This is an analysis of how well Miskatonic Horror solves the dilution problem. First of all, a tip of the hat to ricedwlit, who started a great conversation on this topic a couple of weeks ago. Here’s the link:
Instead of trying to reinvent the wheel, this post complements his thread. As ricedwlit pointed out, dilution isn’t much of a problem with Miskatonic if you only use one or two other expansions. In this thread, I’m looking at what happens if you combine Miskatonic with every other expansion.
By the way, I’m not going to look at Next Act Begins cards, or cards that involve Exhibit Items, at least not yet. The dilution of those cards has been mostly solved, though I still have some nagging doubts. For example, if you play with every expansion, I suspect it will be very, very rare that you’ll actually *need* an Exhibit Item to protect you from the effects of a mythos card. But for now I’ll assume that there is no dilution of Next Acts or Exhibit Items.
I’m looking the dilution of Dunwich cards and Innsmouth cards. Specifically these scenarios:
1) Using the Dunwich board, but not the Innsmouth board
2) Using the Innsmouth board, but not the Dunwich board
3) Using both the Dunwich board and the Innsmouth board
For each scenario, I ran the percentage chance of drawing a Dunwich card, an Innsmouth card, a card that opens a gate in Arkham, or an “other” card (Strange Sightings, Double Doomer, etc.). In each case, the top row is the probabilities that you get if you use only the base game and the relevant expansions (DH, IH, or both DH and IH). In the second row, I add Miskatonic Horror. With each additional row, I add one expansion. The bottom row contains the percentages that you get if you use every expansion in the game.
Also, in ricedwlit’s thread, Tibs and Waddball each suggested house rules for dealing with dilution in Miskatonic Horror:
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 what would happen if you used either rule. I should say right off the bat that I have a general concern about Waddball’s rule. With his rule, drawing an Arkham location would reduce the probability that the next location will also be in Arkham. If you could make an educated guess about what the next Mythos card will be, it may give you an unfair advantage. Having said that, Waddball’s probabilities are often quite favorable.
In case you’re getting impatient, here’s what I found:
If you’re using Dunwich and Innsmouth, dilution is only a minor problem. If you use one board but not the other, dilution is still a major problem, even with Miskatonic. If you use Innsmouth, but not Dunwich, either Tibs’ rule or Waddball’s rule will mostly take care of things. If you use Dunwich, but not Innsmouth, then neither rule will help you. In that case, the only solution I know of is prepping the mythos deck before the game, which I’ll explain below.
Also, no matter which scenario you use, there will be a problem with two cards: “The Story Continues” and “Old Debts Come Due.”
The Story Continues was designed to be used with a 67 card deck. Old Debts Come Due was designed for a 103 card deck. If you play with everything, you have a 295 card deck. That means that, in 15 turns, the chance of drawing Old Debts Come Due decreases from 15% (with 103 cards) down to 5% (with 295 cards). If you play with a very large mythos deck, then you may want to ignore the Wizard’s Hill encounter where the Dark Man offers you a deal. The encounter has no teeth, since the Dark Man will very rarely collect on his debt.
Also, with a large mythos deck, The Story Continues will only be drawn about 5% of the time. This is obviously an issue if you use Bast. Even if you don’t use Bast, the original purpose of the Story Continues was to make it possible that you could get the same mythos cards twice. With a 67 card deck, there was a very real possibility that you could draw The Story Continues, reshuffle the deck, and (for example) get nailed with a particular Rumor card twice in one game. With 295 cards, that could still happen. But it’s very, very unlikely.
1) Playing with the Dunwich board, but not the Innsmouth board
24.51% Dunwich, 75.49% Arkham, 0.00% Other: just base game and 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 that don’t directly relate to the Innsmouth board. All two of them: Strange Sightings and the 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
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. Personally, I still think that’s too much.
In order to take care of these problems, and the problem of the “Old Debts Come Due” card, 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.
The "undiluted values" are what you get if you use only the base game and Dunwich. Except for "other" cards, which assumes base game, DH and MH.
Of course, the Dunwich cards could come from DH and/or MH.
2) Playing with the Innsmouth board, but not the Dunwich board
33.33% Innsmouth, 64.71% Arkham, 1.96% Other: just base game and 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.
With Tibs’ rule, 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’s pretty good.
With Waddball’s rule, it would be pretty much the same:
31.73% Innsmouth, 58.66% Arkham, 9.61% Other
If (like me) you play with only the Innsmouth board, I recommend that you use all the expansions and use either Tibs’ rule or Waddball’s rule. Obviously, Old Debts Come Due won’t be a problem since Wizard’s Hill isn’t in the game.
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.
3) Playing with both the Dunwich board and the Innsmouth board
First of all, it’s not clear what the probabilities even should be. In my opinion, the ideal distribution of probabilities is this:
18.44% Dun, 25.08% Inns, 52.74% Ark, 3.74% Other
This is what you get with the expansions:
18.12% Dun, 24.64% Inns, 55.80% Ark, 1.45% Other: just base game, DH, and IH
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
If you play with just Dunwich and Innsmouth, it’s actually really close to the ideal distribution. If you add all the expansions, it also isn’t too far from the ideal. Dunwich and Innsmouth are a little sleepy, and Arkham is a little busier than it should be, but it’s not too bad.
Here’s how I got the ideal distribution:
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.
Anyway, with Tibs’ rule, these are the results:
22.91% Dun, 31.50% Inns, 38.68% Ark, 6.91% Other
In my opinion, those results are not good. The values for Dunwich and Innsmouth are inflated, and the chance of drawing an Arkham location is way too low. On the other hand, when I showed Tibs these numbers, he seemed to like them. He says that it makes sense that gates are nearly identically frequent between all three regions. If you agree with Tibs, then his rule is a good way to go.
18.97% Dun, 26.08% Inns, 46.63% Ark, 8.32% Other
These results aren’t bad at all. Arkham frequencies take a 6% hit, which is 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.
If you play with both boards, I recommend that you just use all 295 mythos cards. 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.
However, if you still feel like things are off kilter, or if you want “The Story Continues” and “Old Debts Come Due” to have teeth, 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.