Probability in Warhammer Underworlds - Part 2 Defending

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Checkout my Warhammer Underworlds - Contents Page for more articles.
 
This is part 2 of a little series on Probability in Warhammer Underworlds.

A few days ago, I took a look at the probability of a successful attack in Warhammer Underworlds. However, for an attack to be truly successful it has to beat the opponents defence and cause damage.

The black defence dice in Underworlds have 6 sides and 5 unique symbols. The Block symbol, or 'shield' is the symbol that appears on two sides of the die. All of the other symbols only appear once.

With a single die defence and no support, the most effective defence is Block. So, how do we calculate this success.

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


When a single dice 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 Dodge being rolled.

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

So to calculate success (with a single die),  we need to count the number of sides that would be successes and divide it by the number of faces on the die. When calculating success, with multiple dice, we need to consider the chance of failure first, in order to calculate success.

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

As an attacker, we are most interested in the chance of opponent's failure. Whereas the defender, is clearly, more interested in the chance of success.

As block appears on the dice more times than dodge, which is better, a two dice Dodge or a single dice Block?

We will make the assumption that the defence does not have any supports. 


Myari. The 2 dice Dodge defence.

As discussed, each attack dice has one Dodge and a single Crit on it. Therefore, there are 4 chances for failure (4/6). Then there are two dice, so 4/6 x 4/6 = 16/36. The percentage for failure for this defence is (16/36) 44%.  The chance of success is (20/36) 56%. Additionally, the chance for a critical success is 30.5%. Overall,  a slightly better than 50:50 chance.


Ailenn. The 1 dice Block defence.

Each dice has two Block and one Crit on its faces. Therefore, there are 3 chances for failure (3/6) on a single dice. The percentage for failure for this defence is (3/6) 50%. Therefore, the chance of success is (3/6) 50%. The chance for a critical success is 16.67%

Unsurprisingly, in this scenario more defence dice is better, mainly due to the increased chance of rolling a Crit.

How much does guard improve your defence?

Putting a fighter on guard increases the chances of the defence, but is it good enough to be worth using an activation for?


If a two dice Dodge fighter goes on Guard the chance of success increases from 55% to 88%. In other words, they go from failing the defence once out of two rolls to once out of ten rolls!

So, for a Dodge fighter, Guard can play a significant role in their defence. This may be particularly useful for a Dodge fighter with a range attack. As once they are on Guard, they no longer need to move. Hadzu Inspired in the back lines, on Guard could be difficult to remove from the board.


Fighters with block, obviously do gain from Guard but the benefit is less significant. A two dice Block fighter on Guard increases the chance of success from 75% to 88%. In other words, they go from failing the defence once out of four rolls to once out of ten rolls. Clearly still good.

Guard may be of less value to a Block fighter especially, if they need to move/charge to attack.

Calculating defence failure as part of a successful attack.

So how do I calculate the chance that an attack will cause damage?

Chance of attack success x Chance of defence failure = Chance of Damage

Here are some examples of how to calculate chance of damage.

Slakeslash attacks Ailenn, what is the chance he will cause damage?


Slakeslash has a 70.37% chance of success (with his 3 Fury attack) and Ailenn has a 50% chance of failure (with her 1 Block defence).

70.37% x 50% = 35.18% chance of damage.

This does not take into account the chances of Critical success, which improves the chance of damage because the attacker is rolling more dice than the defender. 

Aileen attacks Hadzu, what is the chance he will cause damage?


Ailenn has a 75% chance of success (with her 2 Smash attack) and Hadzu has a 66.67% chance of failure (with his 1 Dodge defence).


86.11% x 44.44% = 49.5% chance of damage.

This does not take into account the chances of Critical success, which improves the chance of damage because the attacker is rolling more dice than the defender. 

Inspired Ailenn attacks Inspired Hadzu, what is the chance she will cause damage?


Ailenn Inspired has a 86.11% chance of success (with her 3 Smash attack) and Hadzu Inspired has a 44.44 % chance of failure (with his 2 Dodge defence).

86.11% x 44.44% = 38.26% chance of damage.

This does not take into account the chances of Critical success, which improves the chance of damage because the attacker is rolling more dice than the defender. 

This one is particularly interesting as the value of extra defence dice, is greater than the value of extra attack dice. Leading me back to Formidable Defence.

Glisette's Formidable Defence

Protect by the Unseen from the Paths of Prophecy Rivals deck


As I was writing this article, I started to consider the role of Glissette. She is clearly in the warband to absorb damage rather than to cause it. She starts with a two Dodge defence and has guard. So she has a solid chance of defence of 88%.

Then I decide to play Protected by the Unseen on her. After all, I want to her to run into the opposing half and stand on an objective. The main point here is that she gains a defence dice. Now her chance of success increases to 96%, in other words she should be successful 19 times out of 20! As a player has 12 activations in a game, they could in theory attack Glissette 12 times. The probability suggests she should survive every attack in a game (although in reality, she will fail first time I try this).
 
One final thought to consider. 

If the number of dice rolled in the attack is higher than the number of defence dice, the chance of success is increased due to the attacker having a greater chance of scoring a Crit.
If the number of dice rolled in the attack is less than the number of defence dice, the chance of success is decreased due to the defender having a greater chance of scoring a Crit.

Having written these two articles, I am starting to think that maybe just running in and trying to hit something is not really the way to play the game... it could be fun though ("Blood for the Blood God" - Magore Redhand). I wonder how magic works? I better take a look!

Part 1 - Attacking Probability can be read here.

Part 3 - Magic Probability can be read here.

Thanks for reading. Who do you rely on to protect the objectives in Underworlds? What are best defensive upgrades? Let me know your thoughts in the comments below. Take care and I hope you come back soon.

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