Hello and welcome to another installment of Horror by the numbers, a series where I take a look at the numbers and probabilities behind some cards from Arkham Horror: The Living Card Game. The past few months has seen the release of The Innsmouth Conspiracy campaign which focuses on the new bless and curse tokens. We’re seeing plenty of cards whose value increase with the amount of bless and curses in the bag and also with any other support cards. Let’s continue looking at these cards and analyzing the numbers behind bless and curse.
Last time, we looked at a few cards from the deluxe box and the first two packs of The Innsmouth Conspiracy. Today we’re going to focus on a group of cards all from the same pack, the recently released Horror in High Gear. In terms of player cards, this pack has been the most interesting one to me so far and I have 4 cards that I want to look at in this article. There’s a little more nuance to these cards so I’ll be diving a little deeper into each one to discuss what some of these numbers mean.
Like in our last article, I will be considering the Night of the Zealot chaos bag on Standard difficulty, which contains 16 tokens. These numbers will vary based on campaign, mechanics that alter the bag and difficulty.
Blessing or Curse?
The first card I want to look at is Blessing of Isis, one that me and any other Father Mateo fans out there can appreciate greatly. With this card, there are a few main questions that we can ask. One of them is probably not “would I succeed the test without it?” since two blesses usually puts you out of range of most bad tokens. The questions were asking here are “what are the chances I activate this?” and “what benefit would this give me?”. For the latter, there’s a discussion to be had around each investigator’s individual elder sign effects, but that’s not the focus here. Let’s try and answer the latter question in a more general sense.
Once again I will be simulating pulls from the chaos bag using the code hosted here. The bag will have only bless tokens. and similarly to my analysis of Paradoxical Covenant, I will be considering three strategies when trying to active Blessing. Two of these will use mystic cards, making them available to both Mateo and Sister Mary:
Simple Pull: Just pulling from the bag. Nothing special.
Statue After Pull: Using Grotesque Statue to pull extra tokens, but only after a bless has already been revealed. After pulling one of those, we activate the ability to find the second bless token. The final probability reflects that chance to both draw the initial bless and pull the second one. Here, we replace the use of Jacqueline’s ability since she does not have access to Blessing of Isis. The numbers for her ability would follow a similar pattern with slightly higher values overall.
Olive Pull: Using Olive McBride on the first pull, we choose two tokens prioritizing getting two blesses. If we can’t, we choose as many bless tokens as possible. For example, if we pull [bless, bless, -3], we’ll choose both the blesses.
Even at first glance we can see the probabilities on the graph don’t climb very high, topping of at around 45% using Olive with a fully blessed bag. Notably, the probability always starts at 0 with 1 token since you’ll always need at least two. Simply pulling from the bag tops off at a measly 13% chance and using Statue can only get you to around 23%. These numbers are not very high and if you consider that some elder sign effects, like Zoey‘s are circumstantial, the outlook isn’t great. An important note is that if you only count the chance to reveal the second bless token using Statue, the numbers go from 11% with 2 tokens to around 60% with a full bag. In a way, you can say that 40% of the time, it works 60% of the time.
Overall, Blessing of Isis is a very cool card, but the chance of it being activated naturally are very low. Even using additional token pulling, it’s not very likely. That being said, this effect can apply to any investigator at your location, making it more likely to trigger in higher player counts. You can even try and activate other characters’ elder signs who would normally not have access to Blessing. Like I stated previously, which elder sign you’re trying to trigger can have a big influence on how good this card is. We also have seen effects in future Innsmouth packs that can force bless and curse tokens to be revealed and that’s where the two cards we’re seeing here really shine. We can discuss those in future articles, but for now, it’s important to note that while powerful, Blessing can also be inconsistent.
Curse of Aeons is, appropriately, the curse token mirror of Blessing of Isis, so any numbers we look at will be identical to the ones we looked at above, given the same strategies. With that, we can reach similar conclusions if we’re trying to use Curse to find a skull token for cards like Song of the Dead or Sixth Sense. That is, using Curse of Aeons is not the most efficient way to achieve this. A key difference here is that there are usually more skull tokens in the bag than Elder Signs so if that’s all you’re trying to achieve, maybe Curse of Aeons doesn’t actually help much.
Let’s take a look at the numbers from a chaos bag that has 3 skull tokens in it, in this case, from The Path to Carcosa campaign. Other campaigns have less and the average is two, but I want to see the high end of the spectrum for trying to draw out the skull. I’ll be using the same strategies as Blessing of Isis, with one addition, since we’ll be looking not only to find a second curse, but also just a straight-up skull token.
Statue Pull: Using Grotesque Statue to pull extra tokens, looking primarily for a skull token, but also for curse tokens to trigger Curse of Aeons. Once again, the numbers for Jacqueline Fine’s ability would be higher, but very similar in shape.
Looking at those numbers, we can see that Curse of Aeons doesn’t really add much to the chance of resolving a skull token, especially outside of Olive McBride. In fact, we can see slight dips with only one curse token in the bag since Curse will never trigger in that case. For simple pulls, the chance goes from 18% with no curses to 28% with a full bag. With Olive the chance goes from 46% to 62% which is a big improvement, but is it enough for a 3 experience card that you also need to draw and play? I’d say that Curse of Aeons definitely isn’t meant to be a tool to simply draw more skull tokens.
So what does Curse of Aeons offer to players? Is it simply a bad mirror to Blessing of Isis? After all, skull tokens need to be made into benefits, while elder signs are always positive effects or big bonuses. The key to understanding Curse of Aeon’s second purpose is remembering that resolving curses is almost always bad. Transforming two blesses into a big number doesn’t change much since you’re succeeding by a decent amount anyways. so for Blessing of Isis, it really is only worth it if you can get a decent effect off. For Curse of Aeons, changing the second curse to a skull, not only can give you side effects, but it can also halt the curse chain. On average and standard difficulty, two curse tokens will probably get you a -6 modifier with the potential to go even lower if more are revealed. Curse of Aeons stops this at whatever the skull token is minus two while still seeing 1 curse revealed for cards like Shroud of Shadows. So how do we measure this impact of Curse of Aeons?
For this analysis, I’ll be taking a look strictly at a fully cursed bag and we’ll be looking at only the cases where Curse of Aeons could have been activated during a simple chaos token pull. Those cases correspond to about 13% of tests with a fully cursed bag. Below, I’ll show a graph that exhibits the chance of pulling two or more curses and failing the test depending on your skill value. The vertical line represent the threshold after which Curse of Aeons would prevent a failure.
From this we can see that if you are exactly 4 points up on a test, Curse of Aeons can save you around 11% of tests you’ll take, or alternatively, 82% of tests where you reveal 2 or more curse tokens. As your skill value increases, the chances of you failing tests decreases and Curse of Aeons will do less work. The break-even point here is around 6 to 7 points up on the test where you would fail approximately 6% of your tests that you could have passed. That being said, it’s not trivial to get to these high values and testing 4 points up is a large enough ask. Overall, there is something here, especially if the bag is being constantly filled. This is especially true since Curse of Aeons removes both curse tokens drawn despite only resolving one.
I’ll leave the more complicated analysis on this card for a future article, but there’s plenty to analyze here with Jacqueline and especially Olive who we’ve seen have a huge influence on these numbers.
A man and his dog
Tristan Botley is a very interesting card to me. First of all, you don’t ever need to trigger his second ability for him to be a perfectly fine card. A 5 cost ally that boosts 2 skills every turn can be very strong. Obviously if you can activate his second ability and put him into play for free and without an action, that is very good. Unfortunately, the condition is a little hard to satisfy, especially since a lot of the cards we’ve seen so far work mostly on revealing two bless or curse tokens. For the sake of disclosure, I’m considering his ability reads as “3 or more of any combination of bless and curse tokens” and doesn’t require 3 tokens of the same type.
With all that, I will start off with an analysis of how likely it would be to incidentally trigger his second ability during a game. I’ll be using other cards that I’ve looked at in this article and the previous and analyzing if Tristan would trigger his ability in any of those cases. We’ll look at a Paradoxical Covenant and Blessing of Isis/Curse of Aeons all utilizing Olive McBride to maximize chances and with equal curse. One consideration we will make here is that Paradoxical Covenant will resolve all bless and curse tokens pulled despite there being an interpretation of that card that stops you from revealing additional tokens after triggering it.
As it turns out, our strategy for trying to activate Paradoxical Covenant works very well if you’re trying to activate Tristan’s ability. After all, we’re trying to reveal as many tokens as possible even if we don’t get the pair right away. With Olive hunting around for 10 bless and 10 curse tokens, we get a nice 67% and a respectable 30% with half those tokens. Besides that we see a base chance of around 16% with an entirely full bag and only 4.5% with half the tokens in. The numbers for the Curse of Aeons case are about halfway between these two. Overall, the conclusion I give here is that Tristan Botley is already strong on his own, but if someone on your team is playing around with these bless and curse cards, the upside of getting him into play for free is way more present.
Unrelenting is another very strong card from this pack but it doesn’t immediately feature any sort of random condition we need to meet like previous cards. Instead, I’m interested in this card in terms of its influence on your chances to pass the skill test. The math here isn’t super complicated, but I’ll take a few cases and see how it changes with Unrelenting. First of all, there’s two cases where you use this card. The most common case, is trying to trigger the draw by sealing the “good stuff” tokens. Ideally, we seal 3 bless tokens but there might be times when we’ll need to seal +1, 0, 0 (on standard difficulty). Let’s see how each of these situations changes your chance of success on a standard difficulty Night of the Zealot. We’ll consider skull tokens a -2, cultist and tablet tokens will be -3 and the elder sign will be a +2.
Here we see that sealing off beneficial tokens in a bag without bless tokens can lower the chances of passing a test at lower skill values, but leaves the higher ones untouched. Ideally you’re not trying to both pass the test and get the card draw in this situation and lowering the chance to pass might even be beneficial for cards like Rabbit’s Foot. On the other hand, sealing 3 bless tokens in a fully blessed bag has very little effect on the chance to pass, even at lower skill values. Given that, maybe think about taking Signum Crucis along with unrelenting.
The next case for this skill card is that you seal non-Auto Fail that would cause you to lose. Here I want to take a look at sealing off the 3 worst tokens from a standard bag but I also want to see the impact of sealing off the only 3 curse tokens in a standard bag versus sealing off the higher negative tokens. Let’s take a look!
When sealing low modifier tokens from clean bag, we see the benefit when we are testing at a slightly higher value, but at very high values, we see a slight inversion. This is due to only one token causing a failure at higher values and with less in the bag, the chance to draw it is higher. The conclusion here is to only use drawing thin if the tokens you’re taking out cause you to fail or if you wan to succeed by larger amounts.
As for the cursed bag, we see a slight difference in where the benefit of sealing lies. When you’re 1 or 2 up, there is a slight advantage in sealing the -3 and -4, mostly due to not being able to pull those tokens anymore, but when you’re at higher values, that strategy doesn’t pay off anymore. Overall, it seems like sealing curses when you’re higher up on the test seems like the optimal strategy.
That’s it for the second installment of Horror by the Numbers. Once again, The Innsmouth Conspiracy is still releasing, so look forward to a bless/curse card analysis as more cards are released. If there’s any other cards you’d like me to analyze, let me know. Otherwise, feel free to send any comments, thoughts or concerns my way through Facebook, Discord or Nightgaunt Mail. See you next time!