There has been some conventional wisdom developing for Gloomhaven perks – removing negative cards is better than adding equivalent positive cards. Let’s find out!

Thanks to user Robyrt on the BGG forums for pointing this out to me!

Let’s simply take a standard starting deck, and compare their distributions when cards are added/removed.

## To add a +2, or remove a -2 ?

For reference, the standard deck has a distribution shown in a previous post, and for “Attack 3” has average damage of 3 and a miss chance of ~7.14%.

Adding a “+2” card to the standard deck yields the above distribution.

Key facts: Average damage = ~3.091, Miss chance = ~6.818%

Above we see the distribution of removing a “-2” from the deck.

Key facts: Average damage = 3.1, Miss chance = ~7.89%

**Verdict**: Removing a “-2” yields (slightly) more damage, on average. About… 0.009 more average damage. Well, that’s not a lot, so if you have ~~an excuse~~ a good reason to choose adding a “+2”. go right ahead.

### A good reason for adding +2:

*Shields. *Monsters can have shields – sometimes large ones. If you anticipate often fighting foes with shields that are large compared to the typical damage on your ability cards, you want help from those big “+2” cards.

For example, when fighting a foe with “Shield 3” using the standard deck, using a basic “Attack 3” card, your distribution looks like this:

The average damage here is ~0.548, and the odds of doing *any* amount of damage are ~35.7%.

Removing a “-2” will indirectly help you, simply because it increases the odds you draw a positive card. Here is the distribution for that shield situation, but with a “-2” removed from your deck:

Looks pretty similar. Here, the average damage is 0.575, which is an improvement of about 0.027 damage. The odds of doing any damage at all increase to 37.5%.

Adding a “+2” should be slightly better than this. Let’s see:

The average damage when adding a “+2” is ~0.614, which is more than double the improvement of removing a “-2”. In addition, the chance of doing some damage is increased to ~38.6%.

### A good reason to remove a -2:

*Enemies don’t have an infinite number of hit points*. When we calculate things outside the game, like average damage, we usually assume that those hits for 6 damage *actually remove 6 hit points from the enemy.* Often, they don’t!

When enemies have few hit points, either by their nature or because your allies have bloodied them up already, you don’t care about max-overkill. (Well, it’s satisfying… sure.) What you really need is reliability.

Anyone who has played tabletop RPGs has seen that hyyuuuge barbarian use Power Attack to swing his hefty axe at a weak foe, only to miss completely. Don’t be that person.

So, removing a “-2” from your deck makes sense to reduce the odds of embarrassing failure. Let’s look at an example when an enemy has 2 hit points (and no shield).

The standard deck, using an “Attack 3” against an enemy with 2 hit points.

The average damage here is ~1.81, and the odds of killing this enemy are ~88.1%.

How does this change if we remove a “-2”?

Average damage here increases to 1.85, and the odds of the enemy biting the dust increase to 92.5%. Nice!

And for adding a “+2”?

Average damage is barely higher than the standard deck, at ~1.82. The odds that the enemy dies are ~88.6%. In this situation, adding a “+2” to your deck has not helped much at all.

## Conclusions?

*Expect to face off with lots of heavily shielded monsters*? Add big positive modifier cards!

*Often find yourself late in initiative order, finishing off weakened foes*? Remove big negative modifier cards!

In my opinion there are strong arguments either way on this one, and it depends on your character class, the player’s style, the group composition, and the enemies encountered (which depends on your role-playing decisions). It’s easy to say “this is the right answer”, but in a well-designed game like Gloomhaven, many choices can be “best” for different situations.

Nice job ! For the next one, i would be interested in your analysis regarding Refresh items perk for three spears’ class ^^

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Firstly – this is just awesome. Kudos on the analysis.

Secondly – a few days ago I wrote a similar article but it’s interesting because we both approached the same question from completely different angles. You go down the route of damage, which is a fantastic way of looking at it and probably the more useful way as well. I went along the lines of the probability of drawing the dreaded “null” card. My article isn’t live yet (it’s scheduled for a few days time as I have a bit of a backlog to go through), but I don’t know if I will put it live after reading this. You put forward such an awesome analysis that approaches the question from a far more logical direction.

If you’re interested – my initial logic was, if you just remove cards you end up concentrating your deck. This means, if you are removing negatives without putting positives in you are actually increasing the odds of you pulling that dreaded “null” card by however many negatives you remove. It’s 1/20 at the start of the game, but if you just remove the negatives it will be 1/20-n (where “n” is the number of cards you remove).

If, however, you remove them and replace them then you keep the probability at 1/20 (assuming you give and take the same amount), whilst also increasing your odds of drawing a positive card. Thus, there is a benefit in also donating money for the blessing in Gloomhaven. It increases your odds of drawing a positive card (until you pull all the blessing cards), whilst also reducing your odds of drawing the “null”.

Dude, once again, this is incredible analysis. Simply amazing.

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Thanks! I think what you say here is getting to the underlying cause of how these deck changes impact damage.

Essentially, the odds of getting a good card are (number of good cards)/20 … so a player may remove bad cards from the deck to improve those odds to (number of good cards)/(20-n)

But as you point out, that pesky “null” card’s odds increase too, since the denominator is decreasing for all! I think this is good to point out.

Lastly, the I really like the tactic of donations/blessings to weigh down the odds of missing (besides the extra chance at 2x). I didn’t think of this at all! I think that tactic is pretty cool and clever. Love it.

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Ahh – I thought I had already responded to this!

I’m glad you like the tactic though – it really does work and is worth a try 🙂

I’ve posted my probability article live now, but have linked through to this one as you provide a completely different kind of analysis. Mines just probability – yours is an actual breakdown of damage! Absolutely awesome dude. I bow down to your superior mathematical breakdown!

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One thing which would be interesting to consider for future articles is also “how often do you expect to fight with advantage ?”.

We’re just beginning with my group (~10 scenario played), but it looks quite important already, and I’d expect the perk choices to be quite different between “never” and “often” as answers to the question.

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