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.