Thanks for the in-depth responses everyone.
The mulligan is an important factor I have overlooked. I was playing
Crucible of Worlds and a bunch of fetch-lands to go with
that. As a result, I usually shuffled my library before activating
Grenzo. Cutting that package now.
I play with a very stable pod (a group of friends from school) whom
I expect to quickly learn the power of Grenzo, so politicking won't
get me very far.
I tried to quantify some of the things we're talking about:
First, I can't think of a good way to compare the efficiency of Grenzo
flips vs other sources of card advantage. To compare them, we'd want
to have a quantity that represents a card's "impact". Then we could
measure how much impact we get for one mana. For non-land cards, the
best approximation of impact I can think of is mana cost (and that's
pretty bad). For lands, I can't think of any. If anyone has any
suggestions, I'd love to hear them.
What I hope to measure is how much worse drawing a card becomes when
we get access to Grenzo.
Because the probability of an activation hitting is about 0.56, every
mana spent to cast cards from the hand has an opportunity cost of 0.28
cards. The efficiency of drawing a card after we gain access to Grenzo
is thus (1 - 0.28 * a), if we play cards with an average cmc of a. (We
subtract from the 1 card we draw the cards we pass up on by playing
the card we drew). It therefore seems reasonable to avoid playing high
cmc cards from our hand if we want to maximize our card advantage.
These cards we treat as dead draws. The following table contains my
results. Each column says how efficient drawing a card becomes if we
avoid playing cards that cost more than a given number of mana.
cmc | efficiency |
0 | 0.35 |
1 | 0.39 |
2 | 0.44 |
3 | 0.46 |
4 | 0.44 |
5 | 0.40 |
6 | 0.37 |
For example, if we only play the 0 cmc cards we draw, drawing a card
becomes 0.35 times as efficient, because we incur no opportunity cost
to play them, but we can only play 0.35 of the cards we draw.
So, when deciding whether to run a source of card draw, keep in mind
that it has a ~0.4 modifier on the number of cards it draws when
Grenzo is out. Please check my reasoning.
Another interesting finding I have made is that a blind Grenzo
activation puts about 2.08 cards worth of mana onto the battlefield.
That means that flipping blindly is about as expensive as playing
cards from the hand mana-wise. (Ten flips save one mana.)
@ThePillowman I probably don't understand your question, because can't
really think of a scenario in which I don't need more lands.
Also, could you elaborate on why pulling from the bottom doubles
thinning efficiency? I don't see why it's relevant to thinning whether
we draw cards from the top or the bottom.
That aside, any thoughts on
Sire of Insanity? It's a dead flip, but
this deck breaks the symmetry so much...
Mindslicer is another card in
a similar vein.