General "Looking for a card"-Thread

Not just black, but if we are talking control, I'm guessing U is in the mix:


Gifted Aetherborn is seconded as a really nice option, and considering the better mana calculation article (IMO), it's really not a big deal to cast it. Effectively the really popular article I can't remember the name of fails to account for the fact that you actually need it in your hand by T2 in order for the T2 calculation to matter at all.
 

Onderzeeboot

Ecstatic Orb
Effectively the really popular article I can't remember the name of fails to account for the fact that you actually need it in your hand by T2 in order for the T2 calculation to matter at all.

I disagree with this philosophy. You want to be able to cast it on turn 2 if you have it in your hand. The fact that you don't always have it in your hand by t2 doesn't mean you don't want a mana base that can support casting it on turn 2.
 
I disagree with this philosophy. You want to be able to cast it on turn 2 if you have it in your hand. The fact that you don't always have it in your hand by t2 doesn't mean you don't want a mana base that can support casting it on turn 2.

The basis of the Karsten article is "certain % fail state casting a thing turn X". The card not being in your hand is fundamental to that math, which he left out. If it's not in your hand, you can't cast it no matter how many mana sources you have! You have other things to be casting at the time. I can't remember the article I saw that includes it, but it makes much more sense to include the "is it in your hand math", otherwise you are being much more conservative with mana or the % fail state you want is actually much lower than you outwardly think.

For instance, if the BB card is only in your hand by T2 50% of the time, your 10% fail state using Karsten's article is actually only 5%
 
Putting this article here as a corollary to and perspective of the Karsten article tossed around all the time:
MANA BASE PROBABILITIES

The most important table for us is the Single mana base failure for turn 1 table about a third of the way down. The columns are number of spells of the type we care about. Recently, eldrazi with {c}. If you only have 1 spell of that type, you have a 8% failure of having the mana on turn 1 with only 4 lands. Four out of sixty. Seven lands is 95% probability to work. (These tables show the probability of failure, not success). Now at 2, 3 and up, the 7 rule becomes quickly a good one. Even at 2 though, 13% failure with 5/60 sources isn't shabby, considering this is T1.

The Karsten article doesn't handle splashes well because it doesn't take probability of even needing the land on a particular turn into account. You might not have even drawn the one eldrazi until turn 8! The table clearly shows that as your color commitment goes up, you land count quickly asymptotes at 16 lands/60, fairly good correlation to Karsten's 14/60 for a fully invested main color.

Anyway, take the data as y'all will.
My take: Good mana bases are still important, but don't panic over your lonely splash if you've only got 3-5 sources.
This is my original post referencing the counter-article to Karsten. Unfortunately the website linked seems to be down or defunct. Red text on the critical point re: the weakness of the Karsten article (weakness in terms of Karsten's own evaluation, percentage of failure states). Splashes in this context would be "one two-pip-two-CMC card in the deck".

Basically, our decks have other things to do be doing that are {B} or {1}{U} etc, so we don't need to be making sure we set up {B}{B} by turn two every game, because the majority of T2s you won't even have the card to cast. Unless the {B}{B} card is literally the deck's only 1 or 2 drop, in which case the deck has other issues.
 

Onderzeeboot

Ecstatic Orb
The basis of the Karsten article is "certain % fail state casting a thing turn X". The card not being in your hand is fundamental to that math, which he left out. If it's not in your hand, you can't cast it no matter how many mana sources you have! You have other things to be casting at the time. I can't remember the article I saw that includes it, but it makes much more sense to include the "is it in your hand math", otherwise you are being much more conservative with mana or the % fail state you want is actually much lower than you outwardly think.

For instance, if the BB card is only in your hand by T2 50% of the time, your 10% fail state using Karsten's article is actually only 5%
Sorry, but hard disagree. I think your reasoning is fallacious. Say you do account for the odds of having your single BB card in hand, prompting you to lower the number of black mana sources you run. There are still going to be a number of games where you will have the BB card in hand on t2, and you just significantly decreased your odds of being able to run it out on turn 2 in those games. The odds of drawing the card don't matter for Karsten's calculation, because you want to play all of the cards in your deck on curve if able. His numbers tell you the number of colored sources you should run to be able to reliably cast your cards on curve.

Now, in a typical draft deck, we might not be able to draft enough fixing to comfortably run that CC drop you drafted if you also drafted another color. In that case you have to choose which mana sources / color to skim on, because an ideal mana base is not achievable. In this case you would take into account the fact that there's only one CC card in your deck and hope to get lucky. Its not something you should be happy doing though, as a player trying to build a solid mana base, because you know you're lowering the odds of casting that CC drop on curve if you do draw it before t2. We, as cube designers, have the power to make life easier on our drafters by being very critical of the number of pip-heavy cards we include in our cube. Mire Triton might have weaker stats than Gifted Aetherborb in a vacuum, but the Triton is much more likely to be castable on t2 in a greater number of decks, and that's a huge boon in my opinion.

In a nutshell, you're saying running 11 black sources for Gifted Aetherborn is plenty because you won't have it in hand before turn 4 most of the time anyway and when you do you probably have something else you can play, whereas I want to run 14 sources because if I draw the Aetherborn on turn 2 I want to be able to play it on that turn since it very likely is the best thing I could be doing that turn and as a 2 drop the card will get progressively less impactful the longer I have to wait before I can run it out. Or rather, I'm saying we can include cards that don't screw over the drafter for picking a seemingly powerful card that turns out to be uncastable on curve most of the time.
 

Onderzeeboot

Ecstatic Orb
This is my original post referencing the counter-article to Karsten.
A CC card is the very opposite of a splash, but I do agree we shouldn't panic about the mana requirements when we are splashing a card. If you have a GW deck running a single Lightning Bolt because you're low on removal, you really don't need 10 red sources. That also has to do with the fact that we don't need to cast Bolt on t1 very often though. Splashing Elite Vanguard is a bad idea, because that card is only excellent when you can cast it on turn 1, and you are usually not going to be able to cast a splash on t1.
 
Sorry, but hard disagree. I think your reasoning is fallacious. Say you do account for the odds of having your single BB card in hand, prompting you to lower the number of black mana sources you run. There are still going to be a number of games where you will have the BB card in hand on t2, and you just significantly decreased your odds of being able to run it out on turn 2 in those games. The odds of drawing the card don't matter for Karsten's calculation, because you want to play all of the cards in your deck on curve if able. His numbers tell you the number of colored sources you should run to be able to reliably cast your cards on curve.

Now, in a typical draft deck, we might not be able to draft enough fixing to comfortably run that CC drop you drafted if you also drafted another color. In that case you have to choose which mana sources / color to skim on, because an ideal mana base is not achievable. In this case you would take into account the fact that there's only one CC card in your deck and hope to get lucky. Its not something you should be happy doing though, as a player trying to build a solid mana base, because you know you're lowering the odds of casting that CC drop on curve if you do draw it before t2. We, as cube designers, have the power to make life easier on our drafters by being very critical of the number of pip-heavy cards we include in our cube. Mire Triton might have weaker stats than Gifted Aetherborb in a vacuum, but the Triton is much more likely to be castable on t2 in a greater number of decks, and that's a huge boon in my opinion.

In a nutshell, you're saying running 11 black sources for Gifted Aetherborn is plenty because you won't have it in hand before turn 4 most of the time anyway and when you do you probably have something else you can play, whereas I want to run 14 sources because if I draw the Aetherborn on turn 2 I want to be able to play it on that turn since it very likely is the best thing I could be doing that turn and as a 2 drop the card will get progressively less impactful the longer I have to wait before I can run it out.

Sorry onder, but the math literally doesn't back you up. You are running into an internal bias that is leading you to needing the mana set up more often then you will have the spell. Very unfortunate the math in my article is behind a bad gateway.

Karsten's article literally fails to account for if cards exist in your hand to be cast, which is conservative on his part, he's setting up mana for cards he's assuming are in the hand, when they may not be. This isn't like I'm just making up invalid arguments. It's a literal hole in his math. You can still use his math, but it will guide you much more conservatively than what happens in actual gameplay. Per my article's math you will literally have equivalent success rate to the success rate presumed in Karsten's article with fewer mana sources, because Karsten's math has a fundamental flaw. That would imply that the success rate you are looking for in reality is actually much higher than the number you plug into your Karsten math; something approaching 100%. If that's what you want to do, go ahead, but from my point of view it's far too restrictive.
 
A CC card is the very opposite of a splash, but I do agree we shouldn't panic about the mana requirements when we are splashing a card. If you have a GW deck running a single Lightning Bolt because you're low on removal, you really don't need 10 red sources. That also has to do with the fact that we don't need to cast Bolt on t1 very often though. Splashing Elite Vanguard is a bad idea, because that card is only excellent when you can cast it on turn 1, and you are usually not going to be able to cast a splash on t1.

It's functionally equivalent. A singular card that stands out in the deck via particular mana requirements.
 

Onderzeeboot

Ecstatic Orb
Sorry onder, but the math literally doesn't back you up. You are running into an internal bias that is leading you to needing the mana set up more often then you will have the spell. Very unfortunate the math in my article is behind a bad gateway.
It is unfortunate. I don't know that I'm running into an internal bias though. Mind you, we're both holding on to our own point of view pretty stubbornly, making you no less biased then me, I believe. To me it honestly sounds as if your article and Karsten's article run calculations that shouldn't be compared one on one.

Karsten's article literally fails to account for if cards exist in your hand to be cast, which is conservative on his part, he's setting up mana for cards he's assuming are in the hand, when they may not be. This isn't like I'm just making up invalid arguments. It's a literal hole in his math. You can still use his math, but it will guide you much more conservatively than what happens in actual gameplay. Per my article's math you will literally have equivalent success rate to the success rate presumed in Karsten's article with fewer mana sources, because Karsten's math has a fundamental flaw. That would imply that the success rate you are looking for in reality is actually much higher than the number you plug into your Karsten math; something approaching 100%. If that's what you want to do, go ahead, but from my point of view it's far too restrictive.

Again, I don't believe it's a hole in his math, the odds of having a card in hand shouldn't factor into his calculations. Karsten's succes rate calculates the odds of being able to cast a given card on curve. From the sound of it, your article's succes rate calculates the odds of being able to succesfully cast a given card when you draw it. Those are literally two different things. Even though they are both named 'succes rate', they don't calculate the odds for the same thing.

The point I wanted to make earlier is, given the choice between two similar options, one priced at 1C, and one at CC (say Mire Triton and Gifted Aetherborn), as a cube designer I would pick the 1C option. The odds of succesfully being able to run out the 1C drop on curve on the back of a typical cube's mana base are significantly higher than being able to run out the CC drop on curve. Even when you draw these cards on later turns, the odds of being able to cast the 1C creature are still higher than being able to cast the CC creature. As a cube designer we have free reign over our inclusions, why include a card that's objectively harder to cast if there are options that are easier to cast?

Karsten's article paints a picture of how hard it is to be able to cast all cards on curve if you run heavy pips or many colors, and rightly so! That doesn't mean you should always run Karsten's numbers or that your deck can't succeed if it dips below his ideal numbers, and that's not what I meant to say. But that's looking at the whole issue from a drafter's perspective. I want to look at this question from a cube designer's perspective, and for me that does make a difference.
 
Sigh is right. Karsten's analysis overstates the need for mana. You only want the BB when you can actually spend it, not always. You don't need to have BB on turn 2 if you don't have Aetherborn in hand.

To use an example. Karsten says you need an umbrella even when it's not raining, while Sigh correctly recognizes that's not true. Karsten is putting the cart before the horse.
 
It is unfortunate. I don't know that I'm running into an internal bias though. Mind you, we're both holding on to our own point of view pretty stubbornly, making you no less biased then me, I believe. To me it honestly sounds as if your article and Karsten's article run calculations that shouldn't be compared one on one.
They use the exact same mathematical basis, just different variables

Again, I don't believe it's a hole in his math, the odds of having a card in hand shouldn't factor into his calculations. Karsten's succes rate calculates the odds of being able to cast a given card on curve. From the sound of it, your article's succes rate calculates the odds of being able to succesfully cast a given card when you draw it. Those are literally two different things. Even though they are both named 'succes rate', they don't calculate the odds for the same thing.
Technically there isn't a hole per the literal phrasing of his article, but there is in how games and cards actually play. Like you literally do need to factor the spell being in your hand into calculations. It doesn't magically appear in your hand 100% of the time on-curve.
My article is calculating success of casting a card by a certain turn. In this case turn 2 (on curve), with that scenario the two writers are aiming to achieve the same thing (checking castability by turn 2), but Karsten is leaving out the actual card variable.

As a cube designer we have free reign over our inclusions, why include a card that's objectively harder to cast if there are options that are easier to cast?
Because the CC card is better by a long shot.


here's bascially what's happening. In real life happening, not just because I want it to be happening.

Karsten:
your mana: some probability based on careful math
the card: 100% of the time in your hand

Other guy:
your mana: some probability based on careful math
the card: some probability based on careful math

Karsten's is by nature going to be too conservative. He has a false assumption.

I went ahead and actually ran simulations to prove my point that Karsten's math is factually wrong to the intent of casting a BB spell on curve (T2). By his estimates, 14 colored mana sources X are needed to hit 90% probability of casting BB on curve. Per the below images, he is more than 5% off. The actual number of times the simulated player failed to cast the card by turn 2 (on the play!) is less than 5%. I validated with a larger sample size to ensure accuracy with approx 0.1%. And yes, I ensured it didn't draw off already-drawn cards.

My simulation draws the specified number of cards from a simulated deck list, {iteration count} number of times, and checks for 1) 2 or more black mana sources 2) 1 spell named "BB". Failure is a on-curve casting failure, and no-cast indicates hands where the BB spell wasn't even applicable. Note that this is the majority of hands.

10,000 iterations (success 95.2%)
Screenshot 2021-02-03 123105.png
100,000 iterations, 0.1% error between runs (success 95.3%)
Screenshot 2021-02-03 123127.png


Screenshot 2021-02-03 123330.png
 
I don't think there's any mathematical error here is there? There are just two different objects, the marginal probability of casting a specific card on turn two versus the conditional probability of casting a specific card on turn two GIVEN that its in your hand. These are both perfectly legitimate probabilities.

I'm not saying you don't have a disagreement though. You disagree about which probability is more relevant for the players and for the designers. Another good one to think about is the probability of casting ANY two drop on turn two. The issue is that this is not just a function of your manabase and a specific card, it's a function of your whole deck.

EDIT: to give examples of why you might care about these different probabilities.

If you are a player and asking yourself "if I pick this specific card, and have it in my opener, will I feel bad because my manabase can't support it" then I think the conditional probability is relevant. If you're asking yourself "I'm an aggro deck and want to curve out. Will picking this specific card mean I cannot do that at least 90% of the time?" Then the probability of casting any two drop on turn two is most relevant.
 
I don't think there's any mathematical error here is there? There are just two different objects, the marginal probability of casting a specific card on turn two versus the conditional probability of casting a specific card on turn two GIVEN that its in your hand. These are both perfectly legitimate probabilities.

I'm not saying you don't have a disagreement though. You disagree about which probability is more relevant for the players and for the designers. Another good one to think about is the probability of casting ANY two drop on turn two. The issue is that this is not just a function of your manabase and a specific card, it's a function of your whole deck.

EDIT: to give examples of why you might care about these different probabilities.

If you are a player and asking yourself "if I pick this specific card, and have it in my opener, will I feel bad because my manabase can't support it" then I think the conditional probability is relevant. If you're asking yourself "I'm an aggro deck and want to curve out. Will picking this specific card mean I cannot do that at least 90% of the time?" Then the probability of casting any two drop on turn two is most relevant.

In this case we are talking about a specific BB card, so the conditional probability would be favored by your estimation. The flaw in Karsten's article or usage of his article is to try to achieve the same outcome as the conditional probability math with a simple marginal probability (can I cast a specific card by a specific turn in my game). Not flawed from a mathematical truthfullness perspective, but flawed from the desired modelled outcome, even per Kartsen. Karsten uses conditional language in his article: WW for supreme verdict (specific ie. conditional card) by turn 4 (specific point in the curve) or RR for splinter twin (specific, ie. conditional card) by turn 4 (specific point in the curve). He finds his results "surprisingly high" for a reason: he's applying one probability for a situation that requires two.

EDIT: in other terms besides marginal, conditional, etc., Karsten is effectively assuming that every spell will be X (BB in this case), and determining failure/success rate off this. Not quite what his assumption does, but it's close.
I forgot he included some mulligan logic in his simulation so I added that in, and for a deck set up per the way Karsten's assumption lays it out, the failure rate is approx. 10%, as expected. The actual situation being discussed (one BB card total) sees it's failure rate half again to approx 2.5% with the mulligan code. that's 4x lower in actual practice than when using the Karsten assumption.
N=50,000, verified at 200,000.
Screenshot 2021-02-03 141037.png
Screenshot 2021-02-03 141237.png
 
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