Territory card symbol distribution on risk maps

[woven cosmos]

My question is this: does anyone know how the territory card symbol distribution works for other maps besides the classic map? For the classic map, there are 42 territory cards with either an infantry, a cavalry, or an artillery symbol (14 of each, 14 x 3 = 42), plus 2 wilds for a total of 44 cards. This means that at the end of your turn (provided you took a territory) you will draw one of these 44 cards.

Now consider Spaceport Sigma. Since it has 96 territories, I would presume it has 32 each of infantry, cavalry, and artillery (since 96/3=32). But how many wilds would the "card pool" have? Would it increase to scale with the number of territories, or would it stay static? Additionally, what happens for maps like Pirate's Bay, where the total number of territories (83) isn't divisible by 3? How does symbol distribution (infantry, cavalry, artillery) work?

I wasn't able to find an answer to this anywhere online, so if anyone has any insight they could provide, that would be greatly appreciated. Thanks!

[quaint reef]

I would assume wild cards make up the difference to ensure the number of infantry, cavalry and artillery are equal

[silent tangle]

2 wildcards per map (it's the primary constant with cards)

Some maps like Supermax have some duplicate cards (while having some missing cards in place)

Only thing to note is the distribution isn't a fixed 1/3 split

[woven cosmos]

Interesting, I wouldn't have thought that there would always be two wild cards. Additionally, if there isn't a fix 1/3 split, what does that mean for the distribution of symbols on territory cards? Is it "always" unbalanced, or is it fluid and just depend on what cards are missing/duplicated? Additionally, do you happen to have access to any resources which show what the symbol distributions are for territory cards on other maps? I'm doing some calculations regarding average card trade value for fixed, and could really use some insight on how the "card pool" works on various maps.

[woven cosmos]

Also apologies for pinging you, I didn't realize that replying to you automatically had pinging turned on

[silent tangle]

Pings on replies are okay - we don't have any public information detailing card distribution just now, it'd be a good suggestion for #risk_ideas though (whether it'd be as an FAQ, a public Google Sheet, or introduced in-game as an "advanced data" info for maps on expand

I'm pretty sure it's fairly random how many of each there are, only surefire way to identify is using 6 player pass & play as you can collect up to 36 cards at a time (and should be able to see most cards within a couple of trades on any map) - some maps like simple world you can run out of cards - which has some unique messaging when that happens too

[woven cosmos]

Alright sounds good, I might make this a suggestion in the risk ideas channel to see if it can gain any traction. And that’s a good idea about doing a pass and play game to figure out the card distribution for maps, I’ll probably try that out too. Thanks for taking the time out of your day to help answer my questions Luci!

[scarlet cairn]

I did research this topic and my spreadsheet is public. It's linked in #risk_strategy but here is the link too.
https://docs.google.com/spreadsheets/d/1JwMvOBRBdgrZgKdJMMKjVrPYGF8zQvJmCuOfZ3vLf9g/edit#gid=817826030
One thing to note is that I can't proof that the cards are randomly distributed, and it seems like 1 card is missing each game, if the map has more than 30 territories. I tested that on Castle which has 31 territories, which means 33 cards, and I was not able to find a card for 15 turns while controlling all 6 players. I did that math for that to happen for 9 turns which is ~0,11%.
Something else to note is that each territory has a fixed figure attached to it. I tested that first on classic with 3 retry's.

[spice thistle]

https://docs.google.com/spreadsheets/d/1zDmp3qmYYWAAhAKoNJIJmzlMZWMGpNfSBf5mzBNL5Jw/edit?usp=sharing Here you go, brute force. It ignores the territory bonus (since that is player/blizzard/game dependent); it doesn't account for a trade in strategy, to optimise card value and it doesn't consider that you can trade in at 6-9 after a kill.

@scarlet cairn maybe just the average value and set on %, are nice to include in your sheet?

[scarlet cairn]

The problem with those is that they are not accurate. It always depends on cards held by you and by the other players. And it also matters which card is not part of the deck for that game. For example if you hold 2 Infantry cards on Mall of the Dead you are still more likely to draw another one than any other card.
And I think that would be a little too much for the overview, but I could make it another tab.
Now I can't think of a way to make that even nerdier, other than some random charts to compare maps in some way.

[spice thistle]

For sure, it assumes no one holds cards, since you can't know before the game. Ah, so every game another card can be missing? Didn't understand that before.

For example if you hold 2 Infantry cards on Mall of the Dead you are still more likely to draw another one than any other card.
Not sure I understand, just took all combinations of cards you can draw from the deck.

[scarlet cairn]

Let's say you play a game of Mall of the Dead and you are the only person to take cards.
Your first card is an Infantry 29/74
Your second card is also an Infantry 28/73
Your odds for your third card are
Infantry 27/72 Cavalry 24/72 Artillery 19/72
And that is when we ignore the random missing card.
This dynamic changes depending on cards held by your opponents, because all players share just 1 deck of cards.

[spice thistle]

Indeed, it doesn't consider game dynamics/what happens in-game, so you always have to be cautious how to use the numbers. It's just static deck properties (and thus also ignores that a card can be missing from that deck).

[woven cosmos]

I think you could calculate on average how many of each card type are in other players’ hands. For example, suppose it’s the first turn, and you went first. You will know what card you got, so you will know how many of each card type are left (ignoring the fact that one random card will be missing). Additionally, once everyone else takes their first turn (assuming they all manage to take a card), they will have a collective 5 cards (assuming this is a 6 player game). You could calculate the probability of what cards those other 5 players drew by just considering all possible 5 card combinations, drawn without replacement, and use EVs to find the average.

An EV just multiplies every possible outcome by its respective probability, and sums all those products up. For example, if you wanted to calculate the EV of number of infantry drawn, you could do (0 (infantry) * probability of drawing 0 infantry in 5 cards + 1 (infantry) * probability of drawing 1 infantry in 5 cards + … + 5 (infantry) * probability of drawing 5 infantry in 5 cards, and this entire sum would give you, on average, the number of infantry you would draw from 5 cards, if you were to repeat draw 5 cards over and over again from the same deck state.

If you do this for artillery, cavalry, and wild cards, you could figure out on average how many of each card type should be left by the time it gets back around to your turn.

[scarlet cairn]

Or you take the base odds and call it a day :D

[spice thistle]

@woven cosmos

An EV just multiplies every possible outcome by its respective probability, and sums all those products up. For example, if you wanted to calculate the EV of number of infantry drawn, you could do (0 (infantry) * probability of drawing 0 infantry in 5 cards + 1 (infantry) * probability of drawing 1 infantry in 5 cards + … + 5 (infantry) * probability of drawing 5 infantry in 5 cards, and this entire sum would give you, on average, the number of infantry you would draw from 5 cards, if you were to repeat draw 5 cards over and over again from the same deck state.
Note that this sum is just the same as % infantry in the deck * # of cards you pick. That's a bit easier to calculate.