faces. Therefore, there are 4 chances for failure (4/6). Then there are three dice, so 4/6 x 4/6 x 4/6 = 64/216. The percentage for failure for this attack is (64/216) 29.6%. Therefore, the chance of success is (152/216) 70.4%

So initially, the hammer attack is slightly better. Now we have to take into account the chances of a critical hit.


Here we can see, that the critical hit percentage is better for three dice rather than two dice. Not really a surprise.

With these two attacks the chances of success are very similar, albeit slightly greater for the Smash. However, the increase chance of a Crit with the three dice Fury results in this attack being harder to stop. The three dice Fury attack is more likely to result in damage to the opponent.



Increasing the accuracy of attacks

Internal Surrender from the Tooth and Claw Rivals deck

Some Warhammer Underworlds cards provide bonus dice to attacks. These in effect are increasing the accuracy of the fighters. 

Bahannar (our 2 Smash fighter) has a 75% chance of success with his attack and a 30% chance of Critical success.

Slakeslash (our 3 Fury fighter) has a 70% chance of success with his attack and a 42% chance of a Critical success.

So how much more accurate, do they become with a bonus dice?

Bahannar 

(3/6 x 3/6 x 3/6 =27/216 chance of failure, therefore 189/216 chance of success).

Has a 87.5% chance of success with a 42% chance of a Critical Success.

Slakeslash 

(4/6 x 4/6 x 4/6 x 4/6 = 256/1296 chance of failure, therefore 1040/1296 chance of success)

Has a 80% chance of success with a 51% chance of a Critical success.

What happens to my accuracy if I lose attack dice?

The obvious answer is I am less likely to be successful with my attacks.
 
Inviolate Prophet from the Paths of Prophecy Rivals deck

How big is the impact of - 1 dice from attacks?

Let's take another look at Bahannar and Slakeslash both trying to attack a fighter upgraded with Inviolate Prophet.

Bahannar would drop to a single dice attack with Smash. His chance of success would be (3/6) 50% with a 17% chance of a Critical Success. This would make him pretty bad and a fairly inefficient use of an activation.

Slakeslash would drop to (4/6 x 4/6 = 16/36 chance of failure, so a 20/36 chance of success)  55% chance of success with a 30% chance of a Critical success. While still not great, the critical success percentage is reasonable. 

Anyway that is enough of my thoughts for today. Next time, I am going to take a look at the probability of Defence.

Part 2 - Defence Probability can be read here.

Part 3 - Magic Probability can be read here.


Thanks for reading. Who do you think the best Aggro fighters are in Underworlds? Which upgrades can turn a mediocre fighter into a hero of legend? Let me know your thoughts in the comments below. Take care and I hope you come back soon.




Comments

Post a Comment

Popular posts from this blog

How I paint Rockgut Troggoth

-
Image
When I began painting my Rockgut Troggoths (Stone Trolls), I wanted them to look as though a flesh and blood creature had started to petrify. Most of the stone terrain in my collection is grey with a greenish tinge. This was the colour I wanted to replicate on my trolls. As I was painting my trolls, I made a note of the colours I used but I did not take any pictures, as I never intended to make a guide. After I had finished painting these miniatures, I decided to write up the method, in case I needed it again. Then, I thought I might as well share it. Paints required. Chaos Black spray Mechanicum Standard Grey spray Skavenblight Dinge Dawnstone Lahmian Medium  Athonian Camoshade Agrax Earthshade Administratum Grey Bugmans Glow  Rakarth Flesh Screamer Pink Cadian Fleshtone Stormvermin Fur Kislev Flesh Karak Stone Xereus Purple Mephiston Red Painting flesh of the Troggoth I began by given the miniature an undercoat with  Chaos   Black spray.  This was then followed with a light spray of 
Read more

How I paint - Gloomspite Gitz- Squigs

-
Image
When collecting Gloomspite Gitz it quickly becomes apparent that at some point you are going to paint squigs. This is my take on a classic red squig. Paints required: Wraithbone spray Khorne Red Army Painter Red Tone Averland Sunset Wazdakka Red Squig Orange Lahmian Medium Reikland Fleshwash Screamer Pink Pink Horror Pallid Wych Flesh Zandri Dust Agrax Earthshade Xereus Purple Genestealer Purple Yriel Yellow Druchii Violet .  Kantor Blue Thousand Sons Blue Ahriman Blue Temple Guard Blue . The miniatures were primed with Wraithbone spray. The scheme works over black, but you must build a nice sold layer of red at the start. This was then followed by a basecoat of Khorne Red . I thinned the Khorne Red with a little water. It took a few coats to get a nice solid finish. The miniature was then given a wash with Army Painter Red Tone thinned with a little water. The eyes were painted in with Averland Sunset .  To highlight the flesh, I began with Wazdakka Red . This was then followed by a
Read more

How I Paint - Skaven - Clan Eshin

-
Image
As I continue to work through the various Warhammer Underworlds warbands, I finally reached Skittershank's Clawpack. The Clawpack are a group of Clan Eshin Skaven. I decided to paint them in classic scheme of brown fur and black robes. Here is my guide.  More of my  How to paint... articles  can be found here. Undercoats The miniature was undercoated with Chaos Black spray . I then gave the whole miniature a basecoat of Mournfang Brown thinned, with water. Once the basecoat was dry, I gave the fur a very light drybrush with Karak Stone .  This may look a little harsh but the washes will fix this in a later stage. Basecoats The next main step, was to block in all the basecoats on the miniature. I began with the flesh on the nose, ears, hands and feet. This was painted with a 1:1 mix of Bugman's Glow and Cadian Fleshtone . I made sure to feather the edges between the fur and flesh on the hands and feet. The eyes were painted in with Mephiston Red.  The tail was painted with a 1:
Read more