[Primer] Elves!

[Koby]

I'm really stupid. Do all those numbers mean you like 3 or 4 DRS? 0-3 Llanowar Elves? I don't math good.

I don't differentiate between DRS or Llanowar Elf or GSZ=0. For this calculation, they are identical.
Likewise, a land could be Forest, Bayou, Savannah, or Fetchland; but not Gaea's Cradle nor Dryad Arbor. I assumed 2 Bayou, 1 Savannah, 1 Forest, 10 fetchland.

Interestingly enough, dropping 1 fetch increases the likelihood of this hand across the board; however there is roughly 0.7% increase when going from 8 to 9 dorks.

[Absolutflipz]

4 Deathrite Shaman.

This card is what made the deck Tier 1.

This is the exact type of comment I was referring to in the first couple lines of my response. There has to be further thought given (aka how many fetches makes him reliable, do I value producing multiple mana moreso than removing cards from the yard, etc..)

Deathrite Shaman is a good card and a buff to the deck. It is not the reason the deck is tier 1. I'd argue the recent success is much more largely due to the printing/discovery of Craterhoof in conjunction with NO to go along with the already strong glimpse/heritage combo.

Ah, I'll just refer to Koby as he seems to be on the same page as I am.

Edit: ha yes, Leo.

[LeoCop 90]

4 Deathrite Shaman.

This card is what made the deck Tier 1.

Deathrite Shaman contributed to it. But the deck improved so drastically because of the printing of deathrite shaman and mainly, in my opinion, cratherhoof behemoth, alongside with the fact that a good deck configuration was found considering that natural order is fantastic with behemoth.

I don't think that playing 3 or 4 deathrite shaman can influence so much the deck, but i prefer to have one more reliable mana dork instead of the 4th deathrite shaman.

Edit: it seems that me and absoluteflipz were posting the same thing in the same moment XD

[nudon]

4 Deathrite Shaman.

This card is what made the deck Tier 1.

+1. Same goes for NO->hoof. I've tested the 4 NO in the main deck and it just gives the deck another "I win" button. Sure, sometimes you'll have an awkward opener with multiple NO in hand but it makes the deck so much faster. As long as you don't over-extend against control, you'll still beat them despite the risk of getting 2 for 1.

So far in limited testing, the 4 NO, 0 llanowar, 4 quirion, 3 birchlore, 1 arbor (moved to sb to make room for more birchlores) has been about a half turn faster. For those concerned about DRS making mana, you can always cut savannah (not that I would it) and the 2nd basic for additional fetches since you're already running multiple birchlores.

[Kayradis]

I started playing Elves about a year and a half ago. Mono-G. Archdruid. Concordant Crossroad. Emrakul kill. Not really fun to be fully honest.

Since the G/B list, I don't have numbers like Koby, but the inclusion of DRS makes the deck way more fluid, provides it with resilience and also an alternate end-game by the DRS grinding the hell out of your opponent.

After a fairly good amount of testing (multiple weeks) I am convinced that the Birchlore > Llanowar/Mystic/Fyndhorn provides better and faster T2 combos/chain. I've used it multiple times against Jund as a 2/2 face-down creature.

I acknowledge Koby's math. It does sound legit. But my guts and experience with the deck make me believe that Lemnear is right and that Llanowar/1CMC Mana-Dork slots could be used to a better efficient.

Up to last weeks, I was running Llanowar as a 1-of.
It's gone now.
Sylvan Safekeeper took the slot.

[nudon]

Hypergeometric function on Excel needs 5 inputs: HYPGEOM.DIST(success, sample, total in deck, deck size, cumulative=FALSE)
When you're adding more conditions, you need to multiply the probabilities.
When you're figuring out ranges, you need to add the probabilities.

Example:
Probability of 1 mana dork AND 1 land AND 1 engine = P(1 mana dork) * P(1 land) * P(1 engine)
Probability of getting between 1 to 5 mana dorks = P(1) + P(2) + P(3) + P(4) + P(5)

Similarly for those interested in calculating probability of getting at least 1 copy of a card/land, you can always take P = 1 - [(deck_size - total_in_deck)/deck_size * (deck_size - total_in_deck - 1)/(deck_size - 1) * .... * (deck_size - total_in_deck - hand_size + 1)/(deck_size - hand_size + 1)]

While giving a good idea of your actual probability of getting 1 mana dork AND 1 land AND 1 engine, that calculation you gave is slightly off. The probability of getting 1 land or 1 engine is correlated with the probability of 1 mana dork.

Edit: Of course adding additional mana dorks increases the percentage of having at least 1 mana dork, exactly 1 land, and exactly 1 engine. However, that doesn't mean it's necessarily correct. Using the extreme example, you can remove everything in the deck aside from lands, glimpses, and NOs and fill them with mana dorks to increase the percentages you gave.

[nudon]

I don't differentiate between DRS or Llanowar Elf or GSZ=0. For this calculation, they are identical.
Likewise, a land could be Forest, Bayou, Savannah, or Fetchland; but not Gaea's Cradle nor Dryad Arbor. I assumed 2 Bayou, 1 Savannah, 1 Forest, 10 fetchland.

Interestingly enough, dropping 1 fetch increases the likelihood of this hand across the board; however there is roughly 0.7% increase when going from 8 to 9 dorks.

The reason for that is because you've fixed your condition to have EXACTLY 1 land in the opener.

[Koby]

Being curious about it myself, I ran a multi-layer analysis of the problem:

How many lands, and how many engines, and how many dorks gives us the best odds of getting the elusive hand we're discussing.

Engine Cards	7	41.61%					8	41.17%
Useable lands	12	38.13%	13	36.14%	14	33.95%	12	38.13%	13	36.14%	14	33.95%
Dorks	8	9	8	9	8	9	8	9	8	9	8	9
Cumulative Sum	65.36%	70.02%	65.36%	70.02%	65.36%	70.02%	65.36%	70.02%	65.36%	70.02%	65.36%	70.02%
Total Probability	10.37%	11.11%	9.83%	10.53%	9.23%	9.89%	10.51%	11.26%	9.96%	10.67%	9.36%	10.03%

Based on this, I think the best build would be 12 lands, 4 Cradle, 2 Dryad Arbor; 8 engines, and 9 dorks. The mulligan rate would be pretty high however, since there's only 12 lands that could tap for mana.

Making the condition 1 or 2 lands would increase it further. I won't calculate Cradle into the mix, but it obviously makes those hands insane too.

Other fun facts -- Lands in opener (Lands = fetches or forest/dual, but not Cradle & Arbor)

	12 in deck	13 in deck	14 in deck
"Auto-mull" 0 Lands	19.1%	16.3%	13.9%
1 Land	38.1%	36.1%	33.95%
2 Land	29.3%	30.98%	32.3%
"Keeper" = 1 OR 2	67.4%	67.1%	66.3%

You can replace these values in the "Useable lands" row in the first table to get a better gauge. It's the same conclusion -- 12/8/9 ratio (Lands, engines, dorks) as the best odds of getting that opener.

[nudon]

If possible, you should change your initial condition to 1 or 2 lands. That would fix the trend of why the % decreases with an increased land count. Also, the % goes up each time you add an additional mana dork. Adding a 2nd or even 3rd llanowar will skew the % up too. However, most of us will agree that it's undesirable to have that many llanowars. The probabilities don't care about cards like visionary/symbiote, which don't do anything for us turn 1. The type of analysis, while helpful, is better suited for decks like belcher/rogue hermit.

[danyul]

You guys are smart.

[Koby]

If possible, you should change your initial condition to 1 or 2 lands. That would fix the trend of why the % decreases with an increased land count. Also, the % goes up each time you add an additional mana dork. Adding a 2nd or even 3rd llanowar will skew the % up too. However, most of us will agree that it's undesirable to have that many llanowars. The probabilities don't care about cards like visionary/symbiote, which don't do anything for us turn 1. The type of analysis, while helpful, is better suited for decks like belcher/rogue hermit.

I don't agree with you regarding discounting these calculations. Elves is flexible enough in the late game when it needs to be. Are we only designing the deck to be able to perform in the late game, or should we push the limit of this deck in the early turns when it's most favored against the majority of the format. Yes, one removal slows down the whole game that's a given. Recount how many of your own games/matches went to goldfish pretty quickly?

Moreover, increasing the Llanowars makes Quirion Ranger into NO that much more consistent as well. It makes late game suffer - yes, and it's a terrible topdeck. However with GSZ and Glimpse and NO, I don't think Elves archetype is suffering for late-game versatility. Visionary and Symbiote also help to reduce dead topdecks in those situations. That's a lot of cantrips and tutoring thus. Birchlore Rangers sort of fall into this metric of mana dorks, but require more 1-drop elves to take advantage so it has its limitation. Increasing the spell count (NO to four), hurts it's usefulness. We're approaching the limit of non-creatures we can include in the deck. With four NO, we're just barely at 31 creatures. That's kind of low IMO.

[nudon]

The main reason why you get 12 lands is because the expectation value of getting 1 or 2 lands in the opener is 60/1.5 = 12.8. If you really wanted to maximize the value of getting only a single land in the opener, the "correct" number of lands would be lower than 12. Also, sometimes 3 lands are ok depending what else is in the hand. 9 mana dorks is certainly better than 8 for the probability you're calculating but 10 is better than 9 and so forth.

[Koby]

The main reason why you get 12 lands is because the expectation value of getting 1 or 2 lands in the opener is 60/1.5 = 12.8. If you really wanted to maximize the value of getting only a single land in the opener, the "correct" number of lands would be lower than 12. Also, sometimes 3 lands are ok depending what else is in the hand. 9 mana dorks is certainly better than 8 for the probability you're calculating but 10 is better than 9 and so forth.

My opinions on Elves are based upon experience from a range of builds, from 10 Forest + 4 Land Grant, to 19 land Survival; and everything in between (including 14 Forest + 4 Cradle + Wood Elves/Symbiote). I'm of the opinion that 18 land is at least one too many to begin with. I've bricked too many times by drawing lands from a Glimpse chain to really feel comfortable in increasing that count.

[nudon]

I don't agree with you regarding discounting these calculations. Elves is flexible enough in the late game when it needs to be. Are we only designing the deck to be able to perform in the late game, or should we push the limit of this deck in the early turns when it's most favored against the majority of the format. Yes, one removal slows down the whole game that's a given. Recount how many of your own games/matches went to goldfish pretty quickly?

Moreover, increasing the Llanowars makes Quirion Ranger into NO that much more consistent as well. It makes late game suffer - yes, and it's a terrible topdeck. However with GSZ and Glimpse and NO, I don't think Elves archetype is suffering for late-game versatility. Visionary and Symbiote also help to reduce dead topdecks in those situations. That's a lot of cantrips and tutoring thus. Birchlore Rangers sort of fall into this metric of mana dorks, but require more 1-drop elves to take advantage so it has its limitation. Increasing the spell count (NO to four), hurts it's usefulness. We're approaching the limit of non-creatures we can include in the deck. With four NO, we're just barely at 31 creatures. That's kind of low IMO.

I'm not discounting these calculations, merely saying it's not the end-all. Yes, birchlore ranger is likely to generate mana on turn 2 due to the plethora of 1 cmc elves in the deck. Sure, it's not as great with quirion ranger but it improves glimpse greatly (which has been somewhat diluted due to the addition of NO). I definitely agree that the limit of non-creature spells is close but the 4th NO has so much raw power that it's worth it.

[Lemnear]

Koby your analysis Looks promising.

I still want to Highlight that Birchlore turns ANY two Elves into mana dorks which is nothing to ignore and I strongly feel they are the mana dorks 9-12 in this deck.

Samples from todays testing:

T1: Windswept Heath for Bayou, cast Birchlore
T2: Tap Bayou for Quirion, tap both elves, bounce Bayou to untap Quirion, play another birchlore, tap 2 Elves, play and tap Cradle, NO sac Birchlore, Swing for 8

T1: savannah, Nettle
T2: Birchlore, tap 2 Elves, Nettle, tap both nettles, Hertiage, tap 3 elves, Glimpse, tap 2 nettles, Symbiote, tap 2 nettles and go nuts

[nudon]

My opinions on Elves are based upon experience from a range of builds, from 10 Forest + 4 Land Grant, to 19 land Survival; and everything in between (including 14 Forest + 4 Cradle + Wood Elves/Symbiote). I'm of the opinion that 18 land is at least one too many to begin with. I've bricked too many times by drawing lands from a Glimpse chain to really feel comfortable in increasing that count.

I know you're very experienced because I messaged you privately when I first picked up the deck/got into legacy. You may be right on the 18 land but the only land I would cut at this point is the 4th cradle since I don't want to drop below 13 t1 playable lands in the deck.

[Lemnear]

I want to give props to the peeps in this thread. This one already contains more value, brainwork and reasoning than the previous one accumulated in a year

[Koby]

I have a whole bunch of awesome turn 2 plays as well. The deck can certainly "belch" out its hand. It tends to do so when you're playing fewer lands too. I don't buy the argument that the deck needs 4 Birchlore Rangers, however. Let's examine our working slots:

1cc Unconditional mana (let's count DRS here for simplicity). This set ramps us into big mana (mana > turn count).

4 DRS
1 Llanowar Elves
4 "GSZ=0"

Second level mana dorks provide ways to reuse first tier dorks via untapping. They have a dependency of 1 card.

4 Quirion Ranger

Third level mana dorks include generating mana throughout the turn. These combo with Nettle Sentinel only, but provide insanely explosive turns. They have a dependency of at least 1 other card.

4 Heritage Druid
2-3 Birchlore Rangers
4 Wirewood Symbiote (not that you need an Elf and a dork (2 other cards) in order to generate mana here)

And that's pretty much 80% of the creatures in the deck. Two slots for win-con with NO (Regal Force / Craterhoof Behemoth / Terrastadon / whatever you fancy), 4 Nettle Sentinel for explosiveness, and 4 Elvish Visionary to generate card advantage. Maybe one or two utility green cards for late game interaction (Ooze, Viridian Shaman, Elvish Archdruid/Priest).

Based on the dependencies, I would first play 4 Quirion Ranger before playing more than 2 Birchlore Rangers. If you want to maximize the third tier mana generation, then by all means play 3 or 4 copies, but you have to cut from the utility slots, not the other mana dorks. Getting the first tier dork is most important to be able to ramp. Third tier dorks cannot ramp on turn 2 without the nut hand of Nettle Sentinel or Gaea's Cradle.

EDIT: I do want to mention that we're pretty much trying to squeeze the last 5% out of the deck. For the most part, there's a lot of variation in the last 5 cards of the deck, and hardly any of them effect the deck greatly. We can design the deck to push more early game combo (less land, more 1 drops) or for a more sustainable build (more land, more NO, more utility); or even a mix between. My stance on this archetype has always been to push it to its fundamental limit of turn 2.

[Absolutflipz]

I have a whole bunch of awesome turn 2 plays as well. The deck can certainly "belch" out its hand. It tends to do so when you're playing fewer lands too. I don't buy the argument that the deck needs 4 Birchlore Rangers, however. Let's examine our working slots:

1cc Unconditional mana (let's count DRS here for simplicity). This set ramps us into big mana (mana > turn count).

4 DRS
1 Llanowar Elves
4 "GSZ=0"

Second level mana dorks provide ways to reuse first tier dorks via untapping. They have a dependency of 1 card.

4 Quirion Ranger

Third level mana dorks include generating mana throughout the turn. These combo with Nettle Sentinel only, but provide insanely explosive turns. They have a dependency of at least 1 other card.

4 Heritage Druid
2-3 Birchlore Rangers
4 Wirewood Symbiote (not that you need an Elf and a dork (2 other cards) in order to generate mana here)

And that's pretty much 80% of the creatures in the deck. Two slots for win-con with NO (Regal Force / Craterhoof Behemoth / Terrastadon / whatever you fancy), 4 Nettle Sentinel for explosiveness, and 4 Elvish Visionary to generate card advantage. Maybe one or two utility green cards for late game interaction (Ooze, Viridian Shaman, Elvish Archdruid/Priest).

Based on the dependencies, I would first play 4 Quirion Ranger before playing more than 2 Birchlore Rangers. If you want to maximize the third tier mana generation, then by all means play 3 or 4 copies, but you have to cut from the utility slots, not the other mana dorks. Getting the first tier dork is most important to be able to ramp. Third tier dorks cannot ramp on turn 2 without the nut hand of Nettle Sentinel or Gaea's Cradle.

I agree with this for the most part. One question/comment tho.

I think counting the 4x GSZ for 0 as a mana dork is not completely telling. Yes, that play on turn 1 gives you a mana elf....however, Green Sun's Zenith is a very valuable card in the deck and often times you're really going to miss having that GSZ in your hand on turn 2, 3, etc if you had to use it for a Dryad Arbor turn 1. This is by no means saying that if you DONT use GSZ for 0 on turn 1, you definitely do...but...

By this, I think there is value in playing an additional (6 elves/4gsz), actual t1 mana Elf so that our GSZ's are not as strained (it's almost half at 4/9ths of them) on being pseudo-mana elves on turn 1, thereby allowing GSZ to be the catchall-tutor more often.

[danyul]

I agree with this for the most part. One question/comment tho.

I think counting the 4x GSZ for 0 as a mana dork is not completely telling. Yes, that play on turn 1 gives you a mana elf....however, Green Sun's Zenith is a very valuable card in the deck and often times you're really going to miss having that GSZ in your hand on turn 2, 3, etc if you had to use it for a Dryad Arbor turn 1. This is by no means saying that if you DONT use GSZ for 0 on turn 1, you definitely do...but...

By this, I think there is value in playing an additional (or 2 additional), actual t1 mana Elf so that our GSZ's are not as strained on being pseudo-mana elves on turn 1, thereby allowing GSZ to be the catchall-tutor more often.

I strongly agree here. I hate using GSZ as a mana dork but sometimes you gotta do what you gotta do. All the Maths don't factor this in necessarily, but if given the choice, I would rather play a utility guy T1 and hold the GSZ as a combo enabler or finisher or whatever you need. But I do appreciate all you smart folks doing number crunching. This shiz is interesting even for the dummies.