gerardpaapu/SerumBelcher.md

## SerumBelcher.md

      
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              SerumBelcher.md
            
          
    Hi all,
I've been looking for some math on whether Serum Powder can be a net
benefit for a deck like belcher that has to mulligan a lot to see
specific cards. The effect of Serum Powder as I understand it is
essentially two things
The benefit is that we can exile cards that we aren't looking for and
draw more cards than if we had used a traditional mulligan.
The cost is that we sometimes have to keep a hand that has a Serum
Powder (a dead card) or mulligan more often because we have one
important card e.g. Mountain, but not enough else to keep because
there are one or more Serum Powder in the hand.
There's some info out there about Serum Powder to mull to exactly one
card in your opening hand, like Leylines or Bazaar, but I couldn't
find anything close to our scenario and I don't really know any math
so I wrote a script to simulate mulliganing with serum powder in
3-land belcher.
https://gist.github.com/sharkbrainguy/456e9dab7f7c97e4b7cde96adf5da6b7
The deck I use in this script is:

4 Chancellor
0-4 Serum Powder
11 Fetch Spell (a one mana green sorcery that can fetch a basic)
4 Renegade Map
2 Forest
1 Mountain
34-38 Other

Our goal is to keep a hand that can hit two land-drops (and hope to
hit the third in the next 2-3 draws), so this is the algorithm:
Keep all hands:

with at least one chancellor and at least two fetch spells
with at least one chancellor, at least one fetch spell and at
least one map
with at least one forest and at least one fetcher
with at least one land and at least one map
with 2 or fewer cards

Exile all hands:

with Serum Powder, no lands and no chancellor

Otherwise mulligan.
I tested with decks that ran 0-4 Serum Powder and also one that runs 0
Serum Powder but 4 extra fetch spells (e.g. 4 copies of Attune With Aether)
The question I ask here “How often will I keep a hand with at least n
cards that are not serum powder?”
Here's the results of mulliganing 100,000 hands:
https://docs.google.com/spreadsheets/d/1uysOISkglhNBUAHN8djfljqB620KkdhybBEKGfAgPMM/edit?usp=sharing
For this question 4 Serum Powder performs best for
n = { 3 (80%), 4 (78%), 5 (72%) }
All options converge at n = { 6 (58%) } and 4 copies performs the
worst for n = { 7 (31%) }.
Adding 4 Attune with Aether performs the same as 4 Serum Powder for n = { 3, 4, 5 } but outperforms it for n = { 6 (63%), 7 (44%) }.
In my (limited) experience, a 5-card hand will often present lethal on
turn 4 but a 4-card hand has to get pretty lucky, so I think n = 5 is
the number I'm most interested in:
|----------------------|---------------|
| Deck                 | 5+ card hands |
|----------------------|---------------|
| 4 Serum Powder       | 74%           |
| 3 Serum Powder       | 72%           |
| 2 Serum Powder       | 69% (nice)    |
| 1 Serum Powder       | 67%           |
| 0 Serum Powder       | 64%           |
| 4 Attune With Aether | 73%           |
|----------------------|---------------|

This shows that for my mulligan algorithm, Serum Powder performs
better than “Other” but not very different overall than running extra
copies of an effect we are already extremely redundant on.
I guess this means the questions are:

Is drawing a Serum Powder after hitting my first two land-drops
any better or worse than drawing an Attune With Aether?
Is better odds at a 7 card hand more important then better odds at
5 cards?

Obviously after you keep your openinng hand, you would rather draw
Faithless Looting, Manamorphose, Street Wraith or Mishra's Bauble than
Serum Powder. I'm not sure how to quantify that difference outside playtesting
or goldfishing a lot?

TL;DR Should I play Serum Powder? IDK Maybe, probably not.