It’s fair to say that rolling modifiers are a bit unsettling for many people due to one peculiar reason: the rules surrounding “advantage”. First, let’s review what these are…
Rolling modifiers: Resolve the effect on the attack modifier card, then draw another! Sounds great!
Advantage: Draw two cards instead of one. Take the better card. Awesome!
But what happens when these two things interact? The Gloomhaven rulebook specifically mentions this to avoid confusion or ambiguity (because it’s a great rulebook).
Rolling modifier + Advantage: “If one rolling modifier card was drawn, its effect is added to the other card played . If two rolling modifier cards were drawn, continue to draw cards until a rolling modifier is not drawn and then add together all drawn effects.”
What’s the problem?
This all seems great, but brings up a concern for many. It may not be immediately obvious, but at the start of the game, advantage guarantees that your attack will not result in a “Miss” card, thus doing zero damage (but still other effects in the attack!). This reassuring trait exists because there is only one “Miss” card in the deck, and it’s the worst, so your advantage let’s you avoid it. Worry no more about that ~7.143% chance of missing!
However, having a rolling modifier in your deck strips away this reassuring guarantee. You could draw those two cards when you have advantage, expecting an awesome addition to your big attack, only to see a rolling modifier card and a Miss card. As the rules state, you then must take both cards, meaning a whopping zero damage. Ouch.
Is it as bad as it seems?
On one hand, yes. It strips away a nice guarantee in the uncertain world of Gloomhaven. It’s not like having advantage was bad (you would have missed without advantage anyway in the previous example), but the certainty of advantage without rolling modifiers allows a player the tactic of busting out their bazillion-damage attack with no fear! With a rolling modifier card lurking in your deck, this isn’t 100% certain.
But let’s not jump to condemn rolling modifier cards, even when you expect to get advantage fairly often in this game. Let’s investigate (Batman voice: “To the MathCave!”) two key questions:
- How do rolling modifiers impact average attack damage with/without advantage?
- What’s the miss chance with/without advantage including rolling modifier cards?
The miss chance thing is really just tied into the first question, but people seem to really dislike missing. For higher attack values, missing is obviously more painful, so that’s another good reason to discuss it.
Average damage with advantage
I usually advocate for looking at entire distributions of damage, because an average is just one measure of a lot of stuff going on, but here I will just lazily compare averages like a chump.
For starters, we can calculate pretty quickly that the average damage of an “Attack 3” ability card is simply 3 normally, but improves to ~3.847 when you have advantage. This is a great improvement. As stated before, it also decreases your miss chance to 0%.
But what if you add in a “+1, rolling” card to the mix? Since you can now miss, will it hurt your average damage, or be a net positive?
Answer: Net positive, but but not by much. The average damage goes up to ~3.887. In other words, you increase the average damage by ~0.04 in exchange for that nice tactical guarantee you had before. (If you were curious, the average damage without advantage increases from 3 to ~3.045)
The chances of missing: Worried about missing that huge attack, even when you have advantage? Don’t worry too much! There is only a 0.65% (that’s less than 1 out of every 150!)
In other words, if this jar contains 149 Every-Flavor Jellybeans that have the sweet taste of victory, crushing your enemies before you, and hearing the lamentations of their women… but just 1 jellybean that was a poop-filled defeat nugget, would you try one?
…but I would probably pick a different perk before one with rolling modifiers if I expected to have advantage often.