So I just got Innsmouth. Last night I thumbed through the IH mythos cards (didn't read any or keep tally of locations) just to see how many of the 36 cards actually showed Innsmouth gates. As it turns out, it's not 25 like in Dunwich, so I had to re-revise my Anti-Dilution, double-deck math.

Then I tried playing a game with all six expansions to see if my numbers might work out. Oh, they did.

I randomly picked a team of five investigators, and Quachil Uttaus as my AO (urk!). The investigators came out of a pool of all of them, because I equally want to test old investigators to see how their Personal Stories hold up. Quachil Uttaus was chosen because I put the 8 AO sheets on the top of my current stack, and rolled a d6 to choose, guaranteeing an Innsmouth AO (and guaranteeing one for the next two games). I used no heralds or guardians, in the interest of seeing Quachil's pure potential.

Silas Marsh was 1st player, and for a long time I used his clues and leeched off of Patrice to avoid drawing the Small Dust cards. I didn't realize that you won't die until deck 3, but I didn't want to risk anything until he at least made it into a gate and sealed it. After an adventure in LiTaS, he managed to seal a gate at the Esoteric Order, and later closed a triangle gate at Devil's Reef (eliminating 3 triangle monsters; two on that gate!!) before being turned into dust.

Early on I passed the Good Work Undone rumor to get Patrice a second Unique item so she could pass her Personal Story. It was a one-clue difference, but at least we didn't lose any seals. Over the course of the game, also I managed to pass Sister Mary's story (with the help of All Quiet), Michael McGlen's story (closing his gate would get rid of the hexes on his spot, but I decided to trash them anyway :-D), and Charlie Kane's story (using much of Michael's starting cash). Silas was replaced by Daisy, who started with Eltdown Shards, used later to prevent QU's track from filling. I failed Daisy's Story early so that I could get Find Gate: I needed to send her in in case Mary got disrupted on her way back to seal the last gate.

Luckily, the last Mythos card did not add doom token 12, and Mary came back, used her Lore skill and Revelation of Script spells to close the gate, and used one of Patrice's clues to help seal it. Peace returned to Arkham.

Some notes and comments:

• Five investigators is more than I usually take in; but keeping track of new characters and everyone's PS pass and fail conditions was daunting. No to mention keeping track of all the chaos on all the boards.
• Patrice is great. I likely would not have won without her clue pool. She is good... (too good?)
• Two rifts opened. I got lucky early on by a bunch of the same symbol combos coming out, and later on when they added only two doom tokens total, so it could have been worse.
• Dunwich got two Wizard's Hill gates, which meant a surge. Only one DH token appeared.
• One Next Act card came out. It might
• Innsmouth got a LOT of gate activity. It might have been luck: if Innsmouth had fewer gates, that would have meant more Dunwich gates and Next Act cards. Only two DOU tokens were added: one from a seal, one from a vortex.
• Patrice's Personal Story: it says "each time you draw a Unique Item, put a clue on this card; if there are two, you pass." I assume that means that she has to draw and obtain two unique items? That is, she couldn't just go shopping immediately and says she drew 3 and passed?
• My Anti-Dilution method Mk3 worked extremely well. All boards and the Next Acts saw plausible activity.

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Anti-Dilution Mk3:

Again, you have to make a small "special" deck of just the cards showing Dunwich gates, Innsmouth gates, Next Act cards, and The Story Continues. However, I have two ways to get the probabilities you need:

The "simpler" method:
When you have to draw a mythos card, roll a die. On a 1-4, draw from the "special" deck. Otherwise, draw from the regular deck. I know that this seems like there will be a lot of non-Arkham gates, but that should be fair considering you're aiming to sum the threats of all three relevant expansions. Just remember that the combined individual threats of these expansions add up to 63.31%. Not using my methods and just drawing off one big mythos deck yields a pitiful 28.07%.

• The chances of drawing a Dunwich gate with this method are 26.04%, compared to 24.51% when using just Dunwich. Only a minor increase.
• The chances of drawing an Innsmouth gate are 34.38%, compared to 32.35% with just Innsmouth. Also a minor increase.
• The chances of drawing a Next Act card are 6.25%, compared to 6.45% with just King in Yellow. This is very close.

The "more accurate" method:
When you have to draw a mythos card, roll two dice. If either are a 1 or 2, draw from the special deck. If neither are a 1 or 2, then roll another die: if it is a 1, then draw from the "special" deck. Yes, I know that this is complicated, but it is very, very close. I plan to take three of my unused dice, putting a "special" face on one side of one of them, and on two sides of the other two. I would then draw from the "special" deck if any of the three showed the "special" result. It seems nuts, but check the results for yourself:

• The chances of drawing a Dunwich gate with this method are 24.59%, compared to 24.51%! Very, very close!
• The chances of drawing an Innsmouth gate are 32.47%, compared to 32.35% Even closer than above!
• The chances of drawing a Next Act card are 5.09%, compared to 6.45%. Not as close as the "simpler" method, but this way Dunwich and Innsmouth don't have a combined 3.55% increase over what they should have.

There you have it. You may think that I'm crazy, or that both of these methods put too much emphasis on non-Arkham gates, but like I have explained to another forum user: The goal is to keep Dunwich, Innsmouth, and King in Yellow from being diluted, and the above methods do quite a nice job. The mutual exclusivity presented by using all the expansions together the normal way makes each of the threats significantly less frequent than using them individually; and yet you get a -1 investigator handicap for each board expansion past the first and a +1 gate limit for using both Innsmouth and Dunwich! It hardly seems fair. Plus, this only deals with the Mythos deck: the location and gate decks are unaffected, and will continue to display bits of all expansion themes, as they should.

Minor suggestion for your second method:

How about getting two D3 and ond D6 and drawing from the special deck if there is any one. Makes it a little easier ^^

Enas said:

That's a good idea. But not for me specifically: I printed out red and green mythos stickers to put on some dice. I draw from the special deck if any show a red symbol

For your advanced method, may I suggest: roll three dice and select from the other deck if the total of all three is less than 12. The chances of pulling from the special deck will be 135/216 = 62.5%. Contrast the roll two dice and if needed roll one more, which has a probability of 136/216 = 62.96%. Pretty close if you ask me.

ricedwlit said:

Wow. That's awesome. My optimum percentage is 63.31%. What you've discovered is both close, and palatable. I guess I would only recommend my 2nd version to those who can actually create the dice, as the percentage is only slightly closer in exchange for the load of effort to make the darned things. But just summing the dice is practical--any Arkham player can do it, easily. When I decide to actually spring this crap on BGG I will make sure to credit you.

Thank you!

ricedwlit said:

Ack, I'm getting AD&D character creation flashbacks! Seriously, rolling 3D6 and not getting any of the six stats over 11 wasn't uncommon .

Tibs said:

Hmm ... 63.31% is the ideal? Then roll three dice and pull from the special deck unless you get a total of 9, 10, or 11. The odds then are 137/216 = 63.43%. With three dice you aren't going to get any closer than this.

Amazing work Tibs, respect!

I am wondering though if there will be any hidden skewing in this that affects other parts of the mythos cards, for example in the frequency of a certain type of environment, the monster symbols, and rumours. Theres probably a trade-off. What do you think?

Way to go, Tibs. Nice work on the numbers.

I've gotta admit that I don't imagine I'll actually bother doing it, since my table is not big enough for more than one expansion board at a time anyway, but it's probably the best work-through of the problem yet.

Regarding dj2.0's point: there's not a lot of correlation between gate locations and other effects as far as I can see, and really this method isn't actually 'dividing' the Mythos deck in any meaningful sense, since the probabilities some out pretty close even with the simple method. Still, I suppose some oddity might emerge. These methods do change the comparative usefulness of a few of the game's other cards - there's an encounter at the Inner Sanctum which stacks the Mythos deck a bit, and a spell whcih does something similar I think. Presumably if you used a way of looking at or re-ordered Mythos cards, you'd have to choose which deck to do it on (which would make the effect more powerful, since you could guarantee you'd be able to affect/predict a particular board) or you'd only be allowed to do it to the main 'Arkham' deck (which limits the ability's usefulness a bit). But it's not a big deal either way.

Thanks guys. Regarding your points:

All the mythos cards that aren't in the special deck are poportionally less frequent than they would be if you used the one large deck. But none of these cards drive core threat mechanics quite as the cards in the special deck do. And the Arkham Encounters and Gate cards are unaffected, so you're not less likely to get a Dark Pharaoh Arkham or Other World encounter, for example.

The chances of getting a rumor or an environment shouldn't be that different; just which rumor. Dunwich rumors will be far more frequent than any other rumors.

@thecorinthian:

Yep. You can sidestep the whole need for this anti-dilution if you use only a couple expansions at a time

This is a great solution... I think that my plan is going to be to just use a set of 10-sided percentage dice(two 10-sided dice, one stands for the 10s the other for the 1s)... 63 or lower draw from the "special deck" 64 or higher, draw from the other deck.

Tibs said:

Some of these are pretty tough rumors -- just finished Scenario 9 today and had to deal with the Riots rumor. Low speed for investigators, so couldn't afford to let it fail, yet by the time I passed it I had to retire two investigators due to injuries.

Sorry guys. I was groggy when I said "I'll address those points" but I forgot one:

When "peeking" at the top mythos cards, either by an encounter or Arcane Insight or some other effect, you roll for each card you look at. So with Arcane Insight, if you roll all three cards from the "special deck," you will look at them, and replace them onto the special deck in whatever order you want, but if at the Mythos phase you roll for the "normal" deck... then too bad! Having absolute knowledge about the Mythos deck with a reuseable spell dos not feel right anyway

ricedwlit said:

BUT on the other hand, if you're using both Dunwich and Innsmouth, you're accounting for one fewer investigator when you put tokens on those rumors. With Kingsport, that's -2 investigators! I actually passed Riots today in a 4-investigator game by spending 6 stamina on the first turn the rumor was out.

So on the one hand, the Dunwich rumors are much more frequent (but no more frequent overall than using just Dunwich alone). On the other hand, they're easier than they normally would be. This, I feel, is a fair trade, considering the other horrors you'll have to cope with.

stwerner92182 said:

Yes, it will be easy to visually separate those dice as ones that are only rolled for the mythos.

Dunno if you have seen this thread on BGG but thought it might be of use:

http://www.boardgamegeek.com/thread/405348

What, pray tell, is the chance of drawing The Story Continues, for the Bast junkies out there?

Tibs said:

Alternatively, for those who like the deterministic approach do it like this:

Roll for each card you my look at. Rearrange them any way you like. Then put them TOGETHER into a 3rd mythos deck. Until that deck is depleted do not roll any dice for the mythos phase, but rather draw from that deck. Quite simple.

flamethrower49 said:

As I understand it, originally The Story Continues was 1 in 67 (Mythos cards).

So to emulate that, someone in our game group suggested removing the Story Continues from the Mythos Decks and using the 3 dice method, on a 17 or 18 now "The Story Continues" [we add discards back into appropriate decks, reshuffle and draw again]. We should probably move the base deck to on 8s, 9s, or 10s [11-13 would also work] if we want to keep the percentage at 62.5% for the special deck [135 out of 216 -- i take it you're actually shooting for 137 out of 216 ~63.4% though but I can't see an easy contiguous series of numbers doing that]...

Hmm, I might finally get some Bast love.

flamethrower49 said:

In a Kingsport-only game, the chances of getting The Story Continues is 1 in 89.

The chances of getting The Story Continues varies a bit depending on which "rolling" method you use (from those above), but it hovers around 1 in 101. So that's kind of cool.

kilrah said:

Quite true, but I kind of liked how this now makes the the next three mythos cards possible, rather than definite. It helped out the issues regarding abuse of Arcane Insight quite nicely.