I tried a few matches on MTGO with different color configurations (Rg, Ru, Rb) and it was fairly miserable; you get outraced by Dredge, Survival, PO, Arclight Phoenixes, and your creatures quickly get outclassed by Humans. The post-sideboard Shops matchup is easy though
By far the best feeling when playing burn was getting a Dark Confidant into play, so if I were to try to push the deck further I would start from there.
A more rigorous take on this debate:
Suppose you are allowed to run as many Leylines as you want. Let p[n] be the probability of winning a tournament with optimal deck construction given the constraint that you must run exactly n Leyline’s.
For any integer n, let S(n) be the following assertion:
max(p, p[n]) > max(p, p, ..., p[n-1])
The “0 or 4” crowd is then asserting that S(4) is true and can be deduced from first principles. Let’s assume they are right.
Now if Leyline is playable, then S(75) is clearly false.
This implies that if you consider the statements S(4), S(5), S(6), ..., S(75), then there is some magic k for which S(k) can be proven to be true from first principles, while S(k+1) cannot.
What is this magic k, and what is so special about it, that allows you to make a from-first-principles argument for S(k) but not for S(k+1)?
If no such k can be identified, then the “0 or 4” crowd must be wrong. It may indeed be the case that 0 or 4 is better than 1, 2, or 3, but that fact cannot be deduced from first principles.
If your premise is
- you must mulligan until you find a Leyline (even if you have zero Leylines in your deck) and you cannot attempt any other deck construction or mulligan strategy
then you and @ajfirecracker are entirely correct. The first Leyline most increases your chance of success, and each subsequent Leyline is weaker than the first (with 75 Leylines obviously useless, unless you're on the draw-go-until-they-deck-themselves plan).
I don't understand why people are so hung up on the (obviously absurd) premise I boxed above. The alternative to running 1 Leyline and mulliganing until you find it is not running 0 Leylines and mulliganing until you find it. It's building a completely different deck with a different strategy for defeating Dredge (such as cantripping into multiple copies of Priest or Rest in Peace.) In this sense a "Leyline mulligan" strategy with 4 Leylines can be more effective than a completely different "cantrip into hate" strategy with zero Leylines which is in turn more effective than a "Leyline mulligan" strategy with 3 Leylines.
This is the argument I and other "4 or 0" people are advancing. Not some straw-man (and incorrect) simplistic assertion about hypergeometric distributions. @dshin's calculations are completely valid but irrelevant to the argument I'm actually advancing.
I again suggest thinking of Workshops as a second view on the same phenomenon. A blue deck with zero non-Moxen artifacts is strictly worse if you add a random Workshop. Once you add the first Workshop and start adding expensive artifacts, you are pursuing a new strategy and now adding three more Workshops is optimal (with diminishing returns as you add more Workshops, with the tipping point well above the maximum allowed 4 copies). The vast majority of Vintage decks want 0 or 4 Workshops. This has nothing to do with p[n].
@ChubbyRain ajfirecracker presented a (well-reasoned) argument against the "0 or 4 Leylines" advice, based on a hypothetical format where 5 Leylines are legal, and offered three potential resolutions to the paradox he constructed. Search for "There are a limited number of ways to avoid that conclusion." to find his post.
I was responding to this argument. I'm not claiming that it's never correct to run 2 Leylines, nor am I claiming that no Vintage deck runs 2 Workshops, but these rare corner cases are not especially germane to analyzing ajfirecracker's argument that the "0 or 4" advice is generically unsound.
I don't consider Tabernacle to be an anti-Dredge card, but it is a strong card in some generic sense
Ichorid is able to operate just fine through Tabernacle, and if you are tutoring it out with a Knight that's fairly slow.
When I see Knight of the Reliquary typically I am much more worried about Bojuka Bog followed by Wasteland.
What about Tabernacle in Shops? Shops can stop Dredge from comboing off using a mix of Wastelands, sphere effects, Ballista, Pithing Needle, Crypt, etc, but then the Tabernacle shines in preventing Dredge from grinding the game out with Zombie tokens.
@evouga Then you are essentially moving the goalposts here, because the almost is what was important to the discussion.
?? We are talking about Dredge here, how is the number of Workshops in your Frenzy Paradoxical Outcome deck the important point of the discussion?
No, but it would be silly to say "run 4 or 0 Shops in your artifact deck"
My comment was tongue-in-cheek, but has a serious kernel to it: the analysis in this thread about 4 vs 0 copies has a major premise that the utility of Leyline of the Void is constant and independent of sideboard cards you've already chosen to include in the deck. Compare to Workshops: the first Workshop you add to a Vintage deck makes the deck an "artifact deck" and dramatically increases the value of each additional Workshop.
If you are on the "Leyline plan" of mulliganing to either a Leyline or a T2 win, the second through fourth leyline have dramatically increased utility by virtue of your choice to include the first. If you are on the "control plan" instead of applying steady disruption with castable cards like Containment Priest, Rest in Peace, Tormod's Crypt, etc, then it may never be optimal to include even one Leyline. There is no contradiction here or anything "magic" about the number 4.
@ChubbyRain Sure. I was very careful to include the "almost" qualifier.
@Aelien Agreed. If you are playing Leyline of the Void, it's for its ability to enter play immediately and uncounterably. If you want 1-3 of the Leyline effect, Rest in Peace is a better alternative as it's more easily castable in the crucial early turns if you dig or tutor into it.