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PV’s Playhouse – Building a Better Manabase

 

Hello!

Now that I’m finally done with reports, I’ve found myself without a topic to write about. Sure, I could write about the rotation, but that presents a couple problems; the first is that the Pro Tour is Extended, and I don’t want to tell the world the things I’m figuring out (yes, I am very selfish). The second is that the format will only exist for the Pro Tour, so it is not interesting for a lot of people. The third is that every writer ever is going to write about that, if they haven’t already, so there isn’t much left for me to say. The idea for this article did, however, come from the rotation. First, my opinion on it:

I saw a lot of people complaining about the rotation, because they lost money or had just finished building decks that are no longer legal, etc. I can understand this point, and I sympathize with those people. As far as I am concerned, though, the rotation was awesome – no one really wanted to play the Pro Tour with the completely outdated format. One problem (the one that the format will not be the same after the Pro Tour, so no awesome tech will come out of it to the “public”) still remains, but that is Wizards’ problem, and not mine (see, I told you I was selfish). I wholeheartedly approve of what they did, including the bans – it seems that, every time Wizards bans something, it makes me happier, so I think they should do that more often, as opposed to doing things like cutting a Pro Tour, which make me unhappy.

Anyway, about one hour after the rotation was announced, I had already accumulated a full box of messages with the words “Faeries” in them. One of them came from a friend who cut/pasted me his list on MSN, and wanted me to tell him what I thought of it. I told him he hadn’t listed the most important part, and then he listed me his sideboard. This was not what I meant.

Sure enough, the sideboard is very important, but at this point it is just futile to build a sideboard in my opinion – you don’t even know what you are going to face, and even if you do you don’t know how the games play out yet, so you don’t know what you need to board. The part I was talking about, and which is always overlooked, was the manabase.

The Ideal Mana Base

Of course, it is not the most important part, but it is just as important as everything else, an importance that does not relate to the amount of attention it gets. Especially in a deck like Faeries, where 30 out of your 35 slots are generally fixed, the manabase is one of the things you can get an edge from. There are two processes players generally use to get to their manabases:

a) They start with something very raw and adjust the mana as far as the games go,
b) They make an educated guess,
c) They find a similar deck and copy the manabase.

Theoretically, there is a perfect manabase waiting for every deck – one that gives you all the best mathematical chances. I cannot calculate this perfect manabase, and I honestly don’t think anyone else can (and if they could they would probably be making millions somewhere instead of building a manabase), so this article is on what I believe is the next best method, which might as well be the best since the best does not exist.

For starters, I am not a fan of method c) myself, though I admit it is useful sometimes when you are just clueless – basically, c) is only good as a starting point so then you can apply a). The problem is that you have no idea where said person got the manabase from, so you might be copying something terrible – they might even have copied the manabase from a different deck themselves, which in turn had it copied from a different deck, and in the end you mind find yourself playing Boros with a manabase that is based on RW [card]Astral Slide[/card] from five years ago.

What I recommend for Constructed, and what I use for my decks, is a cross between methods b and a – you make an educated guess and then, if you have time, you might notice that you are lacking green mana and change it a little bit, for example. For Limited, though, you don’t have this luxury; you have to just make an educated guess. Through the course of my tournaments, I’ve noticed that the process to find a manabase that is used by Pro players is very straightforward – they lay out their decks, split by color or mana cost, look at it for one and a half minutes and then write down “10 Swamps 7 Mountains” – highly scientific, I know. This article will be on how to make your guess more educated, so that you are more likely to get it right, both in Constructed and in Limited. Methods I’ve seen used:

– The amount of cards in each color.

The first thing you should notice is how many cards you have in each color – this is your general guide, and will give you the first impression, but this is all it gives – as a way to find a manabase, you can do much better.

– The colored symbols in the mana cost

There are a lot of methods that consist in adding the colored mana costs in each card and then doing a proportion to get the lands to the same proportion. A rough example to illustrate:

 

This deck has 8 red symbols, 2 white symbols and 4 blue symbols, therefore you need twice as many red sources as blue, and four times as many red sources as white, as well as two times as many blue as white. The basic lands in it should be 4 Mountains, 2 Islands and one Plains.

This method is horrible.

No, really – I know a lot of people do things this way for drafts (Magic Online does this on the “suggest” function, I believe), and it is just bad. There are many flaws with it, to the point where counting this is basically useless, and you are better off just guessing, which at least doesn’t fool yourself – with this method, you are going to believe you’re doing something very scientific, when it doesn’t actually mean anything – the only difference between people who use this method and the ones who just count the number of cards in each color is that this ones think their method is accurate. Just to give you an example of what can happen when you trust this method:

4 Cryptic Command
32 Dawn Elemental

There are 128 white symbols and 12 blue symbols, which puts you at roughly 11 Plains per Island, or 22 Plains and 2 Islands. Good luck casting your Cryptic Commands.

(Ok, ok, I know this is pretty extrapolative, but trust me, this method doesn’t tell you anything.)

So, if this is not enough, what else do you need to take into account?

– How important each color of mana is to you in the early game, particularly turns one and two

Now we are getting somewhere! Of course life is never easy, and there is no mathematical way to calculate how important a card is. When you build a manabase, you have to figure out which land you absolutely need early, and which one you can live without until much later. A deck with 10 creatures that cost R and 1R needs to draw a Mountain very early, because, if it does not, then its cards (and very likely its strategy) are all going to be bad. Basically, if you draw your Mountain on turn 5, it’s going to finally let you play your Goblin Guide – but who wants to play that on turn 5?

Other types of cards are different, and can wait until much later – splashed removal, for example. If your red card is not Goblin Guide but Flame Slash, then the toll on your manabase is much smaller, because Flame Slash on turn five is still excellent. Even the same card can have a different demand on your manabase depending on what you are playing – take, for example, Lightning Bolt. In a Limited deck, Lightning Bolt is a removal like Flame Slash, and you are not in a hurry to play it, it’s going to be good no matter what. If you play Lightning Bolt in a Constructed deck, though, is it because you want a cheap spell, and not being able to play it early defeats the whole purpose of the card. Therefore, even if the card is still Lightning Bolt, the role it plays in your deck changes, and you need the red earlier, and so more sources.

There are certain types of cards that are very unforgiving if you cannot play them on the turn they are meant to be, and so demand more colored sources. The Goblin Guide is an example, Noble Hierarch and Ancestral Vision are two others. Since I began by talking about a Faeries list, let’s take LSV’s example list to work with:

This is not to say I think this list is the best or anything (I changed Mana Leaks for Broken Ambitions), but it is as good as any for me to work with.

In this deck, there are a couple cards that are demanding on your manabase:

 

Those should all be analyzed separately, because they require different things. Of course, all the cards need blue mana, but Ancestral Vision and Cryptic Command are the more demanding ones – Vision needs it on turn one, and Cryptic Command needs three of them. Doom Blade also requires black, but it is not as important to have it early – turn two Bitterblossom is infinitely better than turn four Bitterblossom, but turn two Doom Blade not so much.

First of all, there are 19 blue sources on this deck. This means you have a roughly 94% chance to get one in your opening hand, which is more than enough. I will not flood this article with how I got to those percentages, but I will explain it once I’m done if anyone cares.

For Ancestral Vision, though, you cannot say you have 19 blue sources, because both River of Tears and Creeping Tar Pit do not let you play Vision on turn one, and you REALLY want to play it on turn one, so they might as well not count. That leaves us with 13 blue sources on turn one (assuming Secluded Glen comes into play untapped), which makes the % to have it roughly (whenever I have a % from now on, it’s going to be a rounded number) 84% on the play, and 88% on the draw. That means that, for every 6.25 times you draw Ancestral Vision, you will not be able to play it once. Is that good enough for you?

Lets see how the other numbers get:

Blue Sources ------------  % on opening hand on the play / draw
12  -----------  81%  / 85%
13  -----------  84%  / 88%
14  -----------  86%  / 90%
15  -----------  88%  / 92%

I list the on the draw number mostly for reference, since you have to decide between keeping or drawing before you see this card but after seeing your first 7, but for cards such as Cryptic Command it is more important.

I personally believe that a number between 13 and 14 is fine here. Obviously the more the merrier, and I would say 14 is the ideal number, but I can definitely live with 13. 12 I think is pushing it too much, as 81% is not enough for a card that definitely has to be played on turn 1 like Ancestral Vision.

For Bitterblossom, there are also 13 sources, except that you only need them on turn 2, which puts you at 88% – more than enough.

For Cryptic Command you need four Islands, but only on turn four, and the card is certainly more forgiving than the other two if you can’t play it on the spot.

The deck has 19 blue sources, which gives you a 75% chance to have UUU on turn four. Let’s see how we do with other numbers:

Blue sources ------------- % of having 3 in play by turn four on the play/draw
17  -------- 66% / 73%
18  -------- 71% / 78%
19  -------- 75% / 81%
20  -------- 79% / 85%

The first thing we notice is that adding a land does a lot more for Cryptic Command than it does for Ancestral Vision or Bitterblossom, adding as much as 5%. Those numbers are not absurdly exact, because you might play a turn one Vision and draw four cards on turn four instead, so your chance of finding the fourth land will be higher. Again, I can live with 19, but I would like 20 here.

Still in the Faeries deck, there is something else I want to mention – the sideboard.

A lot of the times, people build their manabases with the deck in mind, and then do not take sideboarding into account. If your deck doesn’t have any blue sources, you obviously don’t put a blue card in your sideboard, since you can’t cast them. When you simply put a card in your sideboard without paying attention to your lands, you are doing exactly this – adding a card that you cannot cast (at least not as much as you think you are casting). In Faeries, this card is Thoughtseize, which will surely be in the board. Thoughtseize is another card that gets much better turn one, and this is very crucial in the mirror; As such, you have to make sure you not only have black mana but you have untapped black on turn one for when you board it in. Since you do not know the sideboard when building the deck most of the time, you sometimes have to go back to fix the manabase.

This deck currently has 11 black sources on turn one. The numbers for them:

9  -------- 70% / 75%
10 -------- 74% / 79%
11 -------- 78% / 82%
12 -------- 81% / 85%
13 -------- 84% / 88%

Here, though it is important to know that, for example, against the mirror, you use those numbers on the draw, since you only need it turn one if you are drawing – if you are on the play, you can count the two Creeping Tar Pits, bringing your total to 13.

78% is fine, since it is not that useless after turn 1, but if mirror is a matchup I expect a lot, then I would probably like to aim for the 81% that 12 provides.

So, what can we do after all those numbers?

As we stand, even if I like where this is, I would like one more untapped black and one more untapped blue, as well as another blue in general. This is easy to solve if you just start adding Underground Rivers, but you might not be able to afford the life – that depends on the format as well. What this shows us, though, is what happens when we start cutting lands – what if we cut a Creeping Tar Pit for a second Pendelhaven? That will not affect Vision and Thoughtseize on the play, but it will affect Bitterblossom and Cryptic Command, and Thoughtseize on the draw, bringing them to numbers I am not willing to accept – this shows me that, if I want a second Pendelhaven, I need an extra land, for example. In Hollywood I played 25 lands and two Pendelhavens, but I shouldn’t have.

It also shows me what happens if I replace Swamp with Drowned Catacomb, for example – I get to a better Cryptic Command on turn four, which I wanted, but a worse Thoughtseize on turn one. I then have to decide which is more important – in my opinion, right now, the Thoughtseize is, even if it is not maindeck (as well as Magus etc), but that might easily be wrong depending on the format. So, even if I don’t particularly like this list, I like the manabase it has.

Another factor you must take into account is whether you can actually win, or survive, without a color. Sometimes you will have 12 black cards and 10 red cards, with all the costs spread evenly, but your goal is to get both at least a red and at least a black – so, even if you have more black cards, you just want to maximize on getting both as opposed to getting “more black than red”. The numbers for a 40 card deck:

Lands --------- % opening hand / % turn four (or three on the draw)
8 -------- 82% / 90%
9 -------- 86% / 95%
10 ------- 89% / 96%

Chance of having both on opening hand and turn four:

10/8 -------- 72% / 89%
9/9  -------- 73% / 90%

In this situation, I’d much rather have 9 of each, since 9 gives me a sufficient chance I will get them both, especially by the middle of the game, which is when you really want to start casting most of your spells. Adding one extra Swamp in favor of one Mountain gives you only one more percent for Swamp on turn four, but takes away five percent from the Mountain, and decreases the chance of getting one of each in both cases.

On the other hand, if you have a lot of double black costs:

Swamps/Mountains ---------- Chance of having BB opening hand / turn 4
10/8 -------- 57% / 80%
9/9  --------  50% / 73%

Swamps/Mountains ---------- Chance of having BBR opening hand / turn 4
10/8 -------- 44% / 73%
9/9  -------- 41% / 69%

Therefore, if having double black is really important, then 10/8 gives you much better percentages in both cases. Every time you need more than one source of the same color, adding another source of that color to your deck will give you more percentage than adding one when you only need one; This happens here, and it happens when you compare what adding a land does for Cryptic Command and what it does for Vision, for example.

Also relevant are the colored costs on activated abilities; A card like Guul Draz Assassin, for example, requires more black than a card like Vampire Lacerator; Student of Warfare more white than Caravan Escort; Vent Sentinel slightly more than Lagac Lizard (imagine for example you are mono-blue splashing for four Vent Sentinels and a Flame Slash – in this deck, you really want at least two Mountains in play, so you can activate the Sentinel and play another one in the same turn. If they were 4 Lizards, you would only need one Mountain in play at any given time).

Last of all, I’m going to talk about a trap that some people make when designing manabases – sometimes, they count lands as multiple colors when they are not quite multiple colors. A card like Adarkar Wastes, for example, counts as both a blue and a white mana source, but not if you are playing a card that costs UW – if you have Meddling Mage in your deck and 8 UW dual lands, the chance to cast him on turn two is only 29%, whereas if you have 8 lands that add blue and then 8 different lands that add white, you have 48% – almost twice the chance.

This is particularly true with fetchlands – a card like Flooded Strand might count as both sources, but not usually when one of the colors is your splash color; When at least one of the colors is a base color, then this problem is less relevant, but you should be wary of splashing cards on lands that are either one or the other, but not both; For example, compare those two manabases:

 

and

 

It is easy to see that, in the second one, it is much easier to find your other colors, since in the first one by the time you fetch a Mountain that means you can no longer use this land to fetch a Plains. Yet, when counting their mana sources, most people would count “5 of each” in both occasions, and get a misleading result.

Well, this is it – I hope I’ve given you some idea of what to think when you’re building a manabase.

Before I leave, I’d like to talk a little bit also about the Community Cup. Though I think it is nice (and congratulations to the guys for winning), it makes me a bit bitter that they have that and not the Invitational. I know I am biased, since I would likely play in the Invitational but not in this, but even when I didn’t have any hopes of playing it I always found it interesting to follow the coverage and to see what cards the people would come up with, knowing they might well be printed. It was also interesting to send decks for certain formats for them to use, and to find out what the best players in the world would build when confronted with wacky formats. The Cup coverage, on the other hand, doesn’t interest me much, as I don’t know any of those people – I mean, getting to see what EDH deck Saito likes is much more interesting to me than getting to see what EDH deck someone I don’t even know likes.

A friend of mine said that he disagreed, that the Community Cup was better for the community, since it was for them, and not for the pros, like the Invitational, so if you could I’d appreciate a reply saying which one of those two you would prefer next year, the Cup or the Invitational. I know they do not compete directly with each other (another department, another budget, etc), but I’m still interested in knowing if I am the only person who thinks like I do.

For anyone who cares, I got the numbers in the article from the program called Magic Workstation. Not many people know, but it has a function that calculates the probability of certain cards being in your opening hand; to reach it, you should go to Tools -> Deep Deck Analysis.

I did some of the math myself, to see if the numbers were correct; The way I did it was to calculate the possible hand combinations, and then the hand combinations that did not have what I wanted. For example, for Ancestral Vision with 13 lands, the math worked like this:

Possible hands: 60! / (7! * 53!) = 386206920
(! is factorial, which means to do 60 * 59 * 58 * 57 etc., until you get to 1).
Hands that do not have a blue land: 47! / ( 7!*40!) = 62891499

Hands that do not have what I want over possible hands: 62891499 / 386206920 = 0.162.

Since this is what I don’t want, what I want is everything else; 1 – 0.162 = 0.837, which matches the 84% that MWS gave me. I did this for three more situations, and they all matched, so I’d say the program is pretty accurate and can be trusted.

Thanks for reading,

PV

92 thoughts on “PV’s Playhouse – Building a Better Manabase”

  1. Not to be too picky, but wouldn’t the “Odds of having a blue source turn 1 to play ancestral visions” be 59! / (6! * 53!) given that you’ve already got ancestral visions in your hand? The percentages change monotonically, so it doesn’t affect your analysis, but I just think that it’s a little more correct this way.

  2. i might be wrong, but to count the number of hands for your deck, i think you want n!/(r!(n-r)!) where n is cards in deck and r is cards drawn (7 in your opener).

  3. Invitational over Community Cup, not even close. The only reason I paid any attention to the CC whatsoever was because Brad Nelson was there.

  4. I find it funny that MWS is like the bane of the Magic community. A lot of sites won’t even mention it because Wizards likes to pretend it doesn’t exist. I personally use it to get a feel for a deck. Any hardcore testing is skewed by the horrid shuffler it has; even if your testing with people you trust to not be terrible magic players.

    Oh, and another awesome article PV. I will definitely be referencing this one over and over again in the future.

  5. Invitational.

    “[G]etting to see what EDH deck Saito likes is much more interesting to me than getting to see what EDH deck someone I don‘t even know likes.” sums it up pretty well.

  6. So what’s an ideal faeries manabase for new extended look like? I’ve been using 4 river of tears and it’s a little tight on colors sometimes.

  7. Kevin H,

    You are correct that the the statistics work that way but the method PV uses is fine because it is a lowball approximation. Your method actually adds to the percentages by thousandsths.

    Also to be extra picky we should actually graph what we are looking for and take integrals of what we want and we can find maxs and mins and then go from there but that seems much more time consuming and almost counter productive.

    Perfecting the manabase takes away from testing time. Figuring out flow of matchups seems much more important then a perfect manabase. Although I guess thats a reasonable debate

  8. Great article PV… really makes me think about manabases.
    Invitational vs. CC:

    I agree with Geno. About the only thing I liked about community cup was Brad Nelson.

    Invitational=Pros playing hilarious formats to get cards printed.
    Community Cup= (Mostly) Non-Pros playing normal or mostly normal formats…… the only argument for this is the famous Wizards employees. But honestly, how many of those can you name other than Rosewater?

    Is this really something we need to consider?

    Invitational. Please.

  9. A. Math Rules. Great article, incredibly informative.

    B. Invitational, not even close. There is always the “storyteller” position, and it seemed like everyone who was at the CC would qualify for that. I’d have more of a chance to go to the CC, (still almost nonexistent) but the invitational is FAR more interesting.

  10. Great article, covers a lot of ground.

    I was always a huge fan of the Invitational. The prize is so awesome (I’d rather have another “Meddling Mage” or “Dark Confidant”-esque card, in terms of flavor / back-story etc. than a draft set). The formats are awesome. The players are awesome. Someone above mentioned that they were only interested was because Brad was in it, and I was the same way (although I was also interested in see how Gavin would do).

    Aje8 mentions Rosewater and I think caring about Rosewater in this context is laughable, but the point remains. In addition to Brad and Gavin as current pros, I paid attention to the CC to see if I could watch Turian or Forsythe play, but since they get as many people out of those who work on Magic as possible, the ringers played only a very few matches. Good for results, bad for coverage, in my opinion.

  11. Thank you very much for this article! I am very fond of them and hope to meet you someday in person to express my appreciation for your writings.
    Also, good luck to your country this Friday. I hope a Seleção teaches that crybaby Cristiano Ronaldo a lesson!

  12. Invitational, not close. I knew a small fraction of the people involved in the CC and realistically I will never be invited to it. If I can’t go to either event I might as well watch pros who I recognise and, as you said, see the cool cards they come up with.

  13. Invitational. I only checked the CC coverage to see pros or former pros play. The invitational is only pros, plus one person chosen for their work in the community, so it is definitely better.

    How do you determine if 1 in 6 misses on Ancestral Visions is acceptable? I always knew how to do the math or that I needed to prioritize based on how early I needed it and doubles, but I never knew how low an acceptable percentage was.

  14. I guess the Community Cup is nice and all, but I’d also much rather see the Invitational come back. Also, as someone mentioned earlier, the backstory of cards like Dark Confidant is pretty fun, and IMO does more for the community than ‘Oh, we get a free draft set or a Sorrow’s Path.’

  15. Gonna add to the flood and say “Invitational.” The cards that result are generally awesome.

  16. Invitational – I’ve been to the PT, and it’s awesome, but as a player I really like the idea of having a chance to get closer to R&D, and the invitational adds that way more than anything else they’ve ever done (aside from the great designer search).

  17. invitational! not even close I normally read the coverage but the CC stuff was so dull I couldn`t muster the interest… invitational.

  18. The Invitational was ridiculously fun every year and seeing the cards evolve over time was spectacular, both year to year and as they were designed.

    If they want to capture some of the “everyman” spirit they can just tweak the field a bit and fill the spots with different people, like they did with Evan Irwin and Steve Menendian. they could even open it up from 16 to 20 spots that way. I think that would even make it more interesting.

  19. What are the chances of casting child of alara (always assuming it is in you first 11) on turn 5, on the play, with 5 Swamps, 5 Mountains, 5 Forests, 5 plains and 5 islands?

    I think it would be a nice extreme to compare things with ><

    so you have 11 cards, 1 is child – this 1st scenario is the one of the extreme ways to do it statistically.

    1st land is 25 / 59

    2nd different land is 20 / 58

    3rd land is 15 / 57

    4th land is 10 / 56

    5th land is 5 / 55

    6th card can be anything + 1/54

    7th + 1/53

    8th +1/52

    9th +1/51

    10th +1/50

    11th is Child ASSUMED which is why we started at 25/59 and not /60

    Wow… it comes out to exactly .02 2% chance! to play child of alara on turn 5 on the play, with any hand that has a child of alara within the first 11 cards.

    I earned a 102 in Statistics in college like 5 years ago and I don’t really remember the exact permutations now to do this but I THINK that 2% is the hardest way…

    The other way would be to assume a random Jank card in your 1st slot and following it up with no lands until your 6th card (the total opposite of the 1st way) and that being
    (1/59 + 1/58 + 1/57 + 1/56 + 1/55) + (25/54)(20/53)(15/52)(10/51)(5/50)

    I think averaging the 2 percentages together would give you an estimation of the average playability of Child of Alara on Turn 5 on the play, assuming a Hand with Child.
    Im too tired to enter in the other one… keep messing up on my computer calculator

    Nice article, btw, pvddr

  20. I definitely would prefer to see the invitational over the cup, because for me the only time I pay attention to the cup would be if it had someone in it that I recognize the name of ie. Nelson

  21. Invitational 100%. Although, were I a WoTC employee, I’d probably prefer the cc. They all seemed pretty pumped over the thing, and maybe the boost in WoTC moral is good for the game in general? Difficult thing to place a value on.

  22. great article as usual PV! you got me on that last example, now i won’t be able to sleep without re-tweaking my manabases LOL.

  23. invitiational but i would like to see them actually print the last invitational card its been almost 3 years since tiago won lol

  24. Definitely prefer the Invitational. I avoided coverage of the CC because I don’t care about random joe schmoe’s playing some designers I don’t know (I check the mothership daily and there were still quite a few I didn’t recognise, and the ones I did know I didn’t care to see play).

    How about they send a reporter to my kitchen table next week? Then you can all get a CC-like multiplayer session covered -_-

    Oh and the invitational cards were always a lot of fun =)

  25. The MWS Shuffler is horrid???

    For those who know computer programming or statistics, this is the code for the shuffler:

    procedure Shuffle(T:TList);
    var i,k,n;
    begin
    n:=T.Count;
    for k:=0 to Min(60,n) do
    for i:=0 to n-1 do
    T.Move(i,i+RandomInt(n-i));
    end;

    – – – – –

    var
    _Seed:array of LongWord;

    procedure moaInitSeed();
    var G : TGuid;
    begin
    ZeroMemory(@_Seed,SizeOf(_Seed));
    _Seed:=getTickCount();
    CreateGUID(G); Move(G,_Seed,SizeOf(G));
    end;

    { Mother-of-All pseudo random number generator}
    { This is a multiply-with-carry or recursion-with-carry generator.}
    { It has a cycle length of 3E+47.}
    { It was invented by George Marsaglia.}
    function moaRandomLongWord(): LongWord;
    var S : Int64;
    Xs,Xn : LongWord;
    begin
    S := 2111111111 * Int64(_Seed) +
    1492 * Int64(_Seed) +
    1776 * Int64(_Seed) +
    5115 * Int64(_Seed) +
    Int64(_Seed);
    Xs := LongWord(S shr 32);
    Xn := LongWord(S);
    _Seed := _Seed;
    _Seed := _Seed;
    _Seed := _Seed;
    _Seed := Xn;
    _Seed := Xs;
    Result := Xn;
    end;

    function RandomInt(V:LongWord):integer; // value in
    var
    r:LongWord;
    begin
    Result:=0; r:=moaRandomLongWord();
    if V>0 then Result:=(r mod V);
    end;

    AKA You have no idea what you are talking about if you call the MWS shuffler horrid. It is about as close to true random as you can get…

  26. Hence… The Truth… I Must make it known!

    A man living in rural Idaho was murdered late last night by the MWSPlay shuffling engine. The man was reportedly found electrocuted by his computer in his basement, with a look of exasperation and shock on his face, and a suspicious game of Magic on MWSPlay showing on his computer.

    “We have reason to believe this was not accidental,” said local detective Frank Stevenson. “We believe that this man was murdered by the MWSPlay shuffler.”

    When asked for comment, the MWSPlay shuffler did not respond. However, research shows that the engine has a long history of crime, including stealing games from people, and screwing several thousand Magic players in its short life.

    “We’ve been trying to find this guy for quite some time”, Stevenson explained. “We’ve almost nabbed him on 3,456 counts of thievery and a few other petty crimes. But this time he went for a big score. We’re not going to let him go this time.”

    People close to the MWSPlay shuffler admit that he was always troubled. “I’ve known the shuffler for years,” said one friend who did not wish to be identified. “He was always shady. He loved to go around screwing nerds out of Magic victories, and even occasionally would rig decks just to see the reaction of people. He was a real sicko. But even for him, murder is a bit surprising. I never thought he would go that far.”

    The local detectives have already issued a warrant for the shuffler’s arrest, but are once again having a hard time locating him. More on this story as it develops.

  27. the bad thing about mws shufler etc is that it is really random!!!
    When u shuffle your deck using your hands is not as close to true Random
    and thats why many people see the diference so exagerated.

    Also when playing MWS you play so many games in such a little time that unoften(unprobable) hands occur much more often than real life!
    You can play in 5-6 hours on MWS more games than if you cometed in every Grand Prix for a year!!

    Its like live poker and net multitabling. During a night of live poker you may not be dealt AA and its no shock but on the internet by playing lets say 5 tables you ll be dealt it many many time during a couple of hours.
    Its just math!

  28. Brian C: Your math is all jumbled up. Among other things it doesn’t take into account that any 6 of the 11 cards can be the wanted ones, not just the first 5 and the 11th.

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  30. Ah, factorials… so many good college memories.

    Invitational for me as well. Although I’d love both. They aren’t mutually exclusive.

  31. Invitational for me as well but you’re not going to get a scientific result by asking this question here of course, as people who would answer community cup generally aren’t reading your articles.

  32. Invitational. At least the winner of the Invitational gets to make a funky card like Meddling Mage, Solemn Simulacrum, or Ranger of Eos. There were some designs I didn’t like (Shadowmage Infiltrator) and some that just didn’t go anywhere (Rootwater Thief), but by and large the cards are interesting.

    Also, I believe this passage was a bit disingenuous:

    “A card like Adarkar Wastes, for example, counts as both a blue and a white mana source, but not if you are playing a card that costs UW – if you have Meddling Mage in your deck and 8 UW dual lands, the chance to cast him on turn two is only 29%, whereas if you have 8 lands that add blue and then 8 different lands that add white, you have 48% – almost twice the chance.”

    If you have 8 U/W lands, you’re only using 8 spots in your deck. If you have 8 U and 8 W, you’re using 16 spots. If you’re comparing apples to apples, what would happen if you had 8 UW vs. 4 U and 4 W? I’m betting the numbers wouldn’t be quite the same…

  33. Invitational =awesome. I still go reread old coverage from time to time.
    CC = boring.
    I like watching the pros. That’s why they exist, as much as a marketing tool as anything else. I’d much rather they just invite the community members to cover he invitational.

  34. I strongly, strongly prefer the Community Cup to the Invitational. My primary reasoning is that I get something material for the Community Cup, though I’m still freaking waiting for my Mirrodin draft set, way to go Wizards =/. Who cares if the Invitational is more interesting? They’re giving ME 12 bucks for the existence of the CC, and they never gave me anything for the existence of the MI.

  35. This article was amazing.

    The CC is not meant to replace the Invitational. I’m pretty sure it was originally intended to keep online players from mutiny. There is a reason it is centered around MODO’s anniversary. I think Wizards insistence on bringing a bunch of paper players into it muddied the waters to some extent. Last year seemed a lot better, the coverage was less boring, people who actually knew something about Magic Online attended, etc. Half the guys that were there this year were plainly clueless about anything to do with Magic Online, and as far as I could tell, only use it for testing for their next PT. I read all of the player blogs and all of them made me cringe. If the goal of the Community Cup is to recognize players who have actively contributed to Magic Online, it mostly failed. If it is to recognize players who have contributed to Magic at large, I think there were better choices that could have been made. I had a really hard time caring about the Community Cup, which is something that I think I’m supposed to be the target audience for.

    Personally, the Invitational was fine. If you must make it one or the other, I’d rather have the Community Cup (if it were run better), but I don’t see any reason not to just have both. But if we’re trading apples for oranges, I’d rather just have another Pro Tour or some more GPs than an Invitational.

  36. The invitational, IMO, was awesome, and was WAY better for the game. Who really cares about the CC? Seriously, yawn. You made 12 bucks? Whoop-die-doo for you. Not having 12 dollars is well worth the enjoyment of having the Invitational back.

    I love playing with invitational cards, it was cool knowing that it was possible for an individual to make their mark on the game like that and leave a legacy behind them. The coverage was always entertaining and these days they could even stream the invitational on the web, it would be epic. Plx bring it back.

  37. @KevinH: you are not entirely right; If I do the math for the chance to have one island in the opening 7, there are still other 6 cards that can be Ancestral Vision. I don’t have to start with one vision and then calculate the Island in the other 6. If I use your method, what is stopping me from finding the chance of an Island and then, with the remaining cards, finding the chance of Vision? They’re both the same (Vision + Island) but you get a different % depending on which one you want to apply first

    @Jim: you are right, this is exactly what I did, 60, 53 and 60-53

    @Bman: I don’t know, I like LSV’s, but I think it might just be to play 26 lands

    @Thepedestrian: sorry I dont even know how to do that :[

    @Others: I agree, the only reason I even got to know what the community cup was was that Brad (and to a lesser extend Gavin) played in it. I’d much rather have 16 of them than one

    @Doobs: well, there isn’t really a way… you have to figure out what you’re willing to give away. It is fine to play a card that you have 50% chance to play on turn one, but you have to know you only have 50% and be fine with it. I honestly don’t know the exact number that is ideal, though I usually set a bottom line that pleases me and then the more the better but not needed, but it’s just whatever makes me comfortable

    @Justin: you’re right. Tiago didn’t really help them either by designing an unprintable card, though 😛

    @awakener: lol

    @Lyle: I mean, for example, that you have Meddling Mage and another color; Imagine you need 8 blue sources, 8 white sources and 8 black sources for another card, with 16 lands – you can either play 8 UW duals and 8 swamps, or you can play 4 UW duals, 2 UB lands, 2 BW, 2 Island, 4 Swamp, 2 Plains, etc – any combination. In this situation, the optimal configuration, if Meddling Mage is the card you want to consider, is 4 Island, 4 Plains, 4 UB duals and 4 BW duals, because that means your U source is never your W source as well. Exact same number of lands and colored sources than 8 Swamp 8 UW duals, but one casts Meddling Mage way more often than the other

    @Chris: that argument is not really valid, since there is nothing stopping them from giving a MDF set for whoever participates in the invitational as well; In fact, with the invitational it is even easier, since they can just give packs to whoever sends a deck to the auction of the people, which is much more interesting to do than to just post a random thing in a forum, without any other purpose, something that doesn’t add anything to anyone, just to gain a pack (and then they can maybe do like 2 sets for the ppl who had their decks chosen, or 3 sets for whoever had the 3-0 decks etc). Anything they give you in the community cup I’m sure can also be given in the invitational so that;s not a factor

  38. For those interested, Google “hypergeometric distribution calculator” to figure out these percentages. It’s nice to get some numbers. I used it to figure out the percentages of opening a Hypergenesis hand with 0, 1, and 2 cascade cards. Good stuff, PV.

  39. A minor nitpick:
    “For Cryptic Command you need four Islands” – you mean three Islands, right?

  40. This is one of those articles that I’ll keep bookmarked for years… Thanks PV.

    Invitational. Card creation > all, but I do think there could be better cooperation between the players and Wizards when it comes to the winner’s card not being something they would ever want to print.

    Also, I’d like to echo your sentiment for adding another Pro Tour back in… I love following the coverage and watching the Top 8 webcasts.

  41. Nice article, you missed the only actual fun thing about mana base’s though, when you realise a mana base that no one else has come up with yet is good enough for competative play and it allows you to play cards together people would otherwise before not think possible. The 5cc control decks with vivids and reflecting pools pretty much stands out head and shoulders above the rest as an example of that. If you do not properly understand manabase’s your never going to be able to do that.

  42. I didn’t care much about the invitational, but I cared absolutely 0 about the community cup, so I’d go with invitational. The interesting thing about the invitational was the weird formats (auction of the people, etc) and seeing what cards invitationalists submitted. BTW when is that counterspell-land the last invitational winner submitted getting printed? ;[

  43. Invitational > Community Cup.
    I always followed the Invitation coverage, but I had absolutely zero interest in the CC, besides watching Nelson play.

    also: I laugh at the fact every time math is mentioned in an article, people dispute and and argue about it.

  44. Invitational, for sure.

    Also, GREAT article PV. Really excellent. One of the best I’ve read this year on any site.

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  46. @PV: The reason that the percentages are different it the subtly different questions they answer. The article’s percentages reflect “what are the chances I have a blue source of untapped mana on turn 1.” My percentage (if I had’ve actually calculated it, but I think you understand what I mean) means “Given I have an ancestral visions, what is the chance I can cast it.” That is more close to the meaning you said in the article “That means that, for every 6.25 times you draw Ancestral Vision, you will not be able to play it once.” Your other percentage (choosing that you have an island, and the odds of a visions in your other 6 cards) is equivalent to “what are the chances I’ll draw visions, given that I have the mana to play it,” which isn’t really that useful of a number.

  47. THe math isn’t quite right on the Ancestral example. Namely because what you care about is the conditional probability of having a an untapped blue source (assuming you have Visions in your opener). If you did it “perfect” you would find an increasing returns to what you have in the article. Ie. a bigger increase from 12-13 and 13-14. Not sure if that changes any of your points.

    But as usual you hit all the general points and this is probably a definitive article.

  48. I liked the invitational formats, but the community cup had more interesting participants. Why do I want to read about some pros playing? I can do that every day, who cares? I don’t know them, they’re just a name and maybe a face I recognize. To PV, they’re his friends and competitors, but to me, they might as well be names out of a phonebook, so I don’t care to read about them. What I cared about were card designs and new strange formats.

  49. Another thing to mention about MWS…

    MWS is BETTER for testing than MODO! There are no rules enforcement so when testing with a friend, you can do things like say “end my turn” while you are fetching up cards from ranger of eos or a fetchland or what have you. You are forced to remember all triggers and your attention to detail improves.

    Then again, you’ll never hear this from a sponsored, spotlight pro who will have angry stakeholders if uttered out of their mouth.

  50. Invitational, hands down. I dont even see this as a choice personally, I used to love the invitational cards.

  51. I quit Magic for awhile then noticed a few players I know had their own Pro Player cards. Part of what brought me back to the game is wanting my own Pro card or the chance to make my own invitational card. Here’s to hoping they bring back the invitational.

  52. I think its really unfair to compare CC to invitational.

    I know that CC reminds us we’ve lost invitational, but making this comparation only ‘levels up’ the CC event, which make things work on the opposite way you wanted.

  53. tl;dr’d the comments, but I’d prefer the invitational. That was always at least enjoyable to watch, while the community cup came and went with a few people mentioning it in articles, but me otherwise being completely untouched by it. I sure as hell wasn’t going out of my way to watch/follow it.

    Generally, when I need to do manabase math, I just open Excel and plug through some math. I’m sure what I’m doing it exactly what MWS is doing, but I find it much simpler to just use a spreadsheet to change my calculations on the fly and have all of my important numbers automatically update through referencing, rather than having to ask specific questions multiple times.

  54. Invitational, I much prefer to see what the pros do and what card they come up with than (mostly) random dudes from the USA.

    Cheers on another great article.

  55. Hi!

    I read your comment on pmppost.wordpress.com on our latest article and I wanted to say that no offense was intended by the writer. He was only expressing how he felt. I hope you didn’t take any offense at all especially since I look up to you guys for inspiration when writing my articles.

    It is nice, however, to see that a pro player notices our articles:)

    Ryan DeVoursney(Halo_Lover)

  56. Just add the make a card to the winner of the Community Cup and 90% of people wouldn’t give a damn either way. Besides the Invitational cost something like 10x more to make happen by comparison to CC.

  57. Invitational, not close. I never have heard of half the people in the CCup, so I only care about them for the free stuff they can win me. The Invitational voting methods, by definition, remove that apathy.

  58. the math is wrong. Kevin H is right. Here’s an example that hopefully makes it obvious. If I set out to answer the question, “How often is my hand pocket Aces when the Ace of Spades is in my hand?” I can’t just calculate the odds of drawing the other three aces in 2 cards. The correct method is to assume I have the Ace of Spades, then calculate the odds the 1 other card is one of the three other Aces. (5.88% using a hypergeometric calculator for population 51, sample 1, successes in pop 3, successes in sample 1). So 5.88% of the time I have the Ace of Spades, I have pocket Aces.

    In the “blue land to suspend Visions turn 1” example, this error amounts to ~6% of those numbers PV gives. The article itself states that 5% is a significant change, so this must be an unacceptable margin of error.

    Another way the article is misleading is in its lack of treatment of mulligans. As a quick proof, wouldn’t we want to exclude all 7 land hands from our analysis of whether we’ll have 1UUU on turn 4, since we will mulligan each and every one of those hands?

  59. before anyone says I misread the article, PV is certainly asking “what percentage of the time I draw Visions can I suspend it turn 1” otherwise he isn’t doing a meaningful analysis, which is just as misleading.

  60. @ Lucas Siow

    That can’t possibly be right. You don’t get increasing returns from adding more cards. Just take the following trivial example. I have a jar with 1 white bead. My chances to draw a black bead are 0. Adding 1 bead adds 50%, Adding a second bead only increases my chances by 13%, then the next by 9% and so forth. By definition diminishing returns.

    @ Jason

    Fish.

  61. @Kevin and others: I see; you guys are right. Though the numbers I have are what I said they were (the chance to have a blue in your opening hand), that is not the most useful number ever – my appologies! If you want to know the chance to have an island assuming one of your cards is a Vision (which is what is relevant), then the math gets a little different. This does not mean everything I said is irrelevant but does change the Faeries example a little. Sorry for that 🙁
    As a side note, if you are on the draw and draw the ancestral visions, the math is also a little bit different

    As far as mulligans go, I think that is a moot point; You might draw 6x Island and Visions too, and then you’d mulligan even if that meets the requirements for t1 vision. By the same level, you might see a hand that cant cast vision, and then mulligan into one that can, improving your %s. I highly doubt you can calculate this and I think it’s pretty irrelevant.

  62. @Ryan: sure, but I was only wrong about the Vision example, he is still not right in the other things he said I said :PP

  63. @MattS: While 6% is a “big” change, you have to remember that the other percentage is going to go down by a similar amount, so the difference in the additional land won’t be that much.

    @PV: I did say, “The percentages change monotonically, so it doesn't affect your analysis.” The numbers still are useful, since they tell you what the odds are of getting appropriately colored mana in your opening hand. You are guaranteed to have *some* action in your opening hand (in that you’d mulligan one with no action), and knowing what distribution you’ll have is useful.

  64. This is an awesome article, I’ve used MWS since beta and I never knew it had that function.

    Like everyone else, I’d rather see the Invitational. Draft sets are nice, and I guess I have a better chance at being invited to the CC, but it’s still so boring to follow. I read that some of these people had 1400 ratings or had been playing for only a few months, and the top players basically drafted their decks for them. How silly is that? I want to see the best players, not FNM.

  65. Great article. Rather have the invitational as well. Not a big fan of MaRo random ideas for formats thou I really enjoyed seeing some pro action and the cards they created that actually came into being printed was awesome. Who didnt love Solemn, Confidant, Avalanche Riders, etc…

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  68. Excellent article. Your example(s) of the Faeries manabase makes your points very clear.

  69. regarding mana base in Faeries, I think River of Tears is overrated. It’s quite unreliable colorwise and as PV said can’t cast Ancestral turn 1. In my Faeries build I use Misty Rainforests with Watery Graves + Drowned Catacombs package. That manabase setup is very flexible: I can pop a fetch eot and avoid damage or just put a dual untapped if needed. On turn 4 I allways have 3 blue available and mostly 2 black too. Here is my full manabase:
    4x Misty Rainforest
    4x Mutavault
    1x Pendelhaven
    4x Secluded Glen
    3x Drowned Catacombs
    3x Watery Grave
    5x Island

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