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By: thewoof2, Christopher Gallon
Feb 23 2015 1:00pm
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Last article I spoke in depth about considerations in a mulligan decision.  This article will try to put those theories into practice and run though some mulligan decision examples.

Know your Tendencies

My tendency is to mulligan on the safe side, this is also partly due to my optimistic nature as I always think I will draw that needed card and can take the chance rather than going down to 6 cards.  In my beginning tournaments this definitely hurt me, I would keep hands that today I would mulligan.  Knowing this has made me more cognizant to my predisposition and I account for it in my decision making.

Current Deck

The deck that I currently run in vintage is a fairly vanilla version of Forgemaster MUD.  I have a lot of experience with this deck which I feel really helps in my ability to make the right decision.  I understand many of you do not use this deck nor play Vintage but that said I will walk you through my analysis and thought process which can help you in your mulligan decision making.  To start let's look at the decklist:

 

Average Converted Mana Cost (ACMC)

This is how I calculate the ACMC for this deck:

  • 8 zero cc spells - I count two Chalice of the Voids as zero cc as I most likely cast them on 0 half the time.  Also note below while I have 8 zero mana spells for the ACMC of this deck I do not count zero cc mana only spells, see below.
  • 3 one cc spells - I put the other two Chalice of the Voids as one cc spells.
  • 11 two cc spells
  • 8 three cc spells - I count the 2 Phyrexian Metamorphs as three cc as I almost never have the blue to hardcast them.
  • 4 four cc spells
  • 4 five cc spells
  • 3 six cc spells
  • 1 eight cc spell

Getting the average you need to multiply each cc spell with the number of spells (e.g. 0*8, 1*3, etc...) then total these, in this case the total is 116.  Then divide this by the number of spells total 43 to get an ACMC of 2.697.  To note, one thing we need to also account for in this deck is we run a lot of sphere effects with both Trinisphere, Sphere of Resistance and Thorn of Amethyst with Tangle Wire as well this puts more mana pressure on the deck than what the ACMC might suggest.

Now one consideration here, in this deck I would also not count 0 cc mana sources in the calculation.  I count Sol Ring in ACMC but the Moxen and Mana Crypt are free to cast so in this case I pull them out.  This puts my decks ACMC at 3.14, knowing the other factors I round up to 4 ACMC for my deck as an estimation of mana needs.

Mana Proportion

This deck needs to get a lot of mana quickly to try and bury your opponents with spheres and threats.  Also to note 5 of the lands are primarily used for mana denial strategies with Wasteland and Strip Mine.  Therefore in addition to the 18 lands the deck runs 5 moxen, Sol Ring and Mana Crypt.  So the mana proportion is purposefully high, we have the 18 lands plus the 7 mana artifacts making the total mana sources at 25.  25 mana sources out of the 60 card deck gives us a proportion of around 42% of our cards are mana sources.  Again this is a tad misleading considering the decks strategy and mana denial land sources but suffice it to say this deck needs mana and wants it fast!

Midgame Mana Curve

I have already mentioned in my estimation average vintage games are 6 turns (or by that time the game is at least decided) so the midgame to consider here is turn 3.  By turn 3 my deck wants its threats to hit, in particular I will want mana access to cast Lodestone Golem, Kuldotha Forgemaster or even ideally some of my 6 cc spells.  So with my deck I will want access to more than my ACMC of 3 by turn 3 which is very possible with all the other mana sources I have and with the lands that give me additional mana like Mishra's Workshop.

Drawing Formula

So let's quickly look at the draw formula again.

100% - [(N/X)^Y] where:

  • N = total number of cards remaining in library NOT of the desired kind, and
  • X = total number of cards remaining in library
  • Y = number of draw steps under consideration

At the start the 60 card deck has 25 mana sources and 35 non-mana sources.

Mulligan Decisions

The following are real examples of hands from this deck using the MTGO sample hand analysis tool.  We will walk through some interesting decisions and then see how they pan out.

Example 1

Considerations:

  1. Only 1 land and 1 Mox Emerald, first turn potential is (Chalice of Void) for 0 and then Sphere of Resistance.  Not a playable hand or high threat level.
  2. Hand is definitely light on mana, chance of getting one mana source next turn is 43% (see math below).
    • N = 53 (Total Left) - 23 (Mana Sources left the 25 take out land and mox) = 30
    • X = 53
    • Y = 1
    • 1-((30/53)^1) = 43%
  3. Cost of Mulligan is 66% so there is a 23% difference in favor of a mulligan.
  4. Mulligan

Just to show how things would have turned out in this case, if you kept the hand your next card would have been:

After your mulligan your new hand would have been:

Judging by the new hand we can say the mulligan decision in this case was the right call.

Example 2

Considerations:

  1. This hand has no real threats but is packed full of mana.  It has Wasteland and if I draw one big threat it becomes a great hand.
  2. With this hand I want to calculate the chance of drawing a big threat in the next 1 or 2 turns at the least.  Let's calculate both.
    • N = 53 - 9 (Estimate of the big threats in deck left) = 44
    • X = 53
    • Y = 1 and Y = 2
    • Chance with 1 turn = 17%.  Chance with 2 turns = 31%
  3. Cost of Mulligan is 66% so there is a 35% difference in favor of a mulligan.
  4. Mulligan

If you kept the hand your next two cards would have been:

I did count Trinisphere as a big threat so you did get lucky drawing it!

Now let's look at your mulligan hand:

In this case the mulligan hand again was the best choice for sure, in fact this hand is very strong as I would lead out with the Thorn of Amethyst so that turn 2 you can Cavern of Souls and make sure you land the Kuldotha Forgemaster.

Example 3

Considerations: 

  1. Again this hand light on mana knowing our desire to get 4 mana by turn 2 so we get access to the larger cc midgame threats.
  2. With this hand I would want to draw a mana source that gives me 2 mana in at least 2 turns.
    • N = 53 - 11 (Ways to get 2 mana) = 42
    • X = 53
    • Y = 2
    • Chance with 2 turns = 37%
  3. Cost of Mulligan is 66% so there is a 29% difference in favor of a mulligan.
  4. Mulligan

If you kept the hand your next three cards would have been:

Now let's look at your mulligan hand:

This one is closer, we did draw the Ancient Tomb in the kept hand but the mulligan hand looks more playable.  I still rather have the mulligan hand so I think it was the right decision.

Example 4

 

Considerations:

  1. This hand is similar to the last example but let's play this one out and see if our findings change or are validated.  I would be more tempted to keep this hand over the last though as one 2 mana source makes an uncounterable Lodestone Golem.  
  2. Let's use similar numbers above, we have a 37% chance to get a 2 mana source in two turns.
  3. Like above the mulligan of cost of 66% is better option.
  4. Mulligan

If we kept and drew three cards we get:

Versus a mulligan hand of:

So this was a lose lose but the mulligan hand is better considering the first hand would have been stuck on 2 mana for 5 turns at least.  But the question here is do we mulligan again 5?

Let's calculate the chance of a two mana source OR a Wasteland/Strip Mine as with Crucible of Worlds that would be nice in the next two turns.

  1. With this hand I would want to draw a mana source in the next two draws.
    • N = 54 - 16 (Ways to get 2 mana) = 38
    • X = 54
    • Y = 2
    • Chance with 2 turns for a 2 mana source or mana denial land = 51%
  2. Cost of Mulligan is 52% with only 5 cards.  This is a wash, again this is guidance so at this point it is your gut call.
  3. I personally would keep.

Unfortunately I cannot find the pictures on this last decision but I remember the outcome.  If you kept the hand and drew you would have gotten another Tangle Wire then a Mishra's Factory.  If you mulligan your hand would have been:

While not a slam decision and in this case you most likely lose with both hands I think all things considered I prefer the keep at 6 cards decision.  Interesting question on the 5 card hand is do you turn 1 Phyrexian Metamorph the Mox Ruby in hopes that you get one more land and can Kuldotha Forgemaster?  Tough call but blind to what my opponent has I would hold off.

Example 5

Considerations:

  1. So this hand can power out a lot due to Tolarian Academy even without a land.  Turn 1 Mox Pearl, Chalice of the Void on 0 and you have 3 mana to most likely use for Thorn of Amethyst.  You have to consider the issue of your opponent killing Tolarian Academy and really hurting you but this hand is very playable.  Then turn 2 you have mana to cast everything in your hand.
  2. Assuming the play above your next draw you do not want a 0 cc spell (because you chaliced on 0) nor do you really want the Staff of Nin or Sundering Titan because you won't be able to play them.
    • N = 7 (5 zero cc spells and the two unplayables)
    • X = 53
    • Y = 1
    • 87% chance you draw something else
  3. Cost of Mulligan is 66% so it is 21% favorable to keep.
  4. Keep noting the risk of opponent killing Tolarian Academy.

If you kept your next 2 draws are:

And if you decided to mulligan:

In this case you drew what you wanted with your original hand but also the mulligan hand is nice.  I don't think you can really go wrong with either choice on this one but I think I liked our keep hand better.

Wrap-Up

Using my vintage Forgemaster MUD deck I used my previous article's theories and applied them.  I hope this shed some light on how you can consider the mulligan decision and be more mindful next time you face that tough decision on how best to proceed!

Woof