Deck Building Math

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Here are a couple of probability charts that should help with deck building:


First, probability of drawing cards by a certain turn:



So, for example, if you have 4 viable first-turn drops and want to know how likely you are to draw them, this would correspond to row 4 column 1, so 83% of the time you’ll be able to play your openers. If you have 2 Mawcors you’d like to play on turn 4, this corresponds to row 2 col 4, so you’ll have them 87% of the time.


Second, probability of having AI play cards on or before a certain turn:



If you’re playing 5 Blood Walls and would like to have at least one out on turn 2, this would be row 5 col 2, or 78%. If you run an EMP on defense, AI will open with it 10% of the time (row 1 col 1).

If you want the probability of playing the cards after a certain turn, just subtract from 1. So, if you’re curious how often the AI will the EMP at a good time (I’d say turn 4 or later), that would be 1-.3=70% of the time.


Trying to keep this short and simple, but I’ll add things as I think of them.

 
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too..much…math.
I dont know how you calculated all of this data, but thanks dwarrior, this really helps.

 
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Nice post, I sometimes make those calculations by myself, having a table with the values is most useful.

 
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Very useful- although I don’t bother with stuff like this, it’s either you know what to play or you don’t, the math is unnecessary after a certain point.

But regardless, good job.

 
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3rd great post! keep up the good work
a real pity that you are in SOE ;)

 
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“Probability to draw a number of certain cards in a certain number of turn”?
I don’t see how I can use this, except to imagine how long I will have to struggle to apply someone’s guide of doing Speedy Missions…

 
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IMO, the most useful bit of this imformation is “Probability of drawing one of X cards on turn 1”. It’s important to know that 90% of the time you’ll be happy with your turn 1 card, so you probably want at least 5 cards that are good on turn 1.

 
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Originally posted by Mastertek:

“Probability to draw a number of certain cards in a certain number of turn”?
I don’t see how I can use this, except to imagine how long I will have to struggle to apply someone’s guide of doing Speedy Missions…

Ouch, DW, you just got dissed by the math nerd of the forums. That’s got to hurt.

On the other hand, it amazes (conerns) me that people think simple probability tables are difficult math. I mean, there’s not even a redraw, replacement, or any other complications.

 
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Originally posted by Tuxedo:
Originally posted by Mastertek:

“Probability to draw a number of certain cards in a certain number of turn”?
I don’t see how I can use this, except to imagine how long I will have to struggle to apply someone’s guide of doing Speedy Missions…

Ouch, DW, you just got dissed by the math nerd of the forums. That’s got to hurt.

On the other hand, it amazes (conerns) me that people think simple probability tables are difficult math. I mean, there’s not even a redraw, replacement, or any other complications.

wat? DWarrior IS the math nerd. I just used… a man’s intuition so far…
On [my] hand, it amazes (concerns) me that people still mention “AI” in this game even though there’s none…

 
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the AI table doesnt take into account the AI cardtype play preference.

 
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Originally posted by Mastertek:
On [my] hand, it amazes (concerns) me that people still mention “AI” in this game even though there’s none…
Originally posted by mightygoose:

the AI table doesnt take into account the AI cardtype play preference.

Wow. Proof just after the assertion of concern.

 
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Originally posted by Mastertek:
Originally posted by Tuxedo:
Originally posted by Mastertek:

“Probability to draw a number of certain cards in a certain number of turn”?
I don’t see how I can use this, except to imagine how long I will have to struggle to apply someone’s guide of doing Speedy Missions…

Ouch, DW, you just got dissed by the math nerd of the forums. That’s got to hurt.

On the other hand, it amazes (conerns) me that people think simple probability tables are difficult math. I mean, there’s not even a redraw, replacement, or any other complications.

wat? DWarrior IS the math nerd. I just used… a man’s intuition so far…
On [my] hand, it amazes (concerns) me that people still mention “AI” in this game even though there’s none…

Not true. This game has just as much as my See ‘n’ Say does. It’s very smart. It taught me that the cow goes “Moo!”

People are going to call it an AI because it’s much easier than saying semi-randomized card picking program. Is it incorrect? Sure, but think about how many people misuse irony.

 
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Definitely no AI here. It is randomly drawing.

As proof.. you can turn on autoplay and let the AI play your offense deck (or get someone to play your defense deck and see).. the AI will sometimes do insanely stupid things.. like Using an airstrike early on when there are no enemy assault cards in the field. (You can structure your deck such that it is impossible to get 3 useless cards, so no rational player would ever waste an airstrike given any 3 cards)

I figure if there was any AI, it’d be coded to at least avoid doing useless things like that.

 
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This game has AI. In it’s infinite wisdom it knows to always use an action card first when you have the game set to auto!

 
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Mastertek: It can be used to see how many siege cards you should pack. For example, by turn 3 you’ll realize that your opponent’s deck is all structures, so running 2 siege gives you only 53% chance to draw them to deal with the threat, while 3 gives you 71%.

I do agree that this is most useful to look at good 1st turn plays, but filling out the rest of the table was just dragging in Excel, and it’ll occasionally come in handy.

Also, the game has no AI, but that’s the easiest way to refer to it. I guess we can also use “CPU”, but then we’ll get computer purists saying it’s not the central pocessing unit that’s playing. We can also call it RNG, but then many people won’t know what that means. AI caught on, you can reackronym it to “Artificial Idiot” if you so desire.

 
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Random number generator?
I would like to know if the RNG is similar to kongai in any way.
Thanks :)

 
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As I may recall, i have been referring to ‘artificial idiot’ ubiquitously as ‘it’ so far…

Originally posted by DWarrior:

Mastertek: It can be used to see how many siege cards you should pack. For example, by turn 3 you’ll realize that your opponent’s deck is all structures, so running 2 siege gives you only 53% chance to draw them to deal with the threat, while 3 gives you 71%.

Yeah, in my ‘deck formula’ thread, I intuitively assign 2-3 cards with Siege in a deck to be reasonably safe against Structure. With 3 Siege cards, there’s only 3% possibility that all those 3 cards will come in later half – last 5 cards (5A3x7! / 10!). I think the problem is just that there are too few cards being played (10) so that this kind of calculation is not as much useful. It would be good in case of building an army of 50 or more :-3

 
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Another interesting table would be “Probability of getting unacceptable starting hands”. If I have 4 EMPs in my deck, what are the odds of starting out with 3 of them? That’s 3.3%.

 
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Easy math, I know, but you get props, because all of us are too lazy to do it (for the most part)

 
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Why do we care about this; at all?

Sure, it’s amusing to see it written out… but are we really going to be using decks with less than 10 cards?

 
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captain catface, these tables are based entirely on 10-card decks… if you use a deck with less than 10 those numbers don’t work.
Anyway, thanks for posting this stuff, it may come in useful.

 
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Originally posted by Captain_Catface:

Why do we care about this; at all?

Sure, it’s amusing to see it written out… but are we really going to be using decks with less than 10 cards?

??? I think you missed the entire point of the tables. The table is for a 10 card deck that needs Kraken in the opening hand or needs 1 of 2 Mawcors by turn 4 or needs 1 Blood Wall on turn 2 and is choosing between running 4 or 5 Blood Walls out of 10 cards.

Meanwhile there are also at least two great reasons to run a short deck:

(1) To get a speedy achieve that has to be done by turn 9, the player only gets to play 5 cards. Adding more cards only increases the chances of a bad opening hand (such as 3 duplicates of your finisher).

(2) Also, when auto-grinding certain NPC missions, you’ll get a lock once you’ve cleared the board and established (say) 6 hp of strike control. Since the game becomes an auto-win, it doesn’t make sense to dilute the deck with extra cards that aren’t Tiamat/Predator/Chronos — that will only increase the chances that your autopilot will misplay and lose the hand for you. I suppose this could also apply to auto-ing vs known decks in the arena.

 
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Awesome job, DWarrior! If anyone wants to do this sort of thing for other situations not provided, here’s a handy chart for calculations.
http://stattrek.com/Tables/Hypergeometric.aspx
Really handy for finding ccg probabilities

 
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Why would you build a deck that requires you to have a specific luck-based event? Meh, just seems like entirely useless statistics to me.

 
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Originally posted by Captain_Catface:

Why would you build a deck that requires you to have a specific luck-based event? Meh, just seems like entirely useless statistics to me.

For one thing, defense decks can’t expect to win most of the time, so it’s better to design them with a plan to win if you get lucky.