The Probability of Two Die Blocks in Blood Bowl

These days, I almost always play Amazons in Blood Bowl leagues. I started as a Norseman, I experimented with Skaven, but ultimately the Amazon are my team. Why? Because I love the consternation it causes my opponent when my girls just don't fall over.

Many of the opponents complain throughout the game that my team never gets knocked over - while their own players are routinely on the ground or, worse yet, knocked off the pitch. They gather up their assists, throw lots of two-die blocks, and assume that this means my players should fall over.

Unfortunately, they vastly underestimate the value of dodge and therefore mis-calculate the probability of my players actually falling over.

Saurus vs. Amazon Linewoman

Let's take an example from today. I just routed my friend's Lizardman team (4-0, partly because he played the second half with only two healthy skinks) and he couldn't believe how rarely the Amazons were getting knocked over.

A Strength 4 Saurus will naturally get two dice against a Strength 3 Amazon Linewoman (assuming that there are no assists involved). Seems good for the Saurus. What are the possible outcomes?

First, we need to figure out the probability of each outcome for one die. The Saurus has a 1/6 chance of knocking the Amazon down and standing up, a 1/6 chance of knocking them both over, a 1/6 chance of falling over himself, and a 3/6 chance of pushing the Linewoman around. Assuming he only considers a Bamf ("Defender Down") as a success, he only has a 1/6 chance of succeeding with one die! (For more on this subject, read my other post about the probability involved in one-die blocks).

With this in hand, we can calculate the probability that either of the two dice will come up with a success. The math is simple: 1/6 + 1/6 - (1/6 * 1/6) = 11/36 or roughly 30% (For more on how this calculation works, see this explanation of the probability involved in rolling dice). Even with the inherent strength advantage, the Saurus has less than a one in third chance of successfully knocking the Amazon over.

Dwarf Blocker vs. Amazon Linewoman

Now let's consider a very different situation: a Dwarf Blocker trying to take down an Amazon Linewoman. In this case, the Dwarf brings Block and Tackle to the table, so the Linewoman is essentially skill-less (Dodge is negated by the Tackle).

Now, the Dwarf has a 3/6 chance of knocking the Amazon down with one die. He also has a 1/6 chance of falling over himself and a 2/6 chance of pushing the Amazon back. If the Dwarf has an assist and he is allowed to choose from two dice, he has a (3/6 + 3/6 - 9/36 = 27/36) 75% chance of knocking over the Amazon. Ouch. That's gonna hutr.

In this case, the addition of Block and Tackle make a huge difference. Whereas the Saurus was unlikely to knock the Amazon over, the Dwarf is very likely to be successful and very unlikely to knock himself over (~2.3%).

Human Blitzer w/ Tackle vs. Amazon Blitzer

Let's say that a Human Blitzer gets a skill-up and takes tackle. No, he feels confident and wants to take out an Amazon blitzer (Block and Dodge).

Thanks to Tackle, he's got a 2/6 chance of knocking her over with one die. 1/6 of the time he'll fall over and 1/6 of the time nothing will happen. The other 2/6 chance is a push-back.

If the Human Blitzer has an assist and chooses from two block dice, he's got a (2/6 * 2/6 - 4/36 = 20/36) 56% chance of successfully knocking over the Blitzer. While he's not as likely as the Dwarf to be successful, the addition of Tackle still gives him a big edge over the Saurus.

Dodge Is Awesome, When Your Opponent Doesn't Have Tackle

The presence of Dodge - and subsequently the presence or absence of the tackle skill - has a huge impact on the outcome of a two-die block. Thanks to Dodge, Amazons are very resilient against teams with few skills (think Lizardmen, Orcs, Humans, Elves). Dwarves are a big problem because the introduction of both Block and Tackle makes most of the Amazon team (besides the blitzers) easy to take down).

The lesson here is that one skill can make a big difference in the outcome of a block. Don't assume that you should be able to knock over the other team just because you get to roll two dice. If that team has Dodge (and half of them might have Block two), you're in for a whole load o' pushing. Get used to it.