An Understated Beast Part 2: Bonus Maths!

 

This article isn’t really one at all, it’s more of a follow-up to the last one. In that article I talked a lot about Cave Drakes, and how shockingly good they are at taking on heroes, especially S4 ones like Elrond. It generated lots of great discussion, some of which prompted me to get my spreadsheet back out again and do some more maths. I’ve included the conclusions from that maths in response to the relevant comments, but I thought they were worthwhile compiling here for anyone else who was interested.

The first was in response to a question from U/ExaltedSlothKing as to when one might use the Gaping Maw Brutal Power Attack. It’s an exceptionally niche rule, and its sphere of application is even smaller than it first appears.

It is theoretically sometimes worthwhile when facing W3 models with no Fate on a turn that you don't charge. Specifically, it gives you a ~67% chance to kill them, whereas Rending normally would only give you a ~59% chance of doing so. That doesn't take into account Might being used on to-Wound rolls, which would give the Rending option an ~87% chance of securing the kill, but it does show that if you have to kill a W3 F0 model this turn AND merely Wounding them won't give you any benefit AND you don't have any Might left, Gaping Maw is an improvement. That's basically only going to happen if you desperately need to kill an enemy hero on the very last turn of the game and they've got no Fate left. Even a single Fate or Might point is enough to make Rend better than Gaping Maw, as will be the case when scoring a Wound but not killing them is an advantage (literally almost every possible circumstance except the one I just listed).

                                                    The Stat Trek Binomial Probability Calculator is really useful for this sort of maths, btw

I think that its only genuine benefit is psychological rather than real. If you've got a model that can insta-kill enemies running around, then your opponent is more likely to let Wounds through on their heroes and save their Fate to try and prevent this. That could let you sneak a Wound onto an enemy leader if they don't think it through carefully or don't do the maths to realise that you're never going to use Gaping Maw anyway. That's basically the only use I can think of for it, although there may be other edge cases where it would be relevant.

                                                                                            Facing this guy maybe? (Cezarreo)

The second interesting bit of maths was suggested by Tiberius from TMAT, questioning whether Elrond would be better off spending his Might on duel or to-Wound rolls instead of Heroic Strikes. As it turns out, the answer is a little complicated.

The benefits of spending Might on to-Wound rolls are fairly easy to calculate, because it will basically let Elrond double his damage output. That would definitely be an edge over Striking in terms of Wounds dealt, letting him kill the Drake in around 10 or so turns instead of 17. However, it would also mean that the Drake would eat him slightly sooner, and he almost certainly would still lose overall.

Spending Might on duel rolls is a lot trickier. I assume that you'd only spend it on turns where you lost combat by one, as using it when you both rolled the same number would only boost up a 2/3 chance of winning the roll-off anyway. When Elrond does roll just beneath the Drake he'd end up with a 2/3 chance of winning the roll-off, which would be a swing from taking heaps of S7 hits to dealing out a few S4 hits back. That seems like it'd be a pretty big deal, I think.

The difficulty is that the odds of the Drake's highest dice being exactly 1 higher than Elrond's is about a 19% chance, and only in 2/3 of those will Elrond actually win the roll-off. That means that using this would increase his odds of winning the fight by a little under 13% and decrease the Drake's odds by the same amount. Factoring that into my calculations was a bit tricky, because the macros involved didn't really want to play nice with me tinkering. It wouldn't have been too hard if I didn't have to calculate it all 3 different ways for when Elrond was charging on horseback, when he was charging on foot (for when he gets dismounted by the Drake), and when the Drake is charging. It's also inevitably inexact, because it's impossible to predict exactly when the Drake will dismount Elrond.

                                                                        Lots of time playing with this spreadsheet (Jeremy Hunthor)

But after making some very generous assumptions in Elrond's favour on this point (giving him a full three cavalry charges before being dismounted), it turns out that after 6 turns of combat he will have done a little over 3 Wounds to the Drake, and it will have averaged a whopping 7.4 back to him. So, he's slightly less outclassed than before, but not by much.

The one upside here is that he probably only had to spend Might modifying duel rolls once in those six turns, so he probably had two Might left to burn on to-Wound rolls. If he spent them to turn two 5's into 6's, that would take his average up to just over 5 Wounds dealt, which is tantalisingly close! So if he manages to roll just a bit more above average AND gets to charge first AND manages to win the fight the first two times he's charged back then he can possibly take on the Drake and win (if it fails its Fate roll).

The first insight I took from that somewhat gruelling bit of maths is that Tiberius’ instinct was right; Elrond should definitely spend his Might on duel and to-Wound rolls. It seems to make the matchup a lot less one-sided than when he Strikes, and a character like Bolg or Elendil might well be able to translate that strategy into an actually positive matchup. The second insight was that Elrond is still definitely in a bad position here. The assumptions I made in his favour were very generous, and he was still realistically 1.5 Wound away from victory. And I didn't even take into account the Drake spending its own Might! So if you've got a S4 hero with no bonuses to Wound and your opponent has a Cave Drake, you're probably best off running the other way.

 

                                                                                            Elrond sounding the retreat (Warhammer Community)

    

Hope you enjoyed those little snippets of maths. The Cave Drake seems to be an extremely efficient little monster, but Gaping Maw is actually even worse than I had assumed it to be. I think you could get away with forgetting it ever existed, although your best option is to talk it up to your opponent as much as possible. Oh, and to hope they haven’t read this article.

Until next week, may your Drake always get the charge!