The nature of eggs is that they are such a versatile food – a staple component in cakes and desserts, as well as in meatloaf and salads. They also make a fantastic component of sandwich fillings; from a delicious curried egg to a fried egg and bacon buttie, or scrambled eggs on toast. Pigtail and I have a bit of an ongoing kitchen battle in terms of preference for our scrambled eggs; she prefers hers on the creamier side, while I prefer mine on the firmer side.

The two aspects that control the final product when scrambling eggs are the mixture of eggs and dairy and the physical action of cooking. Finding that golden balance between allowing enough heat time to cook the eggs with balancing the type of dairy additive (milk vs. cream vs. cream cheese) can determine if you get a soggy mess or a deliciously creamy and firm covering for your toast.

What does all this have to do with Magic (apart from being a clever red herring about eggs)?

The Golden Ratio

Before you all start going and looking for Fibonacci spirals and 1.61803, I’d like to clarify that we’re not talking about the mathematical Golden Ratio , and while what I am going to talk about will enter the realms of some basic mathematics, it will focus on leads to the concepts of perpetual motion machines.

I enjoyed playing Cifka’s Second Breakfast list – once it is wound up to speed, the deck is a functional perpetual motion machine, meaning that application of the correct sequence of operations leads to a recursion of the sequence ad-infinitum, up until the point where the sequence is broken to direct the energy to apply to work outside of the recursion loop.

The Problem With Perpetual Motion

If you’ve ever studied science, you’re likely familiar with the laws of thermodynamics. For those of you who are not, or who have forgotten, here is a quick refresher:

-The first law of thermodynamics is a variation on the laws of conservation of energy. What this means is that energy and matter cannot be created or destroyed, but simply converted or changed into other forms. In Magic, this can be seen in Squirrel Nest. This card allows you to tap a land which would normally produce mana or energy and instead put a creature token into play; hence, this is an example of converting energy into mass.

The second law requires that the entropy (chaos or randomness) of an isolated system (a deck) should not decrease without being worked on by outside forces. It should increase or at the least stay the same. This is referring to inefficiency in converting input energy to an output of work. Essentially, friction kills perpetual motion machines.

Finally, the third law of thermodynamics postulates that the entropy (chaos or randomness) of a perfect crystal at absolute zero degrees should be zero. Therefore, in a perfectly ordered system with no addition of energy, there should be perfect order: no chaos, no surprises.

Magic is interesting in this way – it is an environment whereby we design decks to lower the entropy (aka the chaos) of the system; we specifically manipulate our card choices and design of our deck so that our weapons of choice can perform predictably to our desired end states. Second Breakfast is a working example of a deck that is designed to approach the third law of thermodynamics – each iteration of the deck cycles towards an increasingly perfected ordered state, culminating to form the perfect crystal; you will always draw the exact card you need and produce the perfect combination of mana to fuel the engine.

The first law applies to Magic in the sense that it involved converting card potential from the deck, through your hand, and into play. Once in play, it can convert to energy – back into more potential cards, or to resources. In a perpetual motion machine, this conversion requires that the work produced by each payment of a cost will act as the payment of the next cost ad-infinitum. Conceptually, a properly structured Magic deck containing the right combination of cards could possibly fit with the first law of thermodynamics to engender perpetual motion – a chain reaction (or, essentially, an ‘infinite combo’.)

The problem with the current card pool is that we encounter the second law of thermodynamics – efficiency.

The Friction Fraction

We all know friction – it’s a love/hate relationship. We love that the brakes work on our cars, but we hate the cost of the constant battle with it in our mechanical devices. Friction exists in Magic as well: it manifests in the form of cost exceeding the value of an effect. A relevant and fantastic example of this are the namesake cards for the Eggs archetype.

311 309 308 304 299

The Odyssey eggs are an example of mana (or energy) friction. They cost one mana and one card from hand to cast, then they cost two mana to activate. This nets a return of two mana to your mana pool and a card to hand -a net loss of one mana to friction. This wasted energy could be considered to be “converted” to potential storm count or graveyard resources if you are playing a graveyard-oriented deck, but for now, let us ignore virtual energy and resources and focus on the nature of our perpetual motion machine.

In the battle with Magical friction, a term I have adopted from Vintage cardboard slinging colleagues (who have also been known to play synergy combos) is the “Golden Ratio”. This is a ratio between the input cost of an effect and the work it produces to generate more resources for you to continue the chain. In a frictionless environment, an Odyssey egg would need a zero-mana cost to play, hence costing just the card, followed by tapping and sacrificing itself for two generic mana to produce a single card drawn to hand and two mana back to your pool.

In other words, an efficiency ratio of 1:1.

Energy is converted to matter and then matter converted back to energy – meeting the requirements of the first law of thermodynamics. This meets the requirements of the second law too, as there is no wasted energy in the conversion.  In reality, however, the design of the Odyssey eggs in an isolated system falls short of the golden ratio.

This means that with each card we play, and with every resource we spend in popping Odyssey eggs, we increase the entropy of the play state. The further below the efficiency threshold of the golden ratio, the greater our probability of failure to have the resources to proceed to the next link in the chain. Given also that Wizards of the Coast are yet to (and unlikely to ever) print a card with a converted mana cost of one that reads, “Deal 1 damage to target creature or player, add 1 mana to your pool and draw a card”, we also need to add inefficiencies into our decklists to enable a way to actually finish off the opponent. This is the nature of having to shoehorn deliberate spots of friction into the perpetual motion machine – we simply cannot reach the golden ratio of efficiency.  We can reduce natural friction by playing with the fewest artificial friction points, and we can also reduce natural friction by playing with the most optimal selection of toys, i.e. the cards that most closely skim along the edge of the golden ratio.

Let me ask you however – What would happen if we could beat the golden ratio? What if we could be more efficient than 1:1?

2 + 2 = 5

We’ve over twenty years of card design mistakes to draw upon from Wizards of the Coast. Many of the cards that are now considered mistakes were perfectly reasonable when on the drawing board. Others have since found new and surprising applications in tandem with later printings; these synergies allow the efficiency of many of our Eggs to approach the golden ratio. Imagine casting Mossfire Egg for zero mana, then paying two mana  to sacrifice it for a return of two mana and a card. You’ve pushed the Mossfire Egg into the golden ratio. Imagine now that you had Thought Reflection in play: you would now have broken the golden ratio for the Egg, as you’d be netting two cards to replace the one spent for no change in available mana.

Multiple synergies can attack on multiple axes of resource output, or they can stack to attack a single resource requirement. As an example, if you had Helm of Awakening and Etherium Sculptor in play simultaneously, then Etherium Flask becomes zero mana – play a card, then draw a card.

The Golden Ratio can be attacked on several axes – reduction in mana expenditure, increasing mana output, increasing card advantage and recursion force multiplication. The examples provided above in Helm of Awakening and Thought Reflection are great examples of static mana reduction and card advantage creation when popping an Odyssey Egg; however, while reduction in mana expenditure and increasing card advantage can get us close to the golden ratio, the only way to truly surpass it is to enhance the synergy with a force multiplier. Second Sunrise, the namesake card of Second Breakfast is an excellent force multiplier; popping only a few “eggs” in combination with a synergy enhancer allows for a massive magnification of the output of our eggs. Where before we may have played and popped three or four eggs for neutral value, now we could pop those same eggs for a greater output of cards than we invested. In that scenario, we have now broken past the golden ratio. We’ve now made perpetual motion (in cardboard form at least) possible.

Next Time

I hope you’ve all enjoyed this little segue into mechanical theory. I’ll be following up next time with the other important theory that needs to be applied to make Second Breakfast plausible in Commander. Please stay tuned, and as always, feel free to hit me up in the comments or on Twitter. For now I’ll leave you with these parting words:

“When the stars were right, They could plunge from world to world through the sky; but when the stars were wrong, They could not live.”
― H.P. Lovecraft, The Call of Cthulhu