Hi everyone. Sorry I've been away, work has been nuts. I've been wanting to post about the effects of Miskatonic Horror on dilution, but I haven’t been able to find the time.
Also, a few weeks ago, ricedwlit did a great post on this topic, followed by a great thread. If you haven’t seen it, here’s the link:
http://www.fantasyflightgames.com/edge_foros_discusion.asp?efid=5&efcid=1&efidt=525714&efpag=0
Some of my numbers don’t quite add up with ricedwlit’s, but the difference is never more than a couple percentage points.
Ricedwlit covered whether you could use a few expansions, but he didn’t say whether dilution is a problem if you use all the expansions. In my mind, that’s the real question. Hopefully, the numbers below should give us an idea of what is going on.
In each case, the top row is just the one (or two) expansions that are listed. With each new row you add a new expansion. So, if the first row is Dunwich only, the second row is Dunwich plus Miskatonic, the third row is Dunwich plus Misk plus Dark Pharaoh, etc. The bottom row is what you get if you use all the expansions. I added the expansions mostly chronologically. That’s why Lurker is last. I put Miskatonic in the second row, because I wanted to see how its effects dilute once you add multiple expansions.
This is what the percentages mean:
X% Dunwich: the chance of drawing a card that opens a gate in Dunwich
X% Innsmouth: the chance of drawing a card that opens a gate in Innsmouth, or a card that advances the DOR track (Plans In Motion)
X% Arkham: the chance of drawing a card that opens a gate in Arkham
X% Other: the chance of drawing an “other” card (Strange Sightings, Double Doomers, Next Act Begins, or Intermission)
In my opinion, dilution might not be a problem if you use both the Dunwich board and the Innsmouth board. But if you use only one expansion board, then dilution is definitely an issue.
Also, in the thread above, Tibs and Waddball each suggested rules to deal with dilution.
Tibs’ rule: “draw one, and draw again if it's not Dunwich or Innsmouth”
Waddball’s rule: “if you draw an AH gate or a non-gate, then if the last mythos card was an AH gate, draw and apply a new card”
Just for fun, I analyzed each rule for each of the three cases (Dunwich only, Innsmouth only, Dunwich and Innsmouth). (Disclaimer: As far as I know, both rules were intended to be used only when using board expansion boards.)
Playing with the Dunwich board, but not the Innsmouth board
24.51% Dunwich, 75.49% Arkham, 0.00% Other: just Dunwich
27.59% Dunwich, 67.59% Arkham, 4.83% Other: add Miskatonic
24.54% Dunwich, 69.33% Arkham, 6.13% Other: add Dark Pharaoh
21.05% Dunwich, 68.95% Arkham, 10.00% Other: add KiY
18.87% Dunwich, 70.28% Arkham, 10.85% Other: add Kingsport
17.02% Dunwich, 71.06% Arkham, 11.91% Other: add Black Goat
16.88% Dunwich, 70.46% Arkham, 12.66% Other: add Innsmouth*
15.44% Dunwich, 72.97% Arkham, 11.58% Other: add Lurker
*Even you’re not playing with the Innsmouth board, you might add the mythos cards from Innsmouth Horror don’t directly relate to the Innsmouth board. All two of them: Strange Sightings and Innsmouth Plague. I didn’t include “Plans In Motion” because it advances the DOR track. Not much point in including that card if you don’t use the Innsmouth board.
As you can see, if you play with Dunwich, Miskatonic, and only one or two other expansions, then dilution isn’t too much of a problem, like ricedwlit said. However, if you play with all the expansions, the chance of a gate opening in Dunwich goes down from 24.51% to 15.44%. The chance of a gate opening in Arkham also goes down, but not by much.
Basically, with all the expansions, about 10% of the cards are “other” cards. In order to make room for them, Dunwich takes a 10% hit. So, if you play with just the Dunwich board, Dunwich will be a very sleepy town, even with Miskatonic Horror added.
If Tibs’ rule was implemented, it would result in these probabilities:
28.55% Dunwich, 61.66% Arkham, 9.79% Other
As you can see, with this rule Dunwich would be okay. But Arkham itself would take a 14% hit in order to make room for “other” cards. Instead of Dunwich being sleepy, Arkham would be sleepy.
Waddball’s rule fares a little bit better:
25.19% Dunwich, 64.47% Arkham, 10.34% Other
Arkham still takes an 11% hit, though.
Playing with the Innsmouth board, but not the Dunwich board
33.33% Innsmouth, 64.71% Arkham, 1.96% Other: just Innsmouth
37.93% Innsmouth, 55.86% Arkham, 6.21% Other: add Miskatonic
33.74% Innsmouth, 58.90% Arkham, 7.36% Other: add Dark Pharaoh
31.61% Innsmouth, 61.49% Arkham, 6.90% Other: add Dunwich*
27.95% Innsmouth, 62.19% Arkham, 10.45% Other: add KiY
24.66% Innsmouth, 64.13% Arkham, 11.21% Other: add Kingsport
22.36% Innsmouth, 65.45% Arkham, 12.20% Other: add Black Goat
20.52% Innsmouth, 68.28% Arkham, 11.19% Other: add Lurker
*These are the 11 cards from Dunwich Horror that open gates in Arkham.
We see pretty much the same story as with the Dunwich board. If you play with only one or two expansions, you’ll be okay. If you play with all the expansions, the Innsmouth board takes a big hit in order to make room for the extra “other” cards. Also, Arkham itself becomes slightly more active. I assume this is because of the 11 extra cards from Dunwich Horror.
If we try Tib’s rule here, the probabilities work out to:
32.42% Innsmouth, 58.06% Arkham, 9.52% Other
In this case, Arkham still takes a hit, but it’s only about a 7% hit. That seems pretty good.
With Waddball’s rule, it would be pretty much the same:
31.73% Innsmouth, 58.66% Arkham, 9.61% Other
Playing with both the Dunwich board and the Innsmouth board
18.12% Dun, 24.64% Inns, 55.80% Ark, 1.45% Other: Dunwich and Innsmouth
22.10% Dun, 30.39% Inns, 42.54% Ark, 4.97% Other: add Miskatonic
20.10% Dun, 27.64% Inns, 46.23% Ark, 6.03% Other: add Dark Pharaoh
17.70% Dun, 24.34% Inns, 48.67% Ark, 9.29% Other: add KiY
16.13% Dun, 22.18% Inns, 51.61% Ark, 10.08% Other: add Kingsport
14.76% Dun, 20.30% Inns, 53.87% Ark, 11.07% Other: add Black Goat
13.65% Dun, 18.77% Inns, 57.34% Ark, 10.24% Other: add Lurker
First of all, the “ideal” distribution of probabilities is:
18.44% Dun, 25.08% Inns, 52.74% Ark, 3.74% Other
The ideal distribution is where the undiluted probabilities are shrunk proportionally until they add up to 100%. If you’re playing with just Dunwich Horror, Dunwich cards have a 24.51% chance of being drawn. If you’re playing with just Innsmouth Horror, Innsmouth cards have a 33.33% chance of being drawn. The chance of Arkham cards being drawn is 75.49% (with Dunwich) and 64.71% (with Innsmouth). Those chances average out to 70.10%. There is also a 4.97% chance of drawing “other” cards. I got that last number by calculating the chance of getting “other” cards if you combine DH, IH and MH.
So, the “raw ideal” distribution is:
24.51% Dun, 33.33% Inns, 70.10% Ark, 4.97% other.
In order to get those probabilities to add up to 100%, you need to shrink them down to 75.24% of their original sizes. That results in the “ideal” distribution, above. As you can see, if you play with Dunwich and Innsmouth, but no other expansions (including Miskatonic), the distribution is actually really close to the ideal distribution.
If you add all the expansions, it also isn’t too far from the ideal distribution. Dunwich and Innsmouth are a little sleepy, and Arkham is a little busier than it should be, but it’s not too bad.
By the way, if you use Tibs’ rule, these are the results:
22.91% Dun, 31.50% Inns, 38.68% Ark, 6.91% Other
Those results are dreadful (sorry Tibs!). The values for Dunwich and Innsmouth are inflated, and the chance of drawing an Arkham location is way too low.
Waddball’s rule
18.97% Dun, 26.08% Inns, 46.63% Ark, 8.32% Other
Those results aren’t bad at all. Arkham frequencies take a 6% hit, which is probably tolerable. By the way, Waddball himself reported this distribution: 49% AH, 18% DH, 24% IH, and 9% non-gates. His numbers are close to mine, but I’m not sure why they don’t match exactly. It could be because I consider “Plans In Motion” to be an Innsmouth card, not an “other” card.
So, what’s to be done?
If you play with all the expansions and both boards, you’d probably be okay if you didn’t do anything. Just put everything into one huge mythos deck. Dunwich and Innsmouth would be *slightly* sleepy, but it probably wouldn’t be enough that you’d notice. If you used Waddball’s rule, the probabilities would be even closer, though Arkham would be very slightly quieter than it should be.
I have a couple caveats with these approaches. The first is with Waddball's rule. With his rule, drawing an Arkham location will reduce the probability that the next location will also be in Arkham. The problem is that, if you could make an education guess about what the Mythos deck will do next turn, it may give you an unfair advantage.
My second concern is you will almost never draw “The Story Continues” or “Old Debts Come Due.” If you play with just the Dunwich Horror expansion, each of those cards goes into a 103 card deck. If you play with everything, the deck size is 294 cards, almost three times as big. This means that, if you play with just Dunwich Horror, in 15 turns you have about a 15% chance of drawing Old Debts Come Due. If you play with all the expansions, in 15 turns you would only have a 5% chance of drawing that card. If you play with all the expansions, you should seriously consider removing the Wizard’s Hill encounter where you can make a deal with the Dark Man. He will very rarely collect on his debt.
If you play with just the Innsmouth board, I recommend you use Tibs’ rule or Waddball’s rule. Arkham would be slightly sleepy, but not by much. The Dark Man of Wizard’s hill wouldn’t be an issue, since Wizard’s Hill isn’t in play. However, you would almost never see The Story Continues, which would be an issue with Bast.
If you play with just the Dunwich board, then you have a problem. Playing with all the expansions makes Dunwich way too sleepy. Playing with Tibs’ rule, or with Waddball’s rule, fixes Dunwich, but both rules make Arkham way too sleepy. And the Dark Man of Wizard’s Hill is a problem.
If you play with only the Dunwich board, I recommend you prep the mythos deck as follows:
• 24 Dunwich cards
• 72 Arkham cards
• 5 “other” cards
• The Story Continues and Old Debts Come Due
103 cards total
23.53% are Dunwich cards, which is 96.00% of its undiluted value.
71.57% are Arkham cards, which is 94.81% of its undiluted value.
4.90% are “other” cards, which is 101.49% of its undiluted value.
If you play with only the Innsmouth board, I recommend you throw everything in and use Tibs’ rule or Waddball’s rule. However, if you want the probabilities to be exact, or if you use Bast a lot, you can prep the mythos deck as follows:
• 32 Innsmouth cards (potentially including Plans In Motion)
• 64 Arkham cards
• 6 “other” cards
• The Story Continues
103 cards total
31.37% are Innsmouth cards, which is 94.12% of its undiluted value.
62.75% are Arkham cards, which is 94.12% of its undiluted value.
5.88% are “other” cards, which is 94.72% of its undiluted value.
If you play with both boards, I recommend that you just throw it all in. If you don’t mind playing with Waddball’s rule, it would improve the probabilities. However, if you still feel like things are off kilter, you can prep the deck as follows.
• 19 Dunwich cards
• 26 Innsmouth cards (potentially including Plans In Motion)
• 53 Arkham cards
• 4 “other” cards
• The Story Continues and Old Debts Come Due
103 cards total
18.45% are Dunwich cards, which is 75.26% of its undiluted value.
25.24% are Innsmouth cards, which is 75.73% of its undiluted value.
52.43% are Arkham cards, which is 73.76% of its undiluted value.
3.88% are “other” cards, which is 78.14% of its undiluted value.
Whew! If you made it this far, you deserve, um, something.