Gloomhaven Attack Modifier Cards: What Are The Odds?
Warning: Mild Spoilers Ahead
A couple of weeks ago, my gaming group and I tried, and failed, to beat a Gloomhaven scenario for the second time. I won’t tell you which one, for spoiler reasons, but rather irritatingly we all either died or ran out of stamina when the main bad guy we needed to beat only had 8 health left. This meant that if we had managed to get one or two characters to have one extra turn then we may have won. It smarts. It really, really smarts.
That being said, a few unusual things happened throughout the game, and they all focus on the Gloomhaven Attack Modifier cards. Today I thought we would do a bit of math to try and explain them. What happened?
- The game lasted 24 rounds.
- Our Level 2 Scoundrel drew three “Null” cards throughout the game. Two were one after the other.
- Our Level 3 Mindthief (me) drew four “2x” cards throughout the game. Two were one after the other.
We have both had perks, adding and taking cards from our modifier deck. I have a modifier deck of 20 cards, whereas the Scoundrel has 18. I also gave money to the Church/Sanctuary (or whatever it is called) giving me two additional “2x” cards.
So, with that in mind, let’s look at the odds for the Gloomhaven attack modifier cards and, more importantly, what can be done to beat them?
Gloomhaven Attack Modifier Cards – What Are The Odds?
First thing is first. Every character has the same base modifier deck to begin the game with. The cards they have to draw from are:
- 1x “Null”
- 1x “2x”
- 1x “+2”
- 1x “-2”
- 6x “+0”
- 5x “+1”
- 5x “-1”
To display this graphically, the deck looks like this:
This means your odds are the following, to begin with:
- 1/20 apiece – “Null”, “x2”, “+2”, or “-2”.
- 7/20 – Negative cards.
- 6/20 – Neutral cards.
- 7/20 – Positive cards.
What this means is 1 card in every 20 pulled will be any specific special, or there will be 4 cards in every twenty that mean you pull any type of special. Alternatively, 7 cards in every 20 pulled will be a negative or positive card, with 6 cards out of every 20 being neutral.
Those are, to be completely honest, average odds – there are just as high odds drawing a good card as a bad one. As players, it is in your interest to level up and get perk points (through the mission goals) in order to dilute that deck, remove bad cards, and put better cards in.
Please note: When discussing actual decks the diagrams in this article are purely theoretical from this moment on. I know what the Mindthief deck is like because I play it, however, the other decks are more of a representation.
Leveling Up The Gloomhaven Attack Modifier Decks
I think, and this is the hypothesis going forward without having worked the mathematics out yet – I think the best way to develop the character decks is to put in as many cards as you take out. For instance, the below represents my Mindthief’s Attack Modifier Deck at the moment. The “S” stands for special, as I don’t want to give away any more spoilers than I need to.
The above is my deck at Level 3. As you can see, there is no “-2” card, there are two less “-1” cards, there is one additional “+1”, as well as two special cards.
What this does is keep the deck the at the same amount of cards, whilst also reducing the number of negatives. The odds now are:
- 4/20 – Negative cards.
- 6/20 – Neutral cards.
- 10/20 – Positive cards.
Those odds are significantly better. Rather than 7/20 negative cards there are only 4/20. Rather than 7/20 positive cards, half the deck is now comprised of positive cards. There are 10/20 including the specials. This gets even better with the blessing, as the deck becomes 22 cards, followed by 21 cards when a blessing gets used, followed by 20 again. That is back to the normal stats as laid out above.
When there are two “x2” blessing cards, however, the odds, once again, increase for drawing a card that isn’t the “null”. What is better, they don’t just increase the chance of a positive card being drawn, they decrease the chance of a negative.
Getting the blessing turns the odds to:
- 4/22 – Negative cards.
- 6/22 – Neutral cards.
- 12/22 – Positive cards.
Those are, for level 3, pretty good statistics, and that could explain why three “x2” cards were drawn.
What about just removing the negative cards?
That being said, let’s say, for the sake of argument, the special cards aren’t in there. Instead, what we have is a deck where negative cards have been removed without positives being put in their place. We see a deck that doesn’t have as many negatives, but that also doesn’t have as many positives because of that.
What this shows is what a deck can be like if negatives are removed or replaced. As noted before, please see this as a potential example, and not a representative or real life one.
What’s happening is that the negative cards, although not more frequent, are more likely to come up due to the smaller deck size. This is because the probability is relative.
- 4/18 – Negative cards.
- 6/18 – Neutral cards.
- 8/18 – Positive cards.
4/18 is a higher chance than 4/20 or 4/22. In fact, it’s the difference between a 2/9 chance, 2/10, and 2/11. In a game that lasts 24 rounds, with the potential of 2 attacks per round, those odds start to stack up.
Once again, adding the blessing cards increases the odds, making the theoretical deck a 20 card deck once again.
The two ways to look at Gloomhaven Attack Modifier Cards.
Gloomhaven Attack Modifier cards can be seen in one of two ways. Either, removing the negatives or increasing the positives. I would suggest, looking at the base mathematics, the best approach is a mixture of the two. Whilst removing negatives, make sure that you replace them with positives as soon as possible. Yes, drawing three “Null” cards during a scenario is unlikely; however, it is made more probable if there are fewer cards.
What this means is that, especially with scenarios, it is highly recommended to add blessing cards when given any opportunity to get them. They may cost 10gp per card, but they also dilute the deck down, making it both more probable to get the cards you want, and less probable to draw the cards you don’t.
So, this has been a fairly quick article today; however, talking with the gaming group we all thought it was worth a bit of an exploration. Once again, this is just one part of how probabilities affect board games and is more of an article on probabilities than it is Gloomhaven.
Since writing this article I have also found an incredibly awesome article focused on chance of hitting, missing, and average damage per turn. It’s a different approach, but well worth the read. You can find it here.
So, what are your thoughts? What do you think the best way to build your Attack Modifier Deck is? What have I missed out? Let me know what you think in the comments below.