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Shadows of Brimstone: City of the Ancients» Forums » Rules

Subject: How To Combine Map Decks From Multiple Sets rss

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Graham Martin
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EDIT: As a result of the discussion in this thread, I wanted to post a note that the need to use this method is probably pretty low. If you just want to mix everything together and play, you won't destroy your game experience, but you WILL experience occasional swings of very easy and very hard games. (Bigger swings than with the core deck of 18 cards.)

As I say throughout this thread: play how you like!



In responding to several posts about how to mix map cards together when you have multiple other worlds in your collection, I documented my method a few times. I thought I would post it a stand-alone thread so it could be referenced as needed.

A FEW CAVEATS

1) The method below distinguishes between unique rooms (rooms with advanced encounters) and non-unique rooms (those without advanced encounters.) If you are not playing with the Advanced Encounter rule, you do not need to differentiate between unique and non-unique rooms.

2) This is not an official method of handling this issue. You can just shuffle everything together and let luck guide you where it may. The problem with shuffling every map tile into one big pile is that you can have huge streaks of room types that make the game either too easy or render it unwinnable. If you get 18 passages in a row, you aren’t going to do too well. Likewise, if you draw room after room with no passages, you will have an easier time.

3) I know the game isn’t finely balanced. That is part of the fun for my group. However, the 6 passage to 12 room ration seems fairly important to maintain, hence the method I describe, below.

DETAILS

The game was designed to be played with a specific set of map cards:

1) 6 unique passages

2) 8 Unique rooms (with advanced encounters)

3) 4 Non-unique rooms (without advanced encounters)

I recommend storing your mine map cards in three sets: unique rooms, non-unique rooms, and the six passageway cards. (I put the other six passageway cards from the second base set in my “duplicate stuff I will never use” box along with the duplicate rule book, scavenge cards, and loot cards.)

When making a mine map deck, you should do the following:

1) Shuffle all of your mine unique room cards together, draw 8 unique mine room cards, and return the rest to your storage.

2) Shuffle all of your mine non-unique room cards together, draw 4 non-unique mine room cards, and return the rest to your storage.

3) Shuffle the 8 unique cards and 4 non-unique cards you just drew together with the six unique passageway cards to make your 18-card deck.

4) Play the game!

This is all fine and dandy until you find a gate! Remember, that in all core sets, you have 18 map tiles MAX. So, if playing a core set and you used map tile X in the mines and later go through to the Swamps other word and draw the corresponding map card from the Swamps deck, you can't use it because it is already in play as a mine tile. (The Swamp is printed on the back of the in-play mine tile.) With one box set, you would simply discard that card and draw another swamps card. This means that the ratio of unique, non-unique, and passageway tiles is maintained throughout your while adventure and you will never experience more than 6 passage, 8 unique, and 4 non-unique rooms during one adventure for a total of 18 tiles.

To account for this mechanic when you visit an other world, pull out the map deck for that world and do the following:

1) Divide the new world deck into three piles: Unique, non-unique, and passages.

2) Count up the number of each type of map cards you have already played (unique, non-unique, and passage) regardless of how many worlds you have already visited during the current adventure.

3) Discard random cards from each of the new world piles equal to the number of those types of cards you have already use in the previous world.

4) Shuffle the remaining new world cards together to form your deck and keep playing.

From then on, when you draw a card in the new world, randomly remove a corresponding card type from all previous world decks you have used during the current adventure.

Example:

You find a gate and look through it. You draw Targa from the world card deck which means you need to set up the Targa map deck.

No matter which other worlds you have been in during this adventure until now, you count up all of the types of map cards you have used and find you have gone through 2 passages, 2 unique rooms and 1 non-unique room.

You randomly remove 2 passages, 2 unique rooms, and 1 non-unique room from the Targa map deck, place it on the table and continue with your game.

From that point forward, when you draw a Targa map card, you randomly remove one of that type from all other world map decks in play during this adventure. I do this by drawing from the top of each other world deck (usually just one world) until I find the correct map card type, discard it back to the box, and shuffle the deck.

This ensures you maintain 1) the 18-tile limit, and 2) the ratio of unique, non-unique, and passages for your adventure.



Again, you don’t need to do any of this if you just want to embrace the random chaos that comes with mixing all map cards together. Our group just had one to many adventures where the map tile draw was too punishing. (The game is punishing enough without adding to it.)

Also, we use the Advanced Difficulty rules form the FAQ, so if you don’t use those, you may not care as much about long stretches of passages! That’s one of the great things about this game…you can change it up however you like it!


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Max Maloney
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"If trees could scream, would we be so cavalier about cutting them down? We might, if they screamed all the time, for no good reason." -Jack Handey
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I agree with your principle, but I think you are making this far, far too complicated.

I have a basic set of mine deck cards: 6 passages and 4 generics.

I have all the uniques in a separate deck. Before each game, I shuffle this pile and draw 8 without looking, then shuffle those 8 into the basic pile and I have a deck.

That's all the instructions you need. The preparation of the other world map deck seems completely unnecessary and overly complicated.
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Jee Fu
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Oh yeah, well I think you're BOTH over-complicating it! cool

Shuffle all Map cards together that have the same back. Done.


Explanation:

Having the potential for streaks is fine - the difference isn't that significant, plus it makes Abilities/Items that let you manipulate the Map Deck more valuable (which, lets face it, they need to be - does anyone take any abilities in the Tracker Upgrade Tree?).

The odds of getting 3 passageways in a row in an 18 card Map Deck (one set) are ~2.5%. The odds of getting 3 passageways in a row in an 96 Map Deck (all expansions through Trederra - 4 sets) are ~3.4%. This means that in 100 consecutive draws of 3 Map Cards, this streak will happen only 1 more time than it would have otherwise. This is pretty insignificant. If you also shuffle in the Derelict Ship Map Cards, then the Mine Map Deck gets new Rooms but no new passageways. This actually lowers the chances of this situation to ~1.7% (shuffle all map cards together = less chances of passageway streak than a normal map stack).

Conclusion: If you have both Core Sets, Cynder, Trederra, AND the Derelict Ship then shuffling all the Map Cards together actually decreases your chances of passageway streaks. If you don't have the Derelict Ship, then shuffling everything together will increase your chances of a passageway streak by an extremely small amount.

- Jee

EDIT: Also remember that 2 out of the 6 Passageways have multiple doors in close proximity so it's a bit self-correcting on it's time-drain. It's much easier to have the posse Explore 2+ doors on the same Turn when you're on a 4-Way or 2-Way Passageway Tile, should you wish to make up for the loss of Room.
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Graham Martin
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Dormammu wrote:
I agree with your principle, but I think you are making this far, far too complicated.

I have a basic set of mine deck cards: 6 passages and 4 generics.

I have all the uniques in a separate deck. Before each game, I shuffle this pile and draw 8 without looking, then shuffle those 8 into the basic pile and I have a deck.

So far, you and I are doing almost the exact same thing. The only difference is that I shuffle all generics and draw 4. I like the variety of room.

Quote:
The preparation of the other world map deck seems completely unnecessary and overly complicated.

It takes about 10 seconds. It may be unnecessary, but it isn't complicated in practice. cool
 
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Graham Martin
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Inspector Jee wrote:
Oh yeah, well I think you're BOTH over-complicating it! cool

Shuffle all Map cards together that have the same back. Done.


Explanation:

Having the potential for streaks is fine - the difference isn't that significant, plus it makes Abilities/Items that let you manipulate the Map Deck more valuable (which, lets face it, they need to be - does anyone take any abilities in the Tracker Upgrade Tree?).

The odds of getting 3 passageways in a row in an 18 card Map Deck (one set) are ~2.5%. The odds of getting 3 passageways in a row in an 96 Map Deck (all expansions through Trederra - 4 sets) are ~3.4%. This means that in 100 consecutive draws of 3 Map Cards, this streak will happen only 1 more time than it would have otherwise. This is pretty insignificant. If you also shuffle in the Derelict Ship Map Cards, then the Mine Map Deck gets new Rooms but no new passageways. This actually lowers the chances of this situation to ~1.7% (shuffle all map cards together = less chances of passageway streak than a normal map stack).

Conclusion: If you have both Core Sets, Cynder, Trederra, AND the Derelict Ship then shuffling all the Map Cards together actually decreases your chances of passageway streaks. If you don't have the Derelict Ship, then shuffling everything together will increase your chances of a passageway streak by an extremely small amount.

- Jee

EDIT: Also remember that 2 out of the 6 Passageways have multiple doors in close proximity so it's a bit self-correcting on it's time-drain. It's much easier to have the posse Explore 2+ doors on the same Turn when you're on a 4-Way or 2-Way Passageway Tile, should you wish to make up for the loss of Room.

Thanks for the feedback. As I said in the last sentence of my post, "That’s one of the great things about this game…you can change it up however you like it!"

So, just to be clear, my analysis in this thread is just for us nerds who like to pretend that replicating the designers original odds is important OR for those of us interested in problem solving and figuring out how games work.

Obviously with the chaos inherent in every part of this game, it isn't that big of a deal!

So...nerd disclaimer done with, I would like to do some further analysis, though, because yours ignores a few key issues:

1) Most importantly, you ignore the fact that in the base game design, you will experience a maximum of six passageways. By mixing everything together, you can experience many more than that. Each one you draw is one more HBTD roll which is death, incarnate, especially late in the game.

If I have one space left on the depth track and I have already drawn 6 passageways, I don't want to die because I draw one of the 18 passageways in the deck.

We drew 7-9 passageways our first few games with everything mixed together and it wasn't fun.

2) I agree with your math, but I am not sure how you count 96 map cards.

As far as I can tell, these are the existing products that have mine map cards.


MINE MAP CARDS BY EXPANSION

Passage Room Total
Swamps 6 12 18
Targa 6 12 18
Cynder 6 12 18
Derelict 0 11 11
Trederra 6 11 17
Blasted Wastes 0 0 0
Hellfire 0 1 1
Werewolf 0 1 1
Vampire 0 1 1
Black Fang 0 1 1
Lost Army 0 1 1
Crimson Hand 0 1 1
Total Cards 24 64 88


(Please let me know if I am missing something regarding my numbers of any mine cards or sets as these are the only ones I own.)

So, even if you mixed in the mission pack mine cards, the most I see is 88, not 96.

Excluding the mission packs, you get 24 passages and 58 rooms for a total of 82 mine cards.

Using these numbers, we get the following odds of drawing three passages in a row at the start of the game:

Base set of 18 cards: 2.45%

All sets excluding Derelict Ship: 3.54% (This is a tad higher than the 3.4% you calculated.)

All sets including Derelict ship: 2.29%

All sets, including mission packs: 1.84%

Importantly, while changing something from 2.45 to 3.54 sound small, that is a 44% increase in the probability of that single occurrence.

Likewise, a decrease from 2.45 to 1.84 is a 25% change in probability.

The total range from 1.84 on the low end and 3.54 on the high end is almost exactly a 100% increase in the probability.

But, as you note this really means that starting a game 100 times, you will draw three passages right off the bat anywhere from 1.8 of those 100 to 3.5 of those hundred. Still very small odds, but a significant difference.

And, as I discuss below, this is just the odds of drawing three in a row at the very beginning of the game. There are other factors to consider, as well.

Generally, though, this does mean that mixing in other expansions (except derelict ship) makes it harder. Mixing in the derelict ship or mission packs makes it easier.

I would just add that the % change in the odds is fairly significant.

3) You only compare the possibility of drawing three and exactly three passageways in row at the very start of the game. (6/18*5/17*4/16 = 0.0245.)

There are other odds to compare ranging from drawing two in a row to six in a row as well as the odds of drawing multiple in a row when you haven't done so earlier in the game. (Each room you draw increases the odds of a string of passageways later in the game.) Finally, as I mentioned in item 1, above, the biggest issue is the odds of experiencing 7 or more passages in the adventure.

All of those odds change when you mix all cards together. Combine those effects and you have a bigger change in difficulty than your math suggests. I don't think it will be massive, but it is a bigger change than just the odds of drawing three passages at the start of the game.

So, to repeat my disclaimer, this is just a mental exercise. I like math and puzzles. I like getting into a games guts and seeing what makes it (semi) balanced and fun.

As I said in my OP, the fun with this game is in playing it however you want.

I just hate unfairly losing because we run the game's timer clock to zero by exceeding the max of 6 passageways designed into the base games. (Trederra is tough enough without having to slog through 7-10 passageways instead of a max of 6!)

Dying to monsters or bosses is great. Failing because I drew 7, 8, or 9 passageways instead of a max 6 is not fun for me. YMMV!

Thanks again for the feedback. Again, let me know if I am missing anything!



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Christofer Andersson
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I used to do almost exactly like you. However, I decide that this was taking too much time. Last year I played this game 60+ and preparing the deck takes around 2-4 minutes with shuffling and everything. It adds up and I must have spent 2-4 hours preparing the mine deck since last summer. It was just not worth the time. Now I have all the card mixed together and only re-shuffle when I have gone through all the map cards in the game.
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Graham Martin
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A little more math! (Since I didn't know how to solve this math problem, I decided to use it for self education. Let me know if my math is wrong.)

The following lists the % probability of drawing a 6th passageway at various points in an adventure.

Key:

Draws = How many mine cards you have drawn.

18 = The odds of drawing the 6 or more passageways by that draw when using a standard 18-card core set deck.

71 = The odds of drawing the 6 or more passageways by that draw when using a 71-card mine deck. (All expansions except Derelict Ship and the Mission Packs.)

82 = The odds of drawing the 6 or more passageways by that draw when using a 72-card mine deck. (All expansions except the Mission Packs.)

88 = The odds of drawing the 6 or more passageways by that draw when using a 72-card mine deck. (All expansions!)

I spot checked my math using this Hypergeometric Distribution calculator and it seems to be accurate.



Probability of drawing 6 or more passageways

Draws 18 71 82 88
6 0% 0% 0% 0%
7 0% 1% 0% 0%
8 0% 2% 1% 0%
9 0% 3% 2% 1%
10 1% 7% 3% 2%
11 2% 11% 6% 4%
12 5% 17% 9% 6%
13 9% 23% 13% 10%
14 16% 31% 18% 14%
15 27% 39% 24% 18%
16 43% 47% 30% 24%
17 67% 55% 37% 29%
18 100% 63% 44% 35%


For example, the odds of drawing at least six passages by your 11th draw is only 2% in the 18 card "core deck," but is 11% in the 71-card deck, 6% in the 82-card deck and 4% in the 88-card deck.


Probability of drawing 7 or more passageways
Draws 71 82 88
7 0% 0% 0%
8 0% 0% 0%
9 1% 0% 0%
10 1% 1% 0%
11 3% 1% 1%
12 5% 2% 2%
13 9% 4% 3%
14 13% 6% 4%
15 19% 10% 7%
16 25% 13% 10%
17 32% 18% 13%
18 40% 23% 17%


For example, the odds of drawing at least seven passages or more by your 13th draw is 9% in the 71-card deck, 4% in the 82-card deck and 3% in the 88-card deck.

While not a comprehensive set of stats to figure out the impact on a game, these tables do establish that the risk of extending the adventure increases fairly significantly as you mix decks.

What the impact on the game may be, (1 or 2 extra passages per adventure on average is my guess) may be important to some folks. Those one or two extra hold back the darkness rolls could be make or break.

Anyhoo, just a chance to learn some new math in a fun way!
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Jee Fu
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88 Cards, quite right. I was doing napkin-estimates with no actual cards in front of me. But the numbers work out similarly so I think my point stands: this isn’t going to happen often enough for you notice. It you think it IS happening more often enough for you to notice, then it’s probably confirmation bias. In other words if you played 10 games with both decks without knowing which was which ahead of time (one with 18 and one with 88, pretend they’re both inside equal sized opaque boxes), you still wouldn’t be able to tell which was which - with any kind of reliability - at the end of those 20 games.

A coupla other points:

1) My math regarded “sets of 3 consecutive cards”, not sets of entire Adventures so it applies to more than the start of the game.

2) All the calcs you did are pretty cool. Thanks for crunching the numbers.

3) Most Adventures (in my experience) don’t last more than 7 Tiles. In fact, there is a sizable portion of them that have a hard cap of 5 Tiles (and in those cases passageways are a good thing because the ending trigger is posse-marker based). Even if you go further than that, you have to get to 15 Map Cards before the differences between 18 and 88 become ...even kinda of noticeable by the human experience.

4) While the delta between ~2.5% and ~3.5% may sound substantial when expressed as a meta-percentage (40% increase), it’s not a very meaningful stat. Your chances of having a car accident might go from 0.0001% to 1% simply by getting in your car instead of staying home. That’s a 1,000,000% increase, but lets face it - you’re probably not getting in an accident. Nor would the risk outweigh the benefit (unless you were driving to Taco Bell - then the risk wouldn’t be worth it).

5) Even if there was a substantial difference, I would be ok with that. I don’t consider it an unfair loss if Ive played in the most official manner. If the clock ran out, it means we didn’t respond to the intended challenge well enough - next time we’ll be more efficient with our actions or we’ll invest in items and abilities that manipulate the map deck.

- Jee
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Graham Martin
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Inspector Jee wrote:
88 Cards, quite right. I was doing napkin-estimates with no actual cards in front of me. But the numbers work out similarly so I think my point stands: this isn’t going to happen often enough for you notice. It you think it IS happening more often enough for you to notice, then it’s probably confirmation bias. In other words if you played 10 games with both decks without knowing which was which ahead of time (one with 18 and one with 88, pretend they’re both inside equal sized opaque boxes), you still wouldn’t be able to tell which was which - with any kind of reliability - at the end of those 20 games.


Looking at the math we have done, I tend to agree with you, with a few caveats:

1) Long games are where you will notice the difference, especially with the 71 card deck. The longer your game goes, the more likely it is to go even longer because you have pulled extra passages you wouldn't have pulled with a different ratio. So, with long games, not only is the HBTD failure rate increasing, so is the chance of extending the game due to extra passages, which forces more HBTD rolls.

2) Given the ratio of passageways to rooms in each type of deck, I agree that it will be hard to detect a difference in most cases.

The new ratios are simple % passageways in each type of deck:

18 = 33.3% of the cards in the deck are passages

71 = 33.8% of the cards in the deck are passages

82 = 29.3% of the cards in the deck are passages

88 = 27.3% of the cards in the deck are passages

82 and 88 card decks have a lower ratio of passages to rooms than the 18 base set deck!

Quote:

1) My math regarded “sets of 3 consecutive cards”, not sets of entire Adventures so it applies to more than the start of the game.

You only know the odds of drawing 3 in a row when you know the makeup of the entire deck.

The math you did for the 18 card deck was 6/18 * 5/17 * 4/16 = 2.45% chance. You only have 6/18 at the very start of an adventure.

For example, imagine we play one turn and reveal a room. What are the odds that we will pull three passageways in a row next? That math is 6/17 * 5/16 * 4/15 = 2.94% which is different than at the start of the game.

Likewise, if we imagine we have played 3 cards and revealed 1 rooms, 1 passage, and then 1 more room, the odds of a triple passage showing up next would be 5/15 * 4/14 * 3/13 = 2.19% (Different than the odds at the start of the game.)

Finally, if you were using the 71 card deck with the example above where we have revealed 3 cards already, the odds under this scenario would be 23/68 * 22/67 * 21/66 = 3.53%

That is why I noted that the numbers you quote only apply to the start of adventure.

The odds of pulling three passages in a row at least once in a game are much harder to figure. I don't know the math for that, so I would have to brute force it: Calculate all possible distributions of 18 cards and then count the number of times we find at least three passages in a row.

The math for figuring out how many ways you can arrange 6 passages and 12 rooms if you don't care about the exact passage or room is:

(18!)/(6!*12!) = 18,564 unique combinations.

Since 18,564 is a relatively small # of permutations for a computer, this might be an interesting software problem to figure out things like avg # of passages drawn by card # X or odds of drawing 4 passages in a row at any time during an 18-card game, but I am working on making Blasted Waste cards! Maybe later!

Quote:
3) Most Adventures (in my experience) don’t last more than 7 Tiles. In fact, there is a sizable portion of them that have a hard cap of 5 Tiles (and in those cases passageways are a good thing because the ending trigger is posse-marker based). Even if you go further than that, you have to get to 15 Map Cards before the differences between 18 and 88 become ...even kinda of noticeable by the human experience.

I agree that you only notice a difference in longer games. That said, our average game goes longer than 7 tiles, often ranging toward 9 or 10. We must be doing something wrong! (We do play a lot of the "find two clues and then fight a boss" type of adventures, though.)

Quote:
4) While the delta between ~2.5% and ~3.5% may sound substantial when expressed as a meta-percentage (40% increase), it’s not a very meaningful stat. Your chances of having a car accident might go from 0.0001% to 1% simply by getting in your car instead of staying home. That’s a 1,000,000% increase, but lets face it - you’re probably not getting in an accident. Nor would the risk outweigh the benefit (unless you were driving to Taco Bell - then the risk wouldn’t be worth it).

Yup! That is why I noted "this really means that starting a game 100 times, you will draw three passages right off the bat anywhere from 1.8 of those 100 to 3.5 of those hundred. Still very small odds, but a significant difference."

Quote:
5) Even if there was a substantial difference, I would be ok with that. I don’t consider it an unfair loss if Ive played in the most official manner. If the clock ran out, it means we didn’t respond to the intended challenge well enough - next time we’ll be more efficient with our actions or we’ll invest in items and abilities that manipulate the map deck.

This observation is probably the core of my discomfort. I don't really know what the "intended challenge" (as you put it) is. The rules just say you "may" mix the map cards together, not that you "should" or "must." That, more than anything else, is what makes me want to do the math and compare the odds to the base game. My assumption is that FFP did all of their design and balancing one the base sets using an 18 card deck which means a max of 6 passages, including when you travel to other worlds.

Given their track record, I am doubtful that they did any serious balance testing with the expanded worlds. I get the feeling, and I am sure it is a biased one, that they pumped out the expansions and just said, "Sure! Combine map decks! Whatever....." I think this comes from a sense that FFP isn't the most organized, thoughtful, or even nice organization.

However, all of this math we did plus your well-argued points have definitely persuaded me that this is a much more minor issue than I suspected before this thread.

I appreciate you time and efforts in exploring this issue!
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Jake G.
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This thread has been a very interesting read!
 
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