I'm currently doing some asfan calculations for my cube, so I figured I'd write a guide that can go on the hypothetical "read this if you're new to cube" reading list. I'm going step by step for anyone who is not familiar with the topic, so don't be offended if you already know this stuff. If you have any suggestions for improvements, let me know. Enjoy!
What is asfan?
Asfan is a number that tells you how many cards in a pack are, on average, going to be part of the subset of cards you're calculating asfan for. An asfan of 1,8 removal spells for a set means that, on average, you're going to see 1,8 removal spells in any given pack of that set.
What is asfan good for?
Asfan is a tool you can use when designing your cube. It allows you to compare and contrast your cube to other cubes and actual draft sets. Asfan helps us when we think about the construction of Magic sets and other cubes and that can only make us better at building our own. That's nice and abstract, so what does it do for you, really?
If you have the feeling your cube has too much of x or too little of y, you can crunch the numbers for other cubes and compare.
asfan lets you compare your cube to some of the cubes (commonly called "draft sets") people who do this for a living have contructed.
Say you're in love with how Khans of Tarkir plays. You can calculate asfan for removal, morph, multicolor cards, creatures with prowess and so on and compare those numbers with the numbers of your cube. For example, morphs in Khans had an asfan of 2.15. If your cube only has 0.5, you need more morphs if you're going to imitate Khans.
If you're new to cubing, you could look at cubes of regulars around here, crunch the numbers and get a pretty good idea what a good range for removal, multicolor, and so on for your own cube is.
Keep in mind that there is no "wrong number" for subsets like removal. If the creatures in your cube all have evasion you will need more removal, because removal will be the main way to interact with them. The ways in which your cube is special matter when you do these comparisons.
(Percentage of commons of the subset in decimal form x 10) +
(percentage of uncommons of the subset in decimal form x 3) +
(percentage of the rares of the subset in decimal form x 7/8) +
(percentage of the mythic rares in decimal form x 1/8).
In cube, you just calculate:
Percentage of cards of the subset in decimal form x15
You should calculate your asfan this way even if you do not draft your cube with three packs of 15, because what you want is a number you can compare to those of other cubes and draft sets. The only reason to deviate is if you actually want to know how many cards of a specific subset you see in each pack or grid, but keep in mind that you cannot compare those numbers to other cubes and draft sets anymore.
Example calculation: asfan for removal in my cube
The simplest way to calculate the percentage of cards in a subset is: (number of cards in subset)/(number of cards in cube)
Below is a longer step-by-step description.
At the time of writing, my cube has 405 cards, so 1% = 4.05 cards. My removal subset has 56 spells (W8, U2, B16, R15, G4, MC7, A4). I'm not counting bounce and tap effects and I'm being generous with cards like Blightcaster and Contagion Clasp (they will probably not kill immediately, but might, so I counted them).
To get the percentage of cards, divide the number for the subset (56) by the number for 1% (4.05). I get 13.827, which tells me that removal makes up 13.827% of my cube. Divide by 100 to get the decimal form (0.13827).
At this point all that's left is to multiply by 15, as per Rosewater's formula. The asfan for removal in my cube is 2.07, so on average I will see 2.07 removal spells in every pack.
At this point I'd maybe go and pick some popular draft sets to compare my numbers to. Innistrad removal asfan was at 1.7, Rise of the Eldrazi removal asfan was at 1.9. So my removal numbers are reasonably close to some of the best draft sets of all time. Good for my cube, probably! Had I gotten a removal asfan of 3.8, I may well have to think hard about the way my cube is constructed, as that would be an additional two kill spells per pack. As I said above, it may still be the right number for my specific cube. Asfan is a tool to help us build our own cubes, it is not meant to tie us to preconceived notions about how things are supposed to be done.
Some points worth considering while using asfan:
The term "removal" commonly includes the following effects:
destroy
deal damage
reduce toughness
exile
forcing your opponent to sacrifice a creature
"shuffle into library"
The "shuffle" effects also include cards like Condemn, which do not actually shuffle, but not cards like Time Ebb, because your opponent will just draw the creature again next turn, so it's much closer to effects like bounce which blue gets instead of removal.
Cubes need more counterspells than modern sets. Most modern sets only have 3-5 counterspells total across all rarities, with asfans as low as 0.15 in SoI (meaning you'll see one counterspell every 6 or 7 packs). A single counterspell at common adds much more to asfan than a single counterspell in cube. The average asfan for modern sets seems to be about 0.3, which means a single counterspell every three packs. These sets are not good models if you want a more traditional blue control. Even if you're fine with the modern rate you'll need 7 counterspells at 360 cards and 9 counterspells at 450 to get an asfan of 0.3.
If you care about the distribution of the cards of a subset across colors as opposed to "just" asfan of a subset for your cube, multicolor cards count 0,5 towards both of their colors (so Electrolyze adds 0,5 to blue and 0,5 to red).
This is definitely useful for comparing the amount of "whatever" relative to other cubes. That said, can't you simplify the math to just this formula:
(# of whatever eg. removal)/(total # of cards in your cube) x 15 cards you expect to see in a pack? In your case, 56/405 x 15 = 2.07 average instance of removal per pack.
Heh, I guess you're right. I was focusing so hard on explaining the calculation step by step that I didn't think about taking the simplest math route. I'll include that if I do an update.
1.81, and I was counting stuff like Daze and Havoc Demon but not bounce. I am actually surprised it turned out this low but I suppose I have reason to be happy: too much (quality) removal most definitely ruins a format.
I did not count counterspells at all on the basis that they can't actually remove an existing threat and are very different from all other removal in that respect. I have a special asfan for them. Maybe they should be included, but I couldn't find anything about Wizards counting counterspells as removal either.
Should not be a big problem though, as long as counterspells always/never count, the numbers stay consistent and comparable across cubes and sets.
edit: even if you count counterspells as removal, I don't think you should count Memory Lapse and Remand by the way, as those are like bounce and tap in the sense that they do not remove the problem permamently.
Yeah, I excluded Remand because I consider it bounce. The logic with which I went was essentially 'does it answer a creature (by making it unavailable)?' which is why I included the counters which actually get rid of the spells for good. A lot of the time, they will be used on creatures, after all, since those still constitute a majority of threats in Magic, particularly in the early game when control decks need to buy time.
Makes sense to me as well. I just found an old 2008 Rosewater article where he talks about counterspells as removal:
Blue – Blue has very little creature removal. To deal with creatures it has to rely on its other bag of tricks from counterspells to "bounce" (aka Unsummoning) to stealing creatures.
So it looks like they did not consider counterspells removal 8 years ago. I still don't think counting them as removal is wrong, as long as it's consistently done one way or the other and as long as we keep in mind that e.g. your number is going to be slightly higher than mine by default, because you included them. It'll still be fine for comparisons.
Most of the time including counterspells is only going to add 3-5 cards to the subset, so it's not a massive difference anyway. My removal asfan would go from 2,07 to 2,19.
Counting counterspells as removal makes no sense to me. Counterspell works in 1 timing window and if you miss it they're dead cards. Doom Blade works at any point in the game.
Small update with simple calculation and a new section "some points worth considering while using asfan." If anyone has suggestions for that section, please do tell!
I have recently been thinking about asfan in relation to gold cards in a cube, here’s what I came up with:
In a standard 8-man draft, I would like 1 gold card from each guild to be represented per round of packs, so as to offer/entice/reward drafters for being in that specific guild. This means that there are 10 gold cards per 120 cards (8 players x 15 card packs), resulting in a percentage of 8.33% or an asfan of 1.25. This yields the following:
That's cool, I never thought of using asfan like that. That's a good way of figuring out how many gold cards you want. The numbers are slightly above what most people here are running, so seems reasonable.
Those numbers seem pretty legit. I don't think I would want more than 3 gold cards per guild at 360, and ~4-5 at 540 is about where I want to be as well.
In a standard 8-man draft, I would like 1 gold card from each guild to be represented per round of packs.
This means that there are 10 gold cards per 120 cards (8 players x 15 card packs),
What do you guys think of this thought process and method, and the resulting numbers?
This actually vastly undersells the number of gold cards you'd need if you want to average each guild showing up in a round. Or even nine, or eight.
Your numbers give you the number of gold cards you'd want to get 10 in a round, but not "1 card from this particular guild, "1 card from this particular guild, 1 card from this particular guild, 1 card from this...."
Think of it like this: how many times do you have to roll a die before you have a 50% chance of having rolled every number? It's way more than six. In fact, you only have about a 2% chance of doing that with six rolls.
You're guaranteed to get a unique result in your first try (duh), but on your second go you have a 5/6 chance of getting there. Then, if you did, you have a 4/6 chance for the next roll. And so on.
So the chances are 5/6 x 4/6 x 3/6 x 2/6 x 1/6, or 120/7776. Just over 1.5 percent.
So the number you'd want would be much bigger, for one. It's actually an annoying calculation that I can't remember, but let's say it's 5 per guild at 360. It may be higher. But with 5, that yields 2.083 per pack.
Generously, out of your 8 drafters, you may get 7 guilds represented. Well, you'd have 2.083 gold cards per pack, so multiply by 8 to get 17 gold cards per round. Divide by ten to get 1.7 cards of each guild per round.
If three of the guilds have no drafter, then multiply 1.7 by 3 to see that there are 5 cards per round that have no drafter to take them.
Each individual drafter doesn't want gold cards outside of their color pair, so 1.7 x 9 guilds is about 15 cards that they don't want. Granted, if they were monocolored cards then only 6 of those cards would be expected to be one of an individual drafters colors, but that's still 6 extra cards for a player that they dont have. 18 extra cards in a whole draft. That's probably a big deal.
I'm at about 390 and run 3 gold cards, and I still feel like I want to run a slightly larger cube in order to dilute them further
Thank you! That’s great feedback. I suck at math, and I just started recently thinking about these issues for my cube, so you setting me straight before I get too carried away in a certain direction is definitely helpful!
The thing is, I’m interested in looking at some results that aren’t quite at the 90% clip, but sadly other numbers aren’t analyzed in his piece, and the hypergeometric calculator by itself seems insufficient due to the lack of considering a mulligan strategy.
He kind of loses me with talk of conditional probability and coding a simulation...
Do you know how to do this kind of thing? I’m interested in looking at color requirements in the 66%-83% range.
The issue that I’m having is that the results that you can generate using the hypergeometric calculator are insufficient because they do not account for unkeepable hands that you would mulligan.
Karsten wrote that the exact calculations required the use hypergeometric calculations and conditional probability, but that was too complex and tedious, so he coded a simulation to ease his task.
What is asfan?
Asfan is a number that tells you how many cards in a pack are, on average, going to be part of the subset of cards you're calculating asfan for. An asfan of 1,8 removal spells for a set means that, on average, you're going to see 1,8 removal spells in any given pack of that set.
What is asfan good for?
Asfan is a tool you can use when designing your cube. It allows you to compare and contrast your cube to other cubes and actual draft sets. Asfan helps us when we think about the construction of Magic sets and other cubes and that can only make us better at building our own. That's nice and abstract, so what does it do for you, really?
Keep in mind that there is no "wrong number" for subsets like removal. If the creatures in your cube all have evasion you will need more removal, because removal will be the main way to interact with them. The ways in which your cube is special matter when you do these comparisons.
How do I calculate asfan?
The formula for a normal draft set according to Marc Rosewater:
In cube, you just calculate:
You should calculate your asfan this way even if you do not draft your cube with three packs of 15, because what you want is a number you can compare to those of other cubes and draft sets. The only reason to deviate is if you actually want to know how many cards of a specific subset you see in each pack or grid, but keep in mind that you cannot compare those numbers to other cubes and draft sets anymore.
Example calculation: asfan for removal in my cube
The simplest way to calculate the percentage of cards in a subset is: (number of cards in subset)/(number of cards in cube)
Below is a longer step-by-step description.
At the time of writing, my cube has 405 cards, so 1% = 4.05 cards. My removal subset has 56 spells (W8, U2, B16, R15, G4, MC7, A4). I'm not counting bounce and tap effects and I'm being generous with cards like Blightcaster and Contagion Clasp (they will probably not kill immediately, but might, so I counted them).
To get the percentage of cards, divide the number for the subset (56) by the number for 1% (4.05). I get 13.827, which tells me that removal makes up 13.827% of my cube. Divide by 100 to get the decimal form (0.13827).
At this point all that's left is to multiply by 15, as per Rosewater's formula. The asfan for removal in my cube is 2.07, so on average I will see 2.07 removal spells in every pack.
At this point I'd maybe go and pick some popular draft sets to compare my numbers to. Innistrad removal asfan was at 1.7, Rise of the Eldrazi removal asfan was at 1.9. So my removal numbers are reasonably close to some of the best draft sets of all time. Good for my cube, probably! Had I gotten a removal asfan of 3.8, I may well have to think hard about the way my cube is constructed, as that would be an additional two kill spells per pack. As I said above, it may still be the right number for my specific cube. Asfan is a tool to help us build our own cubes, it is not meant to tie us to preconceived notions about how things are supposed to be done.
Some points worth considering while using asfan:
The term "removal" commonly includes the following effects:
Cubes need more counterspells than modern sets. Most modern sets only have 3-5 counterspells total across all rarities, with asfans as low as 0.15 in SoI (meaning you'll see one counterspell every 6 or 7 packs). A single counterspell at common adds much more to asfan than a single counterspell in cube. The average asfan for modern sets seems to be about 0.3, which means a single counterspell every three packs. These sets are not good models if you want a more traditional blue control. Even if you're fine with the modern rate you'll need 7 counterspells at 360 cards and 9 counterspells at 450 to get an asfan of 0.3.
If you care about the distribution of the cards of a subset across colors as opposed to "just" asfan of a subset for your cube, multicolor cards count 0,5 towards both of their colors (so Electrolyze adds 0,5 to blue and 0,5 to red).
(# of whatever eg. removal)/(total # of cards in your cube) x 15 cards you expect to see in a pack? In your case, 56/405 x 15 = 2.07 average instance of removal per pack.
450 Unpowered Cube Cobra
Should not be a big problem though, as long as counterspells always/never count, the numbers stay consistent and comparable across cubes and sets.
edit: even if you count counterspells as removal, I don't think you should count Memory Lapse and Remand by the way, as those are like bounce and tap in the sense that they do not remove the problem permamently.
So it looks like they did not consider counterspells removal 8 years ago. I still don't think counting them as removal is wrong, as long as it's consistently done one way or the other and as long as we keep in mind that e.g. your number is going to be slightly higher than mine by default, because you included them. It'll still be fine for comparisons.
Most of the time including counterspells is only going to add 3-5 cards to the subset, so it's not a massive difference anyway. My removal asfan would go from 2,07 to 2,19.
Draft it on Cubetutor here, and CubeCobra here.
Treasure Cruise did nothing wrong.
In a standard 8-man draft, I would like 1 gold card from each guild to be represented per round of packs, so as to offer/entice/reward drafters for being in that specific guild. This means that there are 10 gold cards per 120 cards (8 players x 15 card packs), resulting in a percentage of 8.33% or an asfan of 1.25. This yields the following:
360 cube = 30 gold cards
450 cube = 37-38 gold cards
540 cube = 45 gold cards
etc...
What do you guys think of this thought process and method, and the resulting numbers?
Also, follow us on twitter! @TurnOneMagic
This actually vastly undersells the number of gold cards you'd need if you want to average each guild showing up in a round. Or even nine, or eight.
Your numbers give you the number of gold cards you'd want to get 10 in a round, but not "1 card from this particular guild, "1 card from this particular guild, 1 card from this particular guild, 1 card from this...."
Think of it like this: how many times do you have to roll a die before you have a 50% chance of having rolled every number? It's way more than six. In fact, you only have about a 2% chance of doing that with six rolls.
You're guaranteed to get a unique result in your first try (duh), but on your second go you have a 5/6 chance of getting there. Then, if you did, you have a 4/6 chance for the next roll. And so on.
So the chances are 5/6 x 4/6 x 3/6 x 2/6 x 1/6, or 120/7776. Just over 1.5 percent.
So the number you'd want would be much bigger, for one. It's actually an annoying calculation that I can't remember, but let's say it's 5 per guild at 360. It may be higher. But with 5, that yields 2.083 per pack.
Generously, out of your 8 drafters, you may get 7 guilds represented. Well, you'd have 2.083 gold cards per pack, so multiply by 8 to get 17 gold cards per round. Divide by ten to get 1.7 cards of each guild per round.
If three of the guilds have no drafter, then multiply 1.7 by 3 to see that there are 5 cards per round that have no drafter to take them.
Each individual drafter doesn't want gold cards outside of their color pair, so 1.7 x 9 guilds is about 15 cards that they don't want. Granted, if they were monocolored cards then only 6 of those cards would be expected to be one of an individual drafters colors, but that's still 6 extra cards for a player that they dont have. 18 extra cards in a whole draft. That's probably a big deal.
I'm at about 390 and run 3 gold cards, and I still feel like I want to run a slightly larger cube in order to dilute them further
My CubeCobra (draft 20 card packs, 2 packs.)
430, Peasant, Very Unpowered
Why you should take your hybrids out of your gold section
Manamath Article
If you learn to think about things like this often, it clears up a ton of misconceptions.
Probability and combinations really should be emphasized in school over the impractical stuff we force high schoolers to do.
I also teach math to kids so I'm used to trying to be really clear. I hope it comes across as such
My CubeCobra (draft 20 card packs, 2 packs.)
430, Peasant, Very Unpowered
Why you should take your hybrids out of your gold section
Manamath Article
While I got you on the hook, one more cube math issue:
(Disclaimer: I am closet/self-taught hypergeometric calculator abuser)
I’m interested in color requirements for consistently casting my spells, and I’ve read (and re-read) the following:
https://www.channelfireball.com/articles/frank-analysis-how-many-colored-mana-sources-do-you-need-to-consistently-cast-your-spells/
The thing is, I’m interested in looking at some results that aren’t quite at the 90% clip, but sadly other numbers aren’t analyzed in his piece, and the hypergeometric calculator by itself seems insufficient due to the lack of considering a mulligan strategy.
He kind of loses me with talk of conditional probability and coding a simulation...
Do you know how to do this kind of thing? I’m interested in looking at color requirements in the 66%-83% range.
http://stattrek.com/online-calculator/hypergeometric.aspx is what I use, and it works for monocolored cards really easily.
What's the issue you're having specifically
My CubeCobra (draft 20 card packs, 2 packs.)
430, Peasant, Very Unpowered
Why you should take your hybrids out of your gold section
Manamath Article
Karsten wrote that the exact calculations required the use hypergeometric calculations and conditional probability, but that was too complex and tedious, so he coded a simulation to ease his task.
That’s the part I don’t understand.
My CubeCobra (draft 20 card packs, 2 packs.)
430, Peasant, Very Unpowered
Why you should take your hybrids out of your gold section
Manamath Article
My CubeCobra (draft 20 card packs, 2 packs.)
430, Peasant, Very Unpowered
Why you should take your hybrids out of your gold section
Manamath Article
The ASFAN for removal in my cube is 2.875. I'd rather err on the side of saying no to (absurd) aggro than saying yes to (absurd) aggro.
Ignoring what Magic players say isn't the answer, it's listening to what they have to say and doing the exact opposite that's correct.