MTG Mana Curve Simulation for Affinity

This is an attempt to do an almost real-world Magic: The Gathering simulation but for the deck type "Affinity" or "Metalcraft". The reason is that such thing do not exists yet, and Affinity decks are the ones with more complex curve mana ever. So this is a Monte Carlo Simulation for Affinity Deck, that simulates almost a real game.

The approach is an evolution of what Guilherme Braga did with Python, but this is done in C# and does a lot more (really a lot more)

The game let you specify a deck among existing cards, and then it run a Simulation where there is no foe. Let's it. Basically it is just playing alone but following the real Magic: The Gathering rules.

Let me do an example. You Draw

• Vault of Whispers
• Sol Ring
• Frogmite

This simulation plays at first turn in this order: Vault of Whispers, Sol Ring and Frogmite.

It basically follows a Greedy strategy where it prioritize certain cards and check if it can play the cards, and then play the cards, doing all the side effects.

When playing lands, if you need blue mana tries to prioritze blue lands etc.

In example if you draw a

• Urza's Saga

Before playing it, the algorithm check if there is enough mana for it. That means there are already 2 mana in game (Sol ring countin etc.) or 1 mana in play and 1 mana that is going to be played (in hand). Then each turn Lore counter are added to Urza's Saga, and the effects take place, it can be used as land the first turn the second turn creates a Construct token, and the third turn the same before being sacrificed. In this way the Urza's Saga will be played when it is possible to create 2 construct tokens. Which is the optimal play for it. Before sacrificing Urza saga another artifact is searched (Sol Ring, Springleaf Drum or Signal Pest).

The approach I followed, is the simplest possible:

• No foe
• Mostly greedy, with some planning (for Atog and Steel Overseer)
• Just some of the cards for affinity are implemented
• I tried to avoid over-engineering the code

But despite that, the resulting code is incredibly complex

The first results

Running the simulation several times yielded this highly optimized deck that if not blocked would wind at turn 5 99,9% of times. Of course the simulation cannot keep into account "controlling" effects. But this is the starting mana curve base. The average winning turn is 5,07.

Creatures (25):

• 4 x Ornithopter
• 4 x Memnite
• 4 x Signal Pest
• 4 x Frogmite
• 2 x Steel Overseer
• 2 x Thought Monitor
• 4 x Master of Etherium
• 1 x Sojourner's Companion

Artifacts (7):

• 4 x Cranial Plating
• 2 x Springleaf Drum
• 1 x Sol Ring

Lands (28):

• 4 x Urza's Saga
• 1 x Great Furnace
• 4 x Vault of Whispers
• 3 x Mistvault Bridge
• 4 x Seat of the Synod
• 4 x Darksteel Citadel
• 4 x Glimmervoid
• 4 x Island

The improved results (Casual deck)

After tayloring the deck I taylored the strategy (mostly improving the mulligan), after that I re-runned the deck optimization and I found this one, slightly different

Creatures (25):

• 4 x Ornithopter
• 4 x Memnite
• 1 x Thought Monitor
• 4 x Master of Etherium
• 4 x Frogmite
• 4 x Signal Pest
• 4 x Steel Overseer

Artifacts (9):

• 4 x Cranial Plating
• 4 x Springleaf Drum
• 1 x Sol Ring

Lands (26):

• 4 x Urza's Saga
• 1 x Great Furnace
• 4 x Vault of Whispers
• 4 x Seat of the Synod
• 4 x Darksteel Citadel
• 4 x Glimmervoid
• 5 x Island

The Vintage Prototype

I know there should be added also Moxes but the optimizer improved the deck further by adding Tolarian Academy and Ancient tomb. There was some debate whethever the Ancient Tomb should be added to affinity. The simulation removes all the doubts: Ancient tomb makes an improvement but by a very small margin. Also note that this deck was tested with 10 millions simulations for each Card Swap (so it took 30 hours to be generated)

Creatures (28)

• 4 x Ornithopter
• 4 x Memnite
• 1 x Thought Monitor
• 3 x Sojourner's Companion
• 4 x Master of Etherium
• 4 x Frogmite
• 4 x Signal Pest
• 4 x Steel Overseer

Artifacts (10)

• 4 x Cranial Plating
• 4 x Springleaf Drum
• 1 x Sol Ring
• 1 x Lotus Petal

Lands (22)

• 4 x Urza's Saga
• 4 x Vault of Whispers
• 4 x Seat of the Synod
• 4 x Darksteel Citadel
• 1 x Island
• 1 x Tolarian Academy
• 4 x Ancient Tomb

This deck is better by a 1.2% margin over the last version With an AWT of 4,839

The sideboard consideration (for Casual deck)

Swapping out cards for sideboard, makes the deck worse. However we need the Sideboard so I tried to figure out how many cards we can swap out. Let's it: I runned the deck optimization "reversed". It swaps in place holder cards and remove the cards that makes the deck worse (but by the minimum amount possible). So here's a list of cards that can be removed with minimal impact. NOTE: you must follow strictly this order of removal:

Swapping cards for an artifact (Pithing needle, welding jar, Tormod's crypt etc.)

• 1. Remove: Glimmervoid (AWT: 4,948566666666666)
• 2. Remove: Thought Monitor (AWT: 4,9844)
• 3. Remove: Island (AWT: 5,0307)
• 4. Remove: Steel Overseer (AWT: 5,076733333333333)
• 5. Remove: Glimmervoid (AWT: 5,134333333333333)
• 6. Remove: Steel Overseer (AWT: 5,186233333333333)
• 7. Remove: Frogmite (AWT: 5,256633333333333)
• 8. Remove: Glimmervoid (AWT: 5,324666666666666)
• 9. Remove: Ornithopter (AWT: 5,3957)
• 10)Remove: Frogmite (AWT: 5,496833333333333)

Swapping cards for a non-Artifact

• 1. Remove: Glimmervoid (AWT: 4,9482333333333335)
• 2. Remove: Steel Overseer (AWT: 4,993766666666667)
• 3. Remove: Glimmervoid (AWT: 5,0376)
• 4. Remove: Frogmite (AWT: 5,0998)
• 5. Remove: Frogmite (AWT: 5,1700333333333335)
• 6. Remove: Thought Monitor (AWT: 5,239533333333333)
• 7. Remove: Vault of Whispers (AWT: 5,311366666666666)
• 8. Remove: Springleaf Drum (AWT: 5,3952333333333335)
• 9. Remove: Steel Overseer (AWT: 5,4757)
• 10)Remove: Signal Pest (AWT: 5,5757666666666665)

You should note that each card you remove, makes the deck worse (higher AWT), and the worsening becomes worse for each consecutive card removed. Also you note that the cards to be removed are different depending on the type of incoming cards. However there are common cards across the 2 lists:

• Glimmervoid
• Thought Monitor
• Steel Overseer
• Glimmervoid
• Frogmite

I did also a Excell chart to visualize the worsening of AWT by increasing amount of sideboard added cards.

Other findings

• The simulation shows that having the Lotus Petal is almost the same as not having it. The simulation shows the difference of AWT (Average Winning Turn) with lotus petal is slightly worse (~0,01).

• The simulation also shows that Thoughtcast, and Atog, are useless

• Unearth is unnecessary if you use welding jar.

• Mistvault Bridge isn't that bad, it was included in the first version of the deck, only removed in the second version

Running the Simulation

The code is c# and is pretty fast doing 1 simulation of 1 game, however to keep code as simple as possible i avoided unecessary optimizations. So LINQ is all over the place querying for card properties. In example I do not keep an artifact counter when counting Artifacts for Cranial Plating, instead I query all the cards in game everytime someone asks for the creature power.

Also when the DefaultStrategy query the game status, a duplicate of the cards is returned (to avoid accidentaly change of game status, since I'm doing speedy coding and in some place infact I modify the duplicate directly for convenience)

	public class ArtifactAddedPower : IEquippedPowerFeat
	{
		public int GetEquippedPower(Card source, IGameInteraction interaction)
		{
			return interaction.GetPlayCards().Count(x => x.Artifact);
		}
	}

The simulation basically starts from a deck, draws 7 random cards, do the mulligan if certain conditions are not met, and then starts playing card in a realistic order apparently following a good strategy.

Then the simulation is repeated 50000 times and statistics are collected. Now, there is no agreement to which statistics makes a deck better, one idea though is to count the average number of turns the decks takes to do 30 damage (yes it simulate combat phase, keeping into account equipment power, x/x creatures etc). among 50000 games. I know the foe has 20 life, but we have to simulate in some way there are defending creatures and this is a really reasonable way.

So we take as winning condition doing 30 damage and then we get statistics like

• Games won at 1 turn: 0/50000
• Games won at 2 turn: 0/50000
• Games won at 3 turn: 0/50000
• Games won at 4 turn: 4/50000

Average winning turn 6.53255

But not only that, we may want to compare 2 decks that win on average at the same turn, but compare their mana and pick the deck that spends more mana because that means more powerfull cards played (maybe cards which effects depends on what a foe does, a thing that this kind of simulation can't keep into account).

• Average mana spent at turn 1: 2.333
• Average mana spent at turn 2: 3.444

and so on.

Taylor your deck

So what is this simulation good at? Computing mana curves and veryfing hypotesis. In example, I want to verify if "Island" is better than "Mistvault Bridge". I try the 2 decks one with 4 islands and one with 4 bridges, and I run the simulation and I see the one with better average winning turn. You may want to check also all the combinations in between (in example 1 island and 3 bridges)

Another hypotesis to check is if Lotus Petal is worth adding (there are contrasting opinions on the web, the simulation will find an answer easily).

You could also implement easily Placeholder cards that do nothign but have a manacost, the game will play those if it does not find any better cards. this is to check the mana curve after N turns. It may be tremendously usefull.

Also we can make a hypotesis of "Continuity" in the cards domain. In reality I do not think the hypotesis holds, but may help you to find a "local maximum"

That means go with a starting Deck, then try replace 1 card with another one card from a try list. Do that for all the cards in the deck and for all the cards in the try list, and keeps the deck with the better average winning turn try.

Then repeat the process until there is no more improvement. This kind of stuff would require probably Hours to run

Taylor the Strategy

Once you found the optimal deck, you can play around with StrategyVariables and see how the strategy plays (with that deck). The strategy variables should also gives hints at which behavior statistically pay you better during a real match. However notes that a strategy works better with a deck, so by Tayloring your strategy it is possible there is a better deck for that strategy, that means repeat The operation:

TaylorDeck => Taylor strategy => Taylor Deck... etc.

What the simulation does not

The simulation is without an opponent, so it cannot quantify the implicit value of having cards that apply some kind of effects on enemy creatures or some kind of control, like milling or like Tormod's Crypt. Luckily the affinity deck is the kind of deck that want to play "power" and the simulation is especially good at that.

There is no way the simulation will say is good having 4 Tormod's Crypt against a Graveyard deck even if it is an obvious benefit.

however you can put some place holders cards that do nothing, and quantify how much power do you lose for having extra utility cards in the deck.

That's it, if you want to play Power mode, but have also utility cards, the Simulation will tell you how much do you lose in Power thanks to utility cards.

Which may be a great advantage anyway.

A remark, I created the code around the affinity deck. So if you want to simulate another kind of deck (i.e. a Green Aggro). You need to implement the missing cards AND implement a brand new GreenAggroStrategy class implementing IStrategy. Good Luck!

what is not implemented

The deck was designed around blue/black/red affinity prototype, so it is missing green and white mana implementation. (for now)

The deck is missing a real mana allocation strategy, which may matters for multi colored decks (actually the mana is spent in a greedy way, colored mana first). It is not a simple task doing a mana allocation strategy.

contributing

You can contribute in any way you desider and I try to keep all usefull contributions

I.E. You could implement a card (or also just request me to implement that)

Refactorin is wellcome: I'm aware the code is not a good example of software engineering but I developed it in hurry, I left a lot of "TODO" in the code that are good starting points. But the improvements are not limited to TODOs.

AS LONG AS UNIT TESTS PASSES.

The code is heavily tested, I would never accept any change that breaks any unit tests.

unit tests

Unit tests check that given some cards, those are played in a determined order, which basically verify the Strategy of card selection is working.

The unit tests are important because says the code is working, there is no way you can check manually the outcome of 50000 games.

Some tests verify the working of side effects by checking the total damage done or some cards are into play (i.e. Construct tokens from Urza's Saga)