The math behind Mk3 Tough
by Flynnt ·
The world as we know is ending, or so you may think if you have lately visited the privateer press forums or the faction facebook groups. One of the changes that have swept the board is the change to tough. Namely, the fact that if a model is knocked down it does not get to do a tough check anymore.
This seems like a huge change, right? I mean, a model that passes her tough check and its knocked down will get killed by the next attack. However, tough checks were already rare, believe me, they never work out on my games!
So I decided to check the math on it, specifically: “how many more attacks it would take to wipe a unit in Mk2 than it would on Mk3?”. I decided to make a small function to actually measure that (the code is at the end of the post). There are only two variables: how many members does the unit have and what are the odds of actually forcing a tough check. For instance, in a 10 man unit if the attacker needs 5’s to force a tough check:
Mk2- The expected number of attacks that takes to wipe a  man unit is [18.0] Mk3- The expected number of attacks that takes to wipe a  man unit is [16.0]
In a ten man (or troll, or dwarf, or construct) unit, it only takes 2 or 3 more attacks to wipe the full unit:
Also, the troll players just got a unit with shield guard, which should allow the stone to be more forward and give the troopers a +2 ARM. On that case, Mk3 troopers will require more attacks to be fully wiped. That increase in the probability of forcing tough checks saves the units in Mk3.
Furthermore, command checks are gone! People are forgetting that when a unit was reduced to their last members, command checks started to play into action, this is gone in Mk3. Therefore, even though you may need 2 or 3 more attacks to kill all the member on the unit,
Yes, tough has changed. Yes, on the vacuum it will take between 2 and 3 more attacks to wipe 10-man full unit, less than 2 attacks on a 5-man unit. However, an important variable is the armor, increasing it slightly fixes the fact tough has changed. Furthermore, removing command checks makes the unit more durable, even if it is hard to evaluate how much, and it may be enough to keep the units as strong, if not stronger, than before.
This code was used to measure the expected attacks that take to wipe a unit, beta is the probability of forcing a tough check.
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