I have tons to do this weekend, but this mana acceleration question has been interesting enough that I'm putting it off.
I don't want to get too far into the details of my simulator deck because #1 it's not Nic Fit and #2 it's much more linear but there's still a lot of crossover to be learned.
Earlier today I added a manadork to it (something similar to a Birds of Paradise) and ran 1000 game trials at everything from 18 to 30 mana with and without 4 manadorks. My system for data analysis is slow and error prone, so I'm not going to look at all 26 decks right now but instead look for some general themes. If anyone else wants to look through it, let me know and I'll see what I can do to send it to you.
Anyways, the optimal number of land in decks is interesting, I've never seen anyone other than me mention this in an article (probably because I'm the only person crazy enough to try the simulation approach) but the graph for average win turns and lands per deck is actually W shaped. It looks something like this:
http://jacobaldridge.com/wp-content/...05/w-curve.png
In practice the curve is a bit steeper on the left, and a lot less steep on the right. What this means is that the penalty in Magic for playing too few lands is very high, but the penalty for playing too many is actually rather low. How this all relates to manabases, is that the deck I'm using for these tests has found the bottom most points (fastest decks) on the curve to happen at about 22 and 27 lands. With the manadorks that shifted to 21 and 26. Which is basically saying that 21/4 is as good as 22/0.
More interesting to me though, was that a list with no manadorks was significantly faster than a list with them. Remember, I'm using a BoP though, I'm pretty sure DRS changes this because it can hit the opponent and Vet is 2 mana which also changes things a bit. I can however cross reference this with my test deck in my simulator from early this year, which went as high as wanting 28 lands and 2 mana dorks for an optimal setup despite having access to 8 manadorks and lower land count possibilities.
Basically, what this means is that lands are generally worth more than the manadork acceleration but that it doesn't hold true for DRS because DRS also hits the opponent.
Going down this road ultimately puts us in the same spot as Maverick. I've been noticing my lists keep drifting in that direction as well with KotR's, more DRS, and so on. I've yet to figure out if that's a good thing or not.
A Sol land that we could use would be huge.
Edit: Rewrote a paragraph to be more clear.
Last edited by Brael; 11-11-2016 at 06:04 PM.
Do you mean that 22/0 is faster than 22/4, or 26/0 is faster than 22/4?Originally Posted by Brael
22/0 was significantly faster than 22/4. Part of this is due to the type of deck I use for testing (a sligh/burn type thing) but the other part was that BoP just doesn't do anything. It slowed down the fastest wins and couldn't convert that mana provided (or spent) into something productive later in the game. But 26/0 was even faster than that (which is a very normal result). As I type this I actually have another set of tests running, using a BoP with haste. Haste is very under rated, and it's basically what makes BoP terrible. When you get a manadork with haste, you get Fastbond which is banned. I expect mana dorks to perform much more favorably with haste, I'm not quite sure where that gets us because we don't actually have mana dorks with haste but I suppose it's somewhere... perhaps Elvish Spirit Guide or in the enchantment build Exploration.
I'm not sure what the threshold is on doing something productive once you no longer need the mana. DRS is very clearly over that, and I would say that anecdotally Explorer is too because 2 lands early on is just so powerful. But I would probably shy away from other manadorks aside from Dryad Arbor due to the GSZ interaction.
So I think that there's a hardcap on the number of viable MB ramp cards at 14: 4 Vet, 4 DRS, 4 GSZ, 2 Phyrexian Tower.
Edit: Even with haste, generic manadorks don't outperform simply having a land. I'm unsure of an explanation as to why, it could have to do with the creatures power, it could be due to sample size (1000 is low), or it could just be down to deck strategy, or even a combination of all of the above.
Edit 2: Being less cryptic about deck speed numbers, in the batch I just ran (which I should reiterate is not Nic Fit, but still applicable for the purposes of a manabase)
22/0 had an average turn of 4.64
22/4 had an average turn of 4.68
22/4 + haste had an average turn of 4.64
26/0 had an average turn of 4.54
Edit 3: I've thought about this for the past few hours, and I think the reason mana dorks rate so poorly is that they take 3 turns to pull ahead, and they usually take your most important turns. This is fine in formats like Standard, but in Legacy the power level is so high that cards need to start producing value faster than that. This probably plays into why the opening of GSZ to DRS is a weak opening, because you need an additional turn to pay for the mana, but GSZ into Dryad Arbor is really no different than getting a CIPT land. It's productive 1 turn sooner and therefore pays for the investment one turn sooner. Though casting a DRS from your hand is superior to either.
The numbers you need are going to vary by meta and by your decks goal. My goal for example was to get the same consistency in a non blue deck, that the blue decks have. I managed to pull that off but I'm unsure if it's the best way to go about things. I was crazy enough to build a Magic playing AI using two different decks to answer some deck construction questions that can only be answered with data rather than averages and mathematics but I can't apply my system to Nic Fit because anything modal is really, really difficult to explain to a computer and GSZ is basically the epitome of that. I have some ideas to try and solve that problem but they're months away from me having the time to seriously work on it.
What I've found though is that I don't think you're asking the right questions for slots. The question we should be asking isn't how much ramp do we need, but rather do we have things to do at all possible mana outcomes. This is why I'm a big fan of optional mana sinks.
To borrow a wikipedia image
https://en.wikipedia.org/wiki/File:Binary_tree.svg
That's a tree, ignoring the numbers in that example, your first node represents your mana on turn 0. Your possible mana on turn 1 (the next ring of nodes down) can remain 0 if you played nothing, can be 1 if you made a land drop, played a non mana granting spell, or can be 2 if you made a land drop and played a DRS. Now, going into turn 2 you have the starting points of 0, 1, 2. With the possibility of a T2 land drop this becomes 0, 1, 2, 3. The question then becomes, does your deck have the right card composition such that you can reliably use either 1, 2, or 3 mana? Tireless Trackers and Coursers use up 3 well, but those cards are bad when you only have 1 mana to spend. Similarly, lots of 1's can be nice but you need to have a lot of 1 drops in order to use up 3 mana with them on T2, and if you do that you're inviting problems down the line.
So how this all relates to ramp is, what happens when you don't have your ramp cards? I'm pretty vocal on this point, because it's something of a pitfall that I think a lot of people fall into with ramp decks (in all formats). If you need 3 mana to function, you keep a 2 lander, your T1 is a DRS to get you to 3 on T2, and that DRS eats a Lightning Bolt, your entire deck has been shut down. Even when you can ramp, you need a lot of low mana ways to spend that mana, in addition to your bombs.
With a high enough curve you basically force your deck into only working reliably with Phyrexian Towers.
So to go back to your question of roles, before you ever look into ideas like card manipulation, removal, etc I think you have to build your deck skeleton around the idea of mana sources, mana sinks, and mana curve and based on finite outcomes using discrete math rather than the typical probability and averages.
-------------------------------------------------
Another edit, some random brainstorming. Has anyone ever tried Thawing Glaciers in Nic Fit? It would require a few structural changes, but it's one of those cards that dramatically shifts how many lands you need in the deck to be optimal since it's guaranteed land drops. It's also both a mana source and a mana sink.
Last edited by Brael; 11-11-2016 at 10:12 PM.
Looked at one other thing in this data set. It's late and I'm tired so I didn't mark down the probabilities of each mana outcome but I did look at 22 and 26 lands and chart the average you should expect by turn, up to turn 6 (my test data wins by then usually, so the samples get too small after that)
22
T1 - .95
T2 - 1.74
T3 - 2.36
T4 - 2.85
T5 - 3.00
T6 - 3.05
26
T1 - .99
T2 - 1.92
T3 - 2.75
T4 - 3.43
T5 - 3.90
T6 - 4.01
So hopefully that helps answer the curve question a bit. With some acceleration (like say GSZ into Arbor to function as 26 land) you'll plateau at 4 mana by T6, and without it you'll be at 3 mana. Going a bit earlier and looking at T3 which is Legacys fundamental turn you're looking at 2.36 vs 2.75 which is pretty close. The gap doesn't really get substantial in my opinion until T5. And I've noticed that I usually plateau at 5 mana, so the mana acceleration package is probably worth +1 mana to the T3+ numbers.
So basically in your curve, even with acceleration, you're looking at the typical mana development of
1-2-3-4-5-5
So if that's where the game ends (we're a bit slower than that). Filling out the curve is possible with the following combinations (capping at 7 cards, because the rest are land)
T1 - 1 (1)
T2 - 2 (1), T1+T1 (2)
T3 - 3 (1), T2+T1 (2), T1+T1+T1 (3)
T4 - 4 (1), T3+T1 (2), T2+T2 (2), T1+T1+T1+T1 (4), T2+T1+T1 (3)
T5 - 5 (1), T4+T1 (2), T3+T2 (2), T1+T1+T1+T1+T1 (5), T3+T1+T1 (3), T2+T2+T1 (3)
If you were to add all of that up, capping cards spent at 7 you get the following proportions.
T1 - 8 (36%)
T2 - 7 (32%)
T3 - 4 (18%)
T4 - 2 (9%)
T5 - 1 (5%)
Which, if you apply that to 39 cards you get
1 drops - 14
2 drops - 12-13
3 drops - 7
4 drops - 3-4
5 drops - 2
But, this comes with a few inbuilt costs, the first is that it assumes you're giving 1 GSZ slot to a 1 drop (spread the GSZ's out, I like using 1, 2, 4, 5, which averages at 3 and mirrors what I get, I rarely grab the 3 drop CA guys), and it assumes you've got atleast another 6 slots going towards acceleration on T1.
I think that it's probably the ideal curve though. Or atleast, it's the most ideal that I've been able to reason out from redoing this work now, and doing it initially when we made SE fit 8? months ago. In practice though, I run a pretty low curve version of Nic Fit and I've never been able to hit this type of curve. The trickiest part to manage I've found is the 3 drops. I'm low on 2's and high on 3's. This type of curve also tends to not be very friendly to Deed.
@Brael
You're using a Sligh type build for this testing, right?
Have you considered trying mana dorks in a list with no other 1-drops, and a curve of 2/3/4 drops? Obviously the turn will be slower but I think that might be a more accurate model of a Nic Fit deck. Might also be worth trying, say, a deck with 22 lands, 4 Birds, 4 Birds that make 2 mana, and 4 2CMC birds that make 2 mana. Then have the rest of the cards be blank (or alternatively, be Painful Truths) except for ~10 5-6 mana cards that immediately win the game - representing Deeds and finishers that immediately swing the game in our favour.
I hadn't considered it, mainly because I haven't found any 4 drops that seem sufficiently powerful enough for that sort of list. I can try something similar though. Results run at 18, 22, and 26 lands, with either 0/4 BoP, 0/4 Veteran Explorer, 0/2 Sakura-Tribe Elder, 8 Sigarda, and then the remaining slots filled with Painful Truths. The 18 land deck was only run with mana accelerants. In total there were 5 configurations.
Here's the results, 1000 games per deck:
18/10 = 11.114 turns
22/0 = 13.279 turns
22/10 = 12.228 turns
26/0 = 13.081 turns
26/10 = 13.760 turns
Mana development in the 22/0 deck was
T1 - 0.696
T2 - 1.193
T3 - 1.667
T4 - 2.083
T5 - 2.521
T6 - 2.961
T7 - 3.400
T8 - 3.803
T9 - 4.254
T10 - 4.678
T11 - 5.147
T12 - 5.626
Mana development in the 22/10 deck was
T1 - 0.991
T2 - 1.929
T3 - 2.727
T4 - 3.404
T5 - 4.015
T6 - 4.556
T7 - 5.047
T8 - 5.535
T9 - 5.986
T10 - 6.553
T11 - 7.118
T12 - 7.667
If you want anymore details on one of the decks let me know.
The mana count on the 22/0 deck is odd, but I ran the tests 3 times. I think it's an issue with mulligan code (mulligan decisions require strategy specific tuning, and I didn't get that deep into changing things, just adding card types). But accuracy should go up as the turns get deeper in, or I could shrink the sample size a bit and look at the mana growth only in games where the starting hand contained 2+ lands.
Edit: Did precisely what I just mentioned in the above paragraph. Sorry for the edits, but I tend to update this stuff a lot as I think of questions or better ways to do things and then just update my findings. This should be a more accurate mana development for the decks, though it does shrink the sample sizes considerably in the early turns.
22/0 deck
T1 - 1.000
T2 - 1.709
T3 - 2.134
T4 - 2.435
T5 - 2.752
T6 - 3.144
T7 - 3.524
T8 - 3.871
T9 - 4.272
T10 - 4.669
T11 - 5.112
T12 - 5.572
22/10 deck
T1 - 1.348
T2 - 2.185
T3 - 3.035
T4 - 3.783
T5 - 4.422
T6 - 5.018
T7 - 5.574
T8 - 6.131
T9 - 6.646
T10 - 7.209
T11 - 7.685
T12 - 8.068
Last edited by Brael; 11-12-2016 at 05:42 PM.
@Brael
Can you record fizzle numbers? Say, number of games where we don't have 3 mana available by turn 5?
See my edit. I provided some more realistic mana numbers by excluding data where there wasn't enough mana to curve properly in the early turns, basically compensating for my mulligan code seemingly not working correctly.
Under 3 mana by turn 5 is easy.
18/10 - 9.9%
22/0 - 50.1%
22/10 - 5.2%
26/0 - 33.8%
26/10 - 1.9%
Edit: Procrastinating my homework more. I don't want to make a habit of providing these types of details, not because I mind doing it but because it's a real hassle. I'm happy to provide the data for others to do it though. I always struggle with providing information like this though because I think posts which spam a bunch of numbers make for bad posts. Most people just see the numbers and tune out but I don't think graphics do it justice, not everyone is a numbers person though and there's nothing wrong with that. I've just never found a good way to convey the information.
I'm trying it this time in spreadsheet cells with percentages. The numbers are how likely you are to be at each mana outcome on a particular turn so that you can figure out your curve. I think this is a better way to do things than looking at averages. Though it takes longer to compile the information.
http://imgur.com/a/r3V6Q
The ranges in green are probably what you want to shoot for with a curve to operate on
Last edited by Brael; 11-12-2016 at 08:39 PM.
OMG so much awesomeness. Can't pull myself away from The Witcher 3 at the moment, but I'll start pitching in tomorrow.
Some great stuff guys!
Brael, would you be interested in in sharing your code? I'd love to have a look at it.
Sure, but I should warn you it's pretty messy (cleaning it up is one of my projects scheduled with it for winter break when I have some time)
If you run it (it's in Python 3) I would suggest running it on a ramdrive, my database updates are very time consuming and a regular hard drive is too slow to do it well (what takes 20 min on a ramdrive takes 6 hours on my hd, also a project for winter break).
Here's the code, it will remain available for a week, just ask if you have questions on it.
http://pastebin.com/U090D2yW
Thanks! Python isn't the language I'm most used to, but I'll have a dig around.
@Brael
The code you sent me never adds copies of Sigarda to the deck? She isn't listed in BuildDeck().
Hmm, you're right. That's quite a bug (and a good example of why I need to revamp that whole system to just use one list come break time), it shouldn't impact the mana development I posted before though which is the part I was concerned with. One other error you'll find is that if you inspect the database, you will see something odd with Truths/Sigarda though, my columns on Sigarda/Painful Truths have their names flipped.
Ran a set with the Sigarda thing fixed, 26/10 was the fastest deck, by far. But that probably makes sense considering you can't really impact the clock until 5 mana, so the faster you reach that the faster you win.
Wouldn't it make the mana development a bit faster since there are less non-mana cards in the deck?
It makes it a little slower since the decks were x mana/52 cards instead of x/60 but it's not a substantial impact, similar to what you get if you removed the mana dorks. So 22/10 is going to be about what you saw with 22/0 before (maybe this is a good way to express the issue of going over 60 too...)
I just ran another set with the Sigarda thing fixed. The previous post had their average win turns, here's the average mana development.
22/10
T1 - 1.295
T2 - 2.095
T3 - 2.890
T4 - 3.572
T5 - 4.096
T6 - 4.586
T7 - 4.949
T8 - 5.128
T9 - 5.157
T10 - 5.361
T11 - 5.583
T12 - 5.746
26/10
T1 - 1.317
T2 - 2.122
T3 - 3.011
T4 - 3.817
T5 - 4.512
T6 - 5.108
T7 - 5.572
T8 - 5.774
T9 - 5.931
T10 - 6.271
T11 - 6.552
T12 - 7.089
I'll be posting my report to reddit like tomorrow (and linking to it from here) but I just wanted you guys to know, went 4-3 at the Legacy Classic in Columbus today with Sneak Fit. Ended up directly in 32nd.
Deck feels like hot fire. I'm in love.
Was trying out Abzan Fit, absolutely crushed all fair matchups but died miserably to OmniTell & TES
16 creatures
2 DRS
3 Veteran Explorer
1 Qasali Pridemage
1 Scavenging Ooze
1 Tireless Tracker
1 Courser of Kruphix
1 Eternal Witness
1 Meren of Clan Nel Toth
2 Siege Rhino
1 Sigarda, Host of Herons
1 Thragtusk
1 Dragonlord Dromoka
1 planeswalker
1 Nissa, Vital Force
21 spells
3 Path to Exile
4 Cabal Therapy
4 GSZ
3 Sensei Divining Top
2 Abrupt Decay
1 Maelstrom Pulse
1 Painful Truths
3 Pernicious Deed
22 lands
4 Verdant Catacombs
2 Windswept Heath
1 Marsh Flats
3 Bayou
1 Scrubland
1 Savannah
2 Plains
2 Swamp
3 Forest
1 Dryad Abor
1 Phyrexian Tower
1 Volrath's Stronghold
SB
1 Ob Nixilis
1 Garruk Relentless
3 Surgical Extraction
1 Reclamation Sage
2 Thoughtseize
2 Carpet of Flowers
1 To the Slaughter
1 Gaddock Tegg
2 Thalia, Guardian of Thraben
1 Golgari Charm
My MB is a little skewed as I expected a load of Reanimator, Dark Depths based decks, UR Delver & Eldrazi. Completely trashed them with Nissa + Dromoka sealing the deal extremely quick.
SB wise I love the walkers and really really wanna add another Nissa, Vital Force in the 75. Ironically Ob Nixilis did a lot of work as a swiss army knife, killing big fatties like Oblivion Sower & Kotr while also clocking Miracles with his ultimate (they cant really remove walkers outside of Council Judgement)
I hate the Thalias, they did not do much vs matchups where it mattered even when coming down on T2 when I am on the play. Will change into other forms of combo hate. Thing is not really sure which combo hate to use.
@fireiced: Ethersworn Canonist is a pretty good hatebear.
A few other things I've noticed in your code:
- You mulligan to 3 if no creatures - I imagine this skews things when you're running the number of noncreature cards the current test has. Particularly the 22/0 and 26/0 decks, which have only Sigarda for creatures.
- You also bin lands and keep nonlands when scrying, which I imagine reduces the expected odds by a bit.
- If I'm reading it right, the ai will prioritize casting Painful Truths over making mana guys because it values drawing cards more than making late creatures. That'll mean that sometimes you'll have 3 mana t3 and would have 5 mana t5, but if you spend turn 3 casting Truths over Veteran (with pays out t5) and turn 4 casting truths + veteran (paying out t6) over STE, you won't hit when you would have otherwise. Incidentally this would also make the clock a lot slower since the deck won't cast Sigarda unless it has zero copies of Painful Truths left in hand. This might mean that your 'game ends' numbers are actually the point at which the active player casts their seventh Painful Truths and dies, actually. This is supported by your average win numbers for some of the decks - for example, your 18/10 deck had an average end of turn 11, which would require your first attack with Sigarda to be on turn 7, but the deck doesn't expect five mana until after turn six.
- Painful truths is evaluated for play priority as if it draws 3, but doesn't actually draw cards in its additionalplay() script.
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