Hello again, another (potentially stupid) question for your cyclopean wisdom.

Looking the statistics report, I noticed that the mix of KH and IH boards in one game tends to produce the biggest number of defeats. It's even twice that when mixing KH and DH.

Is there some strange dynamic between the expansions or is Innsmouth solely to blame for this? Or is the sample of recorded games too small to be representative?

The reason I'm asking is because Kingsport and Innsmouth are the only boards I have (for the moment at least). There's undoubtedly going to be a game where I'll play using both of them and I would love to be at least a little prepared, haha.

Hamu said:

I suspect that Innsmouth and Kingsport are played by a higher percentage of experienced players than Dunwich or no expansion board. Which makes it stranger.

Maybe Kingsport makes gates bounce on seals on the Arkham board more often, making the DOR track fill up and making the team spend too many clues on that.

Because the presence of Kingsport increases surge frequency. (So many underestimate the danger of the original 11 unstable Locations when played with the proper mix of expansions.) Arkham + Kingsport = Surging Monsterfest. You add Innsmouth Locations to that surge potential...you know how BAD a surge can be to Devil Reef. Even if it's not the surging gate, three Arkham surges in a row (not uncommon at all with Kingsport) equals half a DOR Track, maybe more. The other half fills with Tox's Seal Bounces, and you just lost.

Here's what I think about it.

• KH and IH have the hardest AOs.
• KH and IH have tough heralds. Dunwich's herald has to be downloaded, and it's not extremely threatening.
• KH has nasty rumors, and IH's mythos cards in general are nasty.
• KH has the Epic Battle cards, which hurt more than the Personal Stories help. DH's Injury/Madness cards are generally a big help.
• KH doesn't dilute, so it will always sting no matter what it's paired with.
• DH and IH both dilute, but IH's mechanic is nastier and dilutes more slowly. It makes sense that introducing too many expansions makes them less dangerous overall, and thus, stronger concentrations should be found with fewer expansions.
• Mirroring Tox's response, the fact that KH has no unstable locations means that seals are more likely to add DOR tokens.

Tibs said:

We almost always lose with KH/IH. They are easily the two hardest expansions. And together, even harder. (I now actually think Kingsport is the most difficult.) I've always attributed two of your reasons:

1. "KH doesn't dilute, so it will always sting no matter what it's paired with."

2. "Mirroring Tox's response, the fact that KH has no unstable locations means that seals are more likely to add DOR tokens." (The big Killer for me with IH is Devil Reef and though it comes out less with Kingsport in the mix, it does help much because of the additonal chances of DOR tokens.)

Since I don't play with Epic Battle (except with the four weakest Old Ones), or heralds and completely randomize AO's those factors don't enter in, though, if I did they my ratio would even be worse than almost always lose.

I'd have to look at the rumors, because my memory says Dunwich has the ones I really hate.

Tibs said:

I'm a little confused. Arkham and Innsmouth together have as many unstable locations as Arkham, Kingsport, and Innsmouth. I don't see how adding the Kingsport board to the mix would make the DOR track more active. The only thing the Kingsport board does is it occasionally siphons off an investigator for Rift duty. I can see how the Kingsport expansion in general might make things harder, with its AOs, Epic Battle cards and Mythos cards. But I'd expect that the Kingsport board would only give a slight bump to the challenge. (I don't play with more than one expansion board at a time, so I don't have any empirical evidence.)

Maybe it's that the Innsmouth board actually becomes less dangerous when combined with Dunwich. In contrast, Innsmouth might not become much more dangerous when combined with Kingsport, but at least it doesn't get any easier.

mageith said:

Yeah, Riots, Mad bomber, Nightmare pool. Not the easiest ones to pass, especially in case they appear in the wrong moment of the game

What I meant was that no new unstable locations implied an increase in the frequency of gates opening on seals. Of course when using only Innsmouth, many of the gates are in Innsmouth, so this will add tons of DOR tokens as is.

Tibs said:

Doesn't it mean that there's no change to the frequency of gates opening on seals? As opposed to an increase in frequency?

Gate in Arkham would be more likely in a KH/IH game than in just an IH game (since they're opening at Innsmouth less often). That's where the rationale comes from, but I don't think this is a significant factor now that I'm thinking about it.

Tibs said:

Have you TRIED it?

Of course, I mean that the dominant source of DOR tokens would be monsters flooding Innsmouth, as opposed to a few gate bounces.

Tibs said:

Oh, I see. 3/4 of the gates would be more active (the ones in Arkham) and 1/4 of the gates would be less active (the ones in Innsmouth).

So, if you're playing with just the base game and Innsmouth, around 64% of the mythos cards open a gate in Arkham and 32% open a gate in Innsmouth. If you're playing with the base game, Kingsport and Innsmouth, then 69% of the cards open a gate in Arkham and 26% open a gate in Innsmouth. Also, around 6% of the mythos cards would be gate bursts in Arkham (and it would be 0% without Kingsport).

Would that make the DOR track more active? Actually, probably not. Even though adding Kingsport would add more cards that open gates in Arkham, it also adds gate burst cards, which do not affect the DOR track. There are 7 gate burst cards in Kingsport and 5 in Innsmouth. If we consider only non-gate burst cards, then with Kingsport and Innsmouth, around 63% of the mythos deck would open gates in Arkham and 22% would open gates in Innsmouth. So actually, adding Kinsport to the mix would decrease the frequency of gates opening on seals. It decreases the probability of it happening in Arkham from 64% to 63% (virutally no change), and it decreases the probability of it happening in Innsmouth from 27% to 22% (more significant).

Of course, gate burst cards make the game harder for other reasons. But they do reduce the threat of the DOR track. Unless a gate burst in Innsmouth is followed by a monster surge, like Tibs says.

Tibs said:

Though adding Kingsport would make the Innsmouth gates less active, which means that monsters would be less likely to flood Innsmouth.

Well, my thought is that the increase in monster surges will offset the reduced gates. Also it's worth noting that Kingsport has Arkham-location gate bursts, while Innsmouth does not.

I doubt the there is an increased chance of monster surges overall. The chance of there being a surging gate in Akrham would marginally increase, but it would be balanced by a decrease in the likelihood that a gate will surge in Innsmouth. Overall, I suspect that gates would surge about as often with Kingsport as without it. Adding Kingsport just increases the chance that a surging gate will be located in Arkham (as opposed to Innsmouth.) But it doesn't really matter which gates "surge," since a monster surge affects all open gates. Of course, Kingsport does have 2 Strange Sightings cards, so I guess that would increase the chances of monster surges. By a little bit.

I ran some numbers of monster surges. Hypothetically, let's say that if a location is drawn on a mythos card, and then the same location is drawn again within five turns, it will result in a monster surge. Under that assumption, we can compare the likelihood of monster surges with Innsmouth + Kingsport, compared to Innsmouth alone.

In the base game, there are 10 mythos cards for a "hotspot" location like Independence Square, out of 66 cards total (not counting The Story Continues). Let's say we're playing with the base game only, and a gate opens at Independent Square on turn 1. If *another* Independence Square card is drawn in the next five turns (turn 2 to turn 6), then the gate will probably surge. What are the chances of this?

First, determine the chance that the gate won't surge on the next turn. That chance is 1-(9/65), where 9=the remaining Ind Square cards and 65=the remaining cards total. The chance works out to 86.1%. In other words, there's an 86.1% chance that the next card will not be Ind Square. For turn three, the probability is 1-(9/64), or 85.9%. For turns 4, 5 and 6, the probabilities are 85.7%, 85.5%, and 85.2%. The probability that you will not draw an Ind Sqaure card in turns 2-6 is (86.1% * 85.9% * 85.7% * 85.5% * 85.2%), or 46.2%. So, the probability that you will draw another Ind Square card is 1-46.2%, or 53.7%.

If you play with Innsmouth, there are still 10 Ind Square cards, but the deck size increases to 102. Let's assume the same scenario: Ind Square is drawn on turn 1, and the gate will surge if another Ind Square card is drawn in the next five turns. In that case, the chance of a surge goes down from 53.7% to 37.9%. Incidentally, the chance that an Innsmouth "hotspot" like Devil Reef will surge is slightly greater, since it has 11 mythos cards instead of 10. Devil Reef's chance of surging is 41.3%, slightly higher than the 37.9% chance that Ind Square has.

Now let's add Kingsport. Kingsport adds 22 mythos cards, of which 2 cards open gates in Ind Square. So now the deck size is 124, and a total of 12 cards open gates at Ind Square. In that case, the chance that Ind Square will surge remains the same! The probability "changes" from 37.9145% to 37.9123%. Devil Reef doesn't get any additional cards, of course. As a result, the probability that it will surge decreases from 41.3% to 35.0%.

Therefore, we may conclude that Kingsport does not increase the chances of monster surges. Unless Strange Sightings cards are taken into account. Let's do that!

Innsmouth has 1 Strange Sightings card, which of course causes a monster surge automatically. In the scenario above, we could say that Ind Square will surge if another Ind Square card or a Sight Sightings card is drawn in the next five turns. So, for turn 2, there are 101 cards left in the deck, and 10 of them will cause Ind Square to surge. The chance that Ind Square will surge in turns 2-6 is now 41.3% with Innsmouth, compared to the 37.9% chance if Strange Sightings cards are not taken into account. The chance of Devil Reef surging goes up from 41.3% to 44.5%.

If we add Kingsport, we add 2 Strange Sightings cards. The chance that Ind Square will surge increases from 41.3% to 45.9%. The chance that Devil Reef will surge decreases, but only barely: from 44.5% down to 43.4%.

So, on balance, Kingsport does increase the chance of having monster surges. However, the effect is entirely due to the 2 extra Sight Sightings cards that come with the expansion. It has nothing to do with the extra Mythos cards for Independence Square, since the effects of those cards are negated by the larger deck size. Also, the difference is not very dramatic. The chance of a hotspot surging increases by about 4%. So in a 20 turn game, with Kingsport maybe you'd get 1 extra monster surge per game on average.

I realize that my assumptions do not cover all aspects of the game. Gates other than the game's first gate may surge, or gates may surge in medium or low frequency locations. Or The Story Continues may be drawn, causing all discards to be shuffled back into the deck. However, I think this model is a useful illustration of how the expansions stack up against each other.

Is Kingsport + Innsmouth more difficult?

And the verdict is: avec loves numbers

Tox said:

I keep a photograph of pi on my bedside table. Or is that too much information?

It's possible I'm the only one who cares about this, but I think these results are startling. Aside from its two Strange Sightings cards, Kingsport does not increase the chances of having a monster surge.

I tried adding Kingsport to the base game without including Innsmouth. I left out the four Kingsport mythos cards that do not open gates in Arkham: two Double Doomers and two Strange Sightings. The 18 remaining Kingsport cards were added to the base deck. The chance that Independence Square will surge still goes down slightly, from 53.7% to 51.8%.

Why would adding Kingsport cards make Ind Square less likely to surge? I think it's because Kinsport includes a disproportionate number of low frequency locations: The Science Building, the Historical Society, etc. Kingsport includes 2 mythos cards for each high frequency location and 1 card for each low frequency location. In the base game, I believe the ratio is 10:2. If you want to increase the chance of monsters surges, what you should do is concentrate activity in the high frequency locations. Kingsport does the opposite of that. It distributes activity fairly evenly across the Arkham board.

So what does Kingsport do exactly? Its board does not increase or decrease the number of unstable locations. As far as the number of unstable locations go, Kingsport is a non-factor. The Kingsport mythos cards do slightly increase the chances of having a monster surge. However, that effect is entirely due to the two Strange Sightings cards. The rumors in Kingsport are challenging, but Dunwich's are worse. So, what does that leave? Rift duty? Epic battles? The mighty Shan? I guess the AO's are hard.

I vote for rift duty. Even if you only spend a small fraction of one investigators time on rift duty, that's time not spent sealing gates. While it's true that you can totally ignore the rifts (just as you can ignore the Dunwich horror track), the fact is that they scale no matter how many games are in play. And once a rift opens, you have a chance of advancing the doom track. Hence, I'm guessing people do spend some more time on the rifts (maybe more than they should - I know I tend to) than on stopping the Dunwich horror from awakening.

avec said:

That's the point why Kingsport increases chances of monster surges. Please do not misread this: at the begninning of the game, when all unstable locations are still unsealed, yeah, the chance of having a monster surge at Independence Square is lower with Kingsport Mythos in play rather than without it. But then it's different, since you have so many cards hitting other locations. In a normal game, you won't have Hibbs surging, nor the Historical Society, unless you're very unlucky, but with Kingsport in, the chance for them to surge is greater.

Let me do the math: if we have to have a surge, then we need an open gate. Let's consider the easiest situation possible: 1 gate open in location x and the following Mythos another gate open there. With Arkham only, we have 66 Mythos opening gates in different locations, 1 is used as "base gate", then we have a deck of 65 cards potentially triggering a surge.

- high frequency locations: 9 chances out of 65 -> 13.85% surge
- medium frequency locations: 5 out of 65 -> 7.69% surge
- low frequency locations: 1 out of 65 -> 1.54% surge

if we add Kingsport Mythos, then we have 18 more Mythos with locations depicted on it, then the we have

- high frequency locations: 11 chances out of 83 -> 13.25% surge
- medium frequency locations: 7 out of 83 -> 8.43% surge
- low frequency locations: 2 out of 83 -> 2.41% surge

the only situation in which the chance is lower is for high frequency locations

Not to mention that the fact KH has gate burst can change this even more drastically: with base game only, as soon as you seal a location, then there is no chance you'll see that location surge, but with KH seals can be broken and so the location you sealed can surge again

I agree that Kingsport increases the likelihood that medium and low frequency gates will surge. But intuitively, that doesn't seem like the best strategy for increasing monster surges overall. If I was going to design an expansion that increased the number of monster surges, I'd concentrate gate activity at the high frequency locations. What I wouldn't do is make it so that gate activity was spread more evenly around the board. The reason is simple. If there are a few intensely active locations, it's more likely that multiple mythos cards will be drawn for those locations. If there are lots of mildly active locations, it will increase the number of gates that open, but it will decrease the likelihood of monster surges. Kingsport takes the latter approach.

That's my intuition, anyway. I crunched the numbers and found that my theory was mostly correct. While it's more likely with Kingsport that a gate in a low frequency location will surge, it's still unlikely that a gate will appear in a low frequency location in the first place. In the base gate, there's a 60.61% chance that the first mythos card will show a high frequency location. If that actually happens, there's a 13.85% chance that next card will show the same location (using Julia’s method for determining the probabilities). Therefore, there's an 8.39% that the first mythos card will be a high frequency location AND that it will surge on the next turn (60.61% x 13.85%). There's a 27.27% chance that the first card will be a medium frequency location and 7.69% chance of a medium frequency gate surging. That means there’s a 2.10% that first location will be a medium frequency gate and that it will surge on the next turn (27.27% x 7.70%). There’s a 12.12% chance that the first card will be a low frequency location and a 1.54% of a low frequency gate surging. Therefore, there’s only a 0.19% of a low frequency gate appearing and surging.

Here’s the important part: the total chance of a monster surge in the base game is 10.68% (8.39% + 2.10% + 0.19%). By using this method, we can compare the base game to Kingsport.

Base game:

• Chance of a gate at a high frequency location: 60.61%
• If a gate is at a high frequency location, chance of it surging: 13.85%
• Chance of a surge at a high frequency location: 8.39% (60.61 x 13.85%)
• Chance of a gate at a medium frequency location: 27.27%
• If a gate is at a medium frequency location, chance of it surging: 7.69%
• Chance of a surge at a medium frequency location: 2.10% (27.27% x 7.69%)
• Chance of a gate at a low frequency location: 12.12%
• If a gate is a low frequency location, chance of it surging: 1.54%
• Chance of a surge at low frequency location: 0.19% (12.12% x 1.54%)
• Total chance of a surge: 10.68% (8.39% + 2.10% + 0.19%)

Kingsport (without Double Doomers or Strange Sightings):

• Chance of a gate at a high frequency location: 57.14%
• If a gate is at a high frequency location, chance of it surging: 13.25%
• Chance of a surge at a high frequency location: 7.57% (57.14 x 13.25%)
• Chance of a gate at a medium frequency location: 28.57%
• If a gate is at a medium frequency location, chance of it surging: 8.43%
• Chance of a surge at a medium frequency location: 2.41% (28.57% x 8.43%)
• Chance of a gate at a low frequency location: 14.29%
• If a gate is a low frequency location, chance of it surging: 2.41%
• Chance of a surge at low frequency location: 0.34% (14.29% x 2.41%)
• Total chance of a surge: 10.33% (7.57% + 2.41% + 0.34%)

Kingsport (with all cards used):

• Chance of a gate at a high frequency location: 54.55%
• If a gate is at a high frequency location, chance of it surging: 14.77%
• Chance of a surge at a high frequency location: 8.06% (54.55 x 14.77%)
• Chance of a gate at a medium frequency location: 27.27%
• If a gate is at a medium frequency location, chance of it surging: 10.23%
• Chance of a surge at a medium frequency location: 2.79% (27.27% x 10.23%)
• Chance of a gate at a low frequency location: 13.64%
• If a gate is a low frequency location, chance of it surging: 4.55%
• Chance of a surge at low frequency location: 0.62% (13.64% x 4.55%)
• Total chance of a surge: 11.47% (8.06% + 2.79% + 0.62%)

As we can see, adding Kingsport slightly reduces the chance of a monster surge, unless the Strange Sightings cards are taken into account. If we add Kingsport without the Strange Sightings or Double Doomers, the chance of a surge decreases from 10.68% to 10.33%. Once the Strange Sightings and Double Doomers are added, the chance of a surge increases to 11.47%.

Why does this happen? Well, increasing the chances of a surge at a low frequency location doesn’t count for all that much once you take into account the likelihood that a gate will appear in one of those locations. The increase in the chance of a surge at a medium or low frequency location is more than offset by a decrease in the chance of a surge at a high frequency location.

By the way, these numbers are based on Julia’s method for determining surges. Namely, that a surge will occur only if a mythos card opens a gate and then the very next mythos card shows the same location as the current mythos card. It’s a simple method and obviously it’s a bit arbitrary. I use it here because it supports the same conclusions as my earlier method (i.e., that a gate will surge if any of the next 5 mythos cards shows the same location as the current mythos card). Unsuspecting gamers should keep in mind that these probabilities are artificially low. The chances of a having a monster surge are actually much higher than what is listed above. However, Julia’s method and my method are both perfectly valid for the purposes of comparing expansions. They both point to the same conclusion: When using Kingsport, any increase in the chances of having a monster surge is due entirely to the two Strange Sightings cards.

Also, I have not yet figured out a way of modeling the likelihood of a gate opening, getting sealed, bursting open again, and then surging. That one could be tricky. I suspect it happens rarely, at least from the perspective of probabilities (I've definitely seen it happen).

avec said:

This is the living proof one needs a degree in math in order to understand how an easy boardgame works ::laughter:: Anyway, Kingsport has Strange sightnings card (fortunately) so the chance is higher!

Anyway, jokes aside... this debate is quite interesting. Have you thought about the possiblity of correlating all expansions in order to see which combo is the nastiest for surges?