EDIT: And, we can use one of those slots right away - replace Overgrown Tomb and Lifetap with Thawing Glaciers, Island, and Thoughtleech. (Island/Thoughtleech is better than Forest/Lifetap, since we can use the Island in the opening hand.)

EDIT #4: Instead, we can replace Farsight Mask with Unfulfilled Desires into Waste Not into [/c]Consecrated Sphinx[/c], again replacing Mortiphobia with Screams of the Damned and Voidmage Husher. We need to add Stunted Growth or something similar to keep the opponent's library replenished, so we wind up using four extra cards. I'm not sure whether Insurrection or Thought Reflection is needed to get started; for the moment I will stick with Finest Hour.

The Thawing Glaciers and Mighty Emergence changes seem mostly fine to me. One extra layer The only problem there is that Thoughtleech is a may, so our opponent won't choose to gain the life. Lifetap works, though with just a slightly worse start as the cost.

I think Dual Nature at least causes problems with Sharuum the Hegemon. The etb of free copies would go infinite. There might be other pitfalls with that card.

Consecrated Sphinx seems to lead to an infinite where we donate a sphinx, keep one for us and then just have them trigger each other. Usually that would be limited by one of the libraries, but here we are trying to have just our life as the limiting factor. Doesn't seem to work out.

EDIT: The original reason to get rid of Dual Nature:

Kaho is legendary, so after the boardclear we can cast counte return him, get a dual nature token and have the original die to the legendary rule. Then we can make a hasty copy with mimic vat and return the original to the hand. All without spending any triggers that need to be on the stack under Devastation..

I don't think I agree with the quote that with Dual Nature, we can get the combo started after a board clear without using any resources below the Obliterate marker. We have no hasted Gelectrodes, and we can't use any of the Gelectrode triggers to create one. The quote says we can return the original Kaho back to our hand, but we have no way to bounce it. So unless I am missing something, we do need to use some the stack to reset the stage even with Dual Nature.

However, Dual Nature with Sharuum the Hegemon is certainly a problem. Since Dual Nature saves two cards, if we could replace Sharuum with no more than two cards we would make a profit. Perhaps Grinding Station could be replaced as well; but I'm not seeing a fix at the moment.

Another problem for Unfulfilled Desires is that the opponent can use that (donated) to draw instead of waiting for us to discard. Life for them is available at that stage.

But that also requires a discard, and we can no longer bring cards from the opponent's graveyard back to his library (Mortiphobia is gone).

EDIT: Now that I think about it, the original reasoning for needing Kaho, Minamo Historian (to insure that we used resources from below the Obliterate marker) no longer seems to apply. So, we could theoretically replace the Spellweaver Helix / Spellshift / Kaho, Minamo Historian engine with something more efficient. Something that lets us fetch and cast an instant or sorcery from our library for reasonably cheap (or maybe for a colored mana, and we could make exiling a card in our graveyard cheap.).

Does Angel's Grace work with Pain Magnification? It reads to me as if it replaces the 3 damage effect on us with no damage if we are already on 1, not triggering the donated Pain Magnifications.

Should that chain work somehow we can't take advantage of Mighty Emergence and the second Precursor Golem layer at the same time, since we are not able to change the target of a Fire Covenant copy to creature with a fresh toughness boost at the right time. I did not count the layers to see if you accounted for that, just thought I'd mention it

Heh, yeah I did count the second Precursor Golem layer and the Mighty Emergence layer, I keep doing that. So yeah, down to 19 layers, or a tie. However, we can now remove Mighty Emergence, giving us one more card slot than the previous sequence, and also life gain is higher up in layers, so we can make greater use of our starting 20 life. So I believe the latest sequence is the best, at least at the moment.

Angel's Grace does work with Pain Magnification; the damage is not prevented, Angel's Grace just resets our life total to 1.

EDIT: Whoops - Among the 19 layers for the latest sequence, I counted a layer for Alhammarret's Archive on Curse of the Forsaken, but it looks like we can't. Although Angel's Grace prevents the damage from Spiteful Shadows and Backfire from killing us, it doesn't prevent them from eating away at our damage, so we can't afford to pay for further castings of Fire Covenant. Of course, we could cast a bunch of Fire Covenants right after we gain the life, but that doesn't result in another layer. So, back to 18 layers, or less than the previous sequence.

Okay, in that case there is another infinite: With the Angel's Grace effect on we donate Gelectrode and Night Dealings while the Gelectrode ability targeting us is on the stack. Then we take Night Dealings back and use the free-ish counters.

I think we can fix that by switching Opalescence with Starfield of Nyx, so that we can't take Enchantments back.

EDIT: No, we can make multiple Starfield of Nyxes, and then donate at least one to the opponent. Oh well. The previous sequence is currently better anyway.

EDIT: I've been looking to replace Sharuum the Hegemon, but with no real success. We could replace it with say Arcbound Reclaimer and Neurok Familiar, but that uses up a card slot that we can't afford to spare. Saprazzan Bailiff unfortunately can return enchantment cards as well, including Elvish Guidance. Sanctum Gargoyle, Junk Diver, and Myr Retriever fill much the same role that Sharuum does. Treasure Hunter seems like it would fit the bill, but it's unfortunately white. Roo****er Diver seems to be too expensive to work. You'd think there would be something like Treasure Hunter in red or blue, but I can't find anything like that.

But, perhaps Sharuum isn't so bad. We can't use it to create lots of Sharuum tokens, because they get destroyed from Dual Nature when Sharuum leaves the battlefield. We could do shenanigans with Dual Nature and Sharuum to make more tokens, but that requires bouncing them, so it's not free. So the only thing we can do infinitely is shuffling artifacts back and forth from the graveyard to the battlefield and back, and the only thing that produces is colorless mana. The only thing that messes up with is Sylvan Offering (Distorting Wake doesn't benefit from overspending). We can replace it with say Hunted Phantasm, and then replace Elvish Guidance with Dawn's Reflection, for example. That could complicate the start, but hopefully we still have enough.

EDIT: It just occurred to me, that instead of using Gelectrode, we could get the untapping effect from the resolution of a spell instead, like Insurrection. So for example, we could have three World at Wars, and imprint a World at War and Obliterate on one Spellweaver Helix, and imprint a second World at War and Insurrection on a second Spellweaver Helix. Then when we cast a World at War, we put an Obliterate on the stack, and then an Insurrection on top of it; the Insurrection untaps the token copies of whatever we're using as the hyperstage creature, with the Obliterate lurking on the stack below. This change allows us to use a blue or artifact creature as the hyperstage creature, so we could conceivably get a third stage on top.

Should we consider going for more? This last idea allows us to get rid of Gelectrode, and I think the general notion of untapping as our stage transition benefit allows us to get rid of Kaho, Minamo Historian as well. So, is it possible perhaps that we could handle the hyperstage using something more limited like artifacts, allowing huge amounts of design space for further stages? Or possibly another hyperstage, or a hyperhyperstage? We could repace Obliterate with something that destroys lands and artifacts but not creatures, saving Obliterate for later. (The only thing I can find by a quick search is Wave of Vitriol, which unfortunately destroys enchantments as well, but it could be worked around - we could use colorless mana to build our enchantments back up.)

Before we get ahead of ourselves, the first step is to set up the hyperstage using something limited like artifacts. Of course we can use Rust Tick as the targeter, but we need some way to cast and recycle instants or sorceries at the cost of a resource. Colored mana is the obvious first thought, but now it could also be a nonartifact creature of some kind - there's got to be something out there that works.

What do you think?

EDIT: I think I have one way to make it work: Use Bosium Strip so that we can cast spells from our graveyard, and then have three of the same sorcery card using one mana of whatever color we desire. Insurrection can be replaced by Blinkmoth Infusion. We can replace Obliterate with Wave of Vitriol, but I think it would be allowable to keep Obliterate if we so desired; destroying all creatures doesn't help us since all the Mimic Vats get destroyed at the same time. And it doesn't necessarily hurt the higher stages, since we only go to a lower stage when all our hasted token copies are tapped and no longer used. But please verify that if you can.

Oh wow, getting that many stages after a hyperstage is awesome! I'm still thinking about dangerous infinites with the triple sorcery method of untapping, but so far it seems to be fine.

Doesn't Obliterate interfere with using the creature for the stages? Or do we convert them all into triggers on the stack anyway, whenever we are obliterating?

Hmm, I thought it was okay at first, but I'm not completely sure. One thing we don't have to worry about is losing untapped hasted tokens, since we always process a stage until all the tokens are tapped anyway, and the tapped tokens can just die. The only thing that worries me is the placement of the original creature. If we just leave it on the battlefield, it will be destroyed by an Obliterate, and when you get back to that stage you can't target it with any of the remaining Psychic Battle triggers. So we do want to target it first.

I think the following will work: Target the original creature with one of the Psychic Battle triggers; it dies, and triggers Mimic Vat. Go ahead and imprint it, and then activate the Mimic Vat. Respond to the activation by processing the next stage down. The Mimic Vat will get destroyed later, but the activated ability will still resolve, so long as the original creature remains exiled. I *think* that should work.

Exile all 3 Simian Spirit Guides, Cast Faithless Looting, drawing and discarding, Channel, and Rite of Flame. Cast Rite of Flame from hand and cast Mizzix's Mastery targeting Channel. Cast Channel. Cast Lich's Mirror. Add 15 colourless mana to your mana pool and then use the Lich's Mirror replacement effect to shuffle in and draw 7 cards that will contain the Lich's Mirror and Lion’s Eye Diamond. This is not an infinite loop; it is an indeterminate loop that could happen in a real game, but is statistically unlikely. Given the rules for this challenge allow me the favour of fate, I am going to get Lich's Mirror and Lion’s Eye Diamond in every hand and net 15 colourless mana on each iteration and 3 mana of a colour of my choosing. This is how I will be casting all of the spells from here on out. I did start to count the number of iterations required but it became tedious when I realised how big the other numbers in this post are.

Approximately 2^^20 Doubling Seasons with the third, and 2^^^20 with the fourth. From about here onward we are just going to round to the nearest relevant figure/term.

Now tap a Mimic Vat making 2^(4)20 Boon Reflections and then destroy the other non-artifact creatures putting them under Mimic Vats. Also cast and destroy the Furnace of Rath putting it under Mimic Vats.

Now tap the Mimc Vat with Elite Arcanist under it creating 2^(4)20 Elite Arcanists Imprinting 4x Blinkmoth Infusion and 4x Second Harvest. Tap each of your remaining Mimic Vats and Prototype Portals making a great many things. Use Elite Arcanist with a Blinkmoth Infusion under it to untap all of my artifacts. Make 2^(7)20 Doubling Seasons. Rinse and repeat this process three more times ending with 2^(19)20 Doubling Seasons and (very loosely) somewhere in the vicinity of 2^(20)20 everything else. Now activate an Elite Arcanist with a Second Harvest under it. This is going to do something a bit different, see before we were trying to put one Doubling Season into play from the Mimic Vat but now we are trying to put one Doubling Season into play for each Doubling Season token we have. We now have 2^(2^(20)20)20 Doubling Seasons in play. Now with the additional Mimic Vats we are going to Despotic Sceptre our the rest of our non-token creatures including the original Doubling Seasons and make additional copies of those along the way. Let’s do that again three more times

We are now going to start using f n to describe the number we are at, where f 1 is 2^(20)20 and each consecutive f n will have a number of ^ equal to the previous term.

This brings us to f 5 Doubling Seasons. Now we are going to let those other Prototype Portal abilities resolve.

Unfortunately, I am now out of mana from my lucky loops of Channel & Mirror. Play Gaea's Cradle.

Attack with my Legion putting 4(f 5) Copperhorn Scout triggers on the stack. Crack 2 LEDs and 1 Lifespark Spellbomb to draw and cast the Harmless Offering. Giving my opponent a now tapped Platinum Angel Token.

For each Copperhorn Scout Trigger I will be activating the Elite Arcanists thereby increasing the number of tokens of each type I have by f 4. How many times will I be doing that? Why 4(f 5) of course. So we are going to end up with f (1+16 (f 5)) tokens.

No blocks?

How much damage is my opponent going to take? Well my relatively small number of creatures are each getting +X/+X where X is the number of creatures I control. Each Ancient Ooze equipped with a Cranial Plating gets +1/+0 for each of artifact I have (remember those 3(f 6) Prototype Portals). Each of My Ancient Oozes are */* where * equals the total CMC of all creatures I have in play. But probably most importantly I have f 5 Furnace of Raths in play. Each of my f 5 Ancient Oozes with a multiple of f 6 base power, equipped with + f 6/+0 platings will be dealing damage that is doubled f 5 times.

This comes out at something like this ((cf 5)^3 + 3(f 6)) (where c is the number of different types of creatures I have is). This number is not particularly relevant because, in the grand scheme of these monstrous numbers we are reaching, this might as well be simplified to f 6. Even when you take in to account that each of the f 5 attacking Omnaths will each be gaining (f 5)^2 power thanks to the Sakikos, the doubling or even squaring of a number doesn’t actually increase the number by enough to warrant noting it at this point. The amount of damage they deal with Double Strike will then be multiplied by f 6 and finally we will gain f 7 life.

We do need to leave some mana in our pool for our next combat step when we hit our opponent again fortunately that mana is less than the amount our Gaea’s Cradle generates when it is tapped once.

We can Channel away our f 7 life to cast an Orochi Hatchery which will come into play with (f 7/2) x 2^f (1+ (16 (f 5)) counters on it and will make… such a silly number of creatures.

This number continues going up absurdly and the deck can obviously be built in a way to optimise the absurdity, I chose to include cool cards. The end result is a board state you couldn’t map if you used quarks as cards on a table the size of the known universe. There are currently no notations that can quantify the final number. This is the biggest number used for a practical application to date; bigger even than TREE(50). After attacking on the last combat step, I will Despotic Scepter my Opalescence, crack an LED and a spellbomb to draw and cast Soulblast which will deal an amount of damage equal to the amount of damage I have already dealt multiplied by 2 to the power of the amount of damage I have already dealt.

I think I win the challenge. My apologies Mr. Graham.

NOTE: My formatting may not have copied over very well. I will try to update any errors.

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"He who is skillful in winning against the enemy does not wrestle with him" - Lao Tzu

"All Warfare is deception" -Sun Tzu

"Magic is just another form of Warfare" - Anonymous

Approximately 2^^20 Doubling Seasons with the third, and 2^^^20 with the fourth. From about here onward we are just going to round to the nearest relevant figure/term.

The math with Knuth up-arrows doesn't work out that way. the third mimic vat will put 2^(2^20) doubling seasons into play. The fourth will then put 2^(2^(2^20) into play. the n-th will put 2^(2^(...(2^20)...)) with n-1 ^s. Knuth up-arrow notation then writes that as 2^^n or thereabout (the 20 makes it not fit nicely, but we are rounding a lot here anyway).

Getting more arrows is somewhat harder. The function f you used later seems more likely to correspond to up-arrows but I didn't check if that works out correctly.

And while your Lichs Mirror+Channel combo can not be used for arbitrary amounts of mana in a game by declaring it as a loop we can still play it out as long as we want. By playing it out arbitrarily long we can later reach arbitrary amounts of damage. The non-repetitive parts of most combos here take longer than the lifespan of the universe to play out anyway, so we can't say we don't have the time. So for the purpose of the challenge here this counts as an infinite loop and disqualifies the deck. But that part seems to just be for the setup, so you can probably find replacements if you want to work on the deck some more

Thank you for your contribution, GodAmongEquals! I notice that you joined on 1/31/2006 and this is your first post.

Iijil is right about the error with Knuth arrows, and also the Lich's Mirror + Channel combo. Although it may be statistically unlikely for you to draw and be able to play Lich's Mirror many times, you are already doing that in your combo, so you can't really draw a line and say "I can only repeat it THIS many times, and then it becomes unreasonable". In any case, the rules of the challenge state that the outcome of chance events always work out in your favor, so you can obtain arbitrary amounts of damage (by creating arbitrary amounts of colorless mana and casting Orochi Hatchery, say).

To illustrate the correct use of Knuth arrows:

After the second Mimic Vat activation adding a Phantasmal Image token, you wind up with 2^20 + 20 Doubling Seasons, or more than 2^^4. After the third, you get more than 2^2^20, or more than 2^^5. After the fourth, more than 2^^6. Then you cast Blinkmoth Infusion, which allows you to add a Phantasmal Image token four more times, which gets you to 2^^10. Repeat the process three more times for more than 2^^22. Then you cast Second Harvest. Now, the key point here is that all the new tokens come onto the battlefield at the same time. In particular, you don't add one of the Doubling Season tokens first, increasing to 2^^23, then add a second Doubling Season token, increasing to 2^^24, and so on; all the new tokens come onto the battlefield at the same time, so all are multiplied by the same number 2^^23. So we wind up with more than (2^^23)*(2^22) Doubling Seasons, which is essentially 2^^23. You then can get four Mimic Vats imprinted with Doubling Seasons, which increases your number of Doubling Seasons to 2^^27. Then you cast Second Harvest three more times, which brings you up to 2^^30.

So the number of Doubling Seasons you have at that point is between 2^^30 and 2^^31, not f 5.

Attacking with Copperhorn Scout allows you to exponentiate several times for each trigger, so that brings you to more than 2^^(2^^31).

2^20 is the first step. 2^(2^20) is the second. 2^^20 is strangely equal to 2^(2^20). 2^(2^(2^20) is the third step. Which means you are raising 2 to the power of 2^^20 which is strangely like raising 2 to the power of itself 2^20 times or as it is sometimes written 2^^^20. Forgive my sass. Knuth-up arrow writes it as m^^n when it is the number to the power of itself n times. 2^(2^20) is the same as 2^1048576 which is the same as 2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2 which is the same as 2^^20. When you try to put 1 Doubling Season in play you will end up putting a number into play equal to 2^x where X is the number of doubling seasons already in play.

Correct me if I went wrong somewhere.

Someone pointed out to me that if you Mirrorweave the Hatchery tokens after phasing each of the relevant Elite Arcanists out you make the number less difficult to round and also increase it faster.

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"Magic is just another form of Warfare" - Anonymous

You seem to resolve the exponentiation in 2^2^2^...^2 from left to right, but right to left is the correct way. (as in compatible with what everyone else is talking about in the context of Knuth up-arrows)

2^^20 = 2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^2)))))))))))))))))). That's 20 2's on the right hand side. I explicitly wrote the brackets here so the order of operation is clear.

In comparison 2^(2^20) is bigger than 2^(2^16) = 2^(2^(2^(2^2))) = 2^^5 but a lot smaller than 2^(2^65536) = 2^(2^(2^(2^(2^2)))) = 2^^6.

If you pile up multiple copies of that, it makes all the triggers go on the stack at once, which is unfortunate because it really inhibits its ability to affect the growth rate meaningfully. Furthermore, if the design is built around a series of "you can't be allowed to get this effect more than once per instance you recur a particular card", it's not even safe, same as a card like Rings of Brighthearth would be. But it is the most fascinating new engine part they've released in quite a while.

That's a very interesting card, but it doesn't seem like it would fit into any of our current or previous decks. It wouldn't help with with any card with a trigger like "Whenever a creature enters the battlefield...", because instead of getting X triggers you would get X(Y+1) triggers put on the stack at about the same time, before you had the chance to do anything. So the effect would just be multiplicative. If you had a card that said "Whenever this creature enters the battlefield...", that _would_ receive a noticeable benefit from having Panharmonicons. But that combo wouldn't be very efficient in our old layer decks, and in our new decks, by the time you get to adding layers, ETB for creatures and artifacts have already been mooted. So sadly, doesn't look like this card can help us.

Each time I try and put a Doubling Season in play I will be adding 2^n where n is the current number of Doubling Seasons I have. I can afford to destroy and vat three Doubling Seasons before I channel myself to 0. The first one will create 2^8 Doubling Seasons and the second will attempt to add a further 2^(2^8) or 2^256 or 2^^5. Each additional Doubling Season that I try and put in play will add 2^n thus increasing the number by 1 after the ^^ such that 2^^5 becomes 2^^6 and so on.

I destroy my Boon Reflection and then make 2^^7 copies putting it under a vat and then sac my Children of Korlis which will gain me 20(2^^7) life. I now have enough colourless mana to continue operating Vats, Portals, and Elite Arcanists.

The first step here is to create as many Braids of Fire and Paradox Hazes as I can before I move to my second upkeep. Using one Elite Arcanist with a Second Harvest under it and equipped with 2^^14 Illusionist's Bracers I can attempt to put 2^^14 Doubling Seasons in play. Whenever I try and put 1 Doubling Season in to play I instead put 2^n where n is the current number so when I try and put a number of Doubling Seasons in to play equal to n I instead put 2n^n or (2(2^^14))^(2^^14). Let's simplify this down and say that it is 2^^2^(2^^2) because each Illusionist's Bracers trigger is separate we repeat this process for each Bracers. So 2^^2^(2^^2)... which ends at 2^^(2^^2) or 2^^^2. Each iteration will then grow by 1 ^ such that we end with a number bigger than 2^(6)2. If we have been exiling our Elvish Spirit Guide along the way, Shuffling it back in with Riftsweeper, and drawing it with Puresteel Paladin we also have GGGGGG floating which we can use to activate one of our many Rhys, the Redeemed to increase by 3 more arrows but that will also net GGG and so on such that we end with G in our pool and 2^(11)2. If we then create Paradox Hazes and Braids of Fire' we will have 4(2^(2^(11)2)) Paradox Hazes and four time that many Braids of Fire which will give us 2(sum of the numbers 1 to (2^(2^(11)2))) combat steps. We'll call this number C.

In order for our opponent to not die we have to Donate one of our tapped Platinum Angels before the first damage step.

The 2^(11)2 Sword of Feast and Famine Triggers will allow us to all of our current Rhys, the Redeemed for each trigger, which can each be equipped with an equal number of Illusionary Masks that will continue our pattern. Each Rhys, the Redeemed activation will attempt to put n^n tokens into play but we have n triggers. So our first will raise n^n the second will raise (n^n)^(n^n) and so on. Resulting in an n step process whereby we raise n to the power of itself and then raise that number to the power of itself. We can also write this as n^^^n each step of this process will then be repeating this thereby raising the number of arrows in our solution by ^ for each step. Given that we are activating n Rhys this will result in n^(n)n. When our creatures deal damage for the second time thanks to Double Strike we will get to repeat this process starting with n^(n)n there by getting to a stage of n^(n^(n)n)n. Here is where we introduce f. For each combat phase we will be increasing our term number of f by 2, with term f (1) being n^(n)n and f (2) being n^(n^(n)n)n. If this were all that were happening we would end up at f (c), but we also have Sakikos to contend with.

To work out how much green mana we get from Sakiko, we need to work out how much combat damage we are dealing each combat damage step. Let's start with how much life we have. Let's assume we have spent all of our life as colourless mana so far. After dealing damage we are going to have f (1) Boon Reflections and an equal number of Children of Korlis. If we sac one Child we will gain the life we have lost so far multiplied by 2 to the power of the number of doubling seasons we have, let's round that to 2^f (1). We can then repeat this process by Channeling down to zero whereby we will then attempt to gain 2^f (1) life, again after multiplying it by 2^f (1). Repeating this Process f (1) times will give us ((2^f (1))^f (1)). To measure the sum of our total life gain we will be adding the sum of the set 2^f (1)^1... ((2^f (1))^f (1)). This is the power of each of our Ageless Entities. Because each of these will then deal damage and add mana to our mana pool equal to the damage they deal (which is increased by the Furnace of Rath's but not by a relevant amount in terms of the rounding we are doing). It means that the number of times we can activate our Rhys each combat step is actually going to be equal to the f of our previous combat step. So when we arrive in our second main phase we have f (f (1)) rather than just f (2). At the end of all our combat steps we will have f (f (f (f ( ... where there are c function of functions in our chain. Our total damage is somewhere beyond that.

First off, if you're on the play turn 1, there is absolutely no way to make use of Paradox Haze or Braid of Fire: anything you can do to get them onto the battlefield must have happened after you missed the deadline for them to trigger.

Because Braid of Fire ends up being useless, Aggravated Assault is also useless, but it's an extremely dangerous card to look out for in any case: even a simple Tormod's Crypt would give you the freedom to imprint Black Lotus on Prototype Portal before copying the tokens, and that's way too good.

2^^(2^^2) is 2^^^3 (because there are three instances of 2), not 2^^^2. You really don't want to get stuck on 2^^^^(...anything...)^^^2, because that number reduces to simply 4.

One iteration of something like Elite Arcanist doesn't "add an arrow", it adds one to the number at the end of the arrows. Building off the previous example, 2^^(2^^(2^^2)) is 2^^^4, not 2^^^^2. Any expression you build using iterated ^^ operators will be simplified in terms of ^^^, exactly one arrow beyond the iterated one. To get to ^^^^, you have to be able to iterate an even larger process, one on the power of ^^^ to begin with. And so on: in order to add more arrows, you have to keep finding larger loops which can be dynamically repeated a number of times commensurate with the output value of your sub-loops, with each loop you can manage to wrap around the rest being worth just one extra arrow.

I can't help but think there's actually potential in Lich's Mirror. The ability simultaneously refuels a bunch of resources off a trigger that can be tied to other things pretty easily, I can't help but think it can be used the same way as Obliterate on the Helix. The trick would be making sure that it doesn't just reset everything (the way it's intended) so progress would need to be stored in spells on the stack or permanents you don't own or floating mana or storm count or some such thing, and then to not be infinite, the process would necessarily involve something that won't reset with it, so like a chancellor that only triggers at the start of turn or something that otherwise triggers at the start of a phase or a card that exiles itself when it resolves.

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Zedruu: "This deck is not only able to go crazy - it also needs to do so."

tstorm823: Hmm, I dunno about Lich's Mirror. As you've pointed out, the problem is making progress without going infinite. Using up a start of turn or phase trigger would likely mean that we can only use the Lich's Mirror a few times. In our latest decks, we've needed to be able to bring back exiled cards for the hyperstage (although we do have combos that can enact a stage without bringing back any cards from exile, for example using cards like Skirge Familiar to generate mana), so we can't use exiling as a one-way ticket anymore. If we can, that's still only a small number of repititions of Lich's Mirror. So it would have to have each Lich's Mirror be very powerful to set a record (Each one would need to be worth a new hyperstage, or maybe an activation of a hyperhyperstage for example.).

GodAmongEquals: I'd like to go over your math, so for the moment I'm going to assume that your deck can do everything you say it does without checking it particularly carefully (Although, as SadisticMystic points out you can't actually generate any mana from Paradox Haze / Braid of Fire to pay for Aggravated Assault.). I'm not sure how you get up to 2^^14 Illusionist's Bracers, but let's assume you have that many Bracers and 2^^13 Doubling Seasons. The first time you resolve a Second Harvest spell, attempt to add 2^^13 Doubling Seasons, and each one gets replaced with 2^(2^^13) = 2^^14 Doubling Seasons, so you get (2^^13)(2^^14) ~ 2^^14 Doubling Seasons. Then the next Second Harvest will increase it to 2^^15, then to 2^^16, and so on. So after 2^^14 Second Harvest spells, you will get to 2^^(2^^14) Doubling Seasons total. If you then generate 2^^(2^^14) Illusionist's Bracers, and attach them to a second Elite Arcanist imprinted with Second Harvest, you will then pump the number of Doubling Seasons up to 2^^(2^^(2^^14)). After four Elite Arcanists you will therefore have about 2^^(2^^(2^^(2^^(2^^14)))) Doubling Seasons, or between 2^^^7 and 2^^^8 Doubling Seasons. Each Rhys the Redeemed activation (while equipped with an updated number of Illusionst's Bracers of course) will do the same thing, so after five Rhys activations you will get more than 2^^^12 Doubling Seasons. Then, Serra's Sanctum will allow for about 2^^^12 more Rhys activations, bringing the number of Doubling Seasons up to 2^^^(2^^^12). Ignoring Sakiko for the moment, each Sword of Feast and Famine will allow you to untap Serra's Sanctum and therefore take X Doubling Seasons to 2^^^X, so if you equip a creature with 2^^^(2^^^12) Swords of Feast and Famine and deal combat damage with it, that will allow you to pump the number of Doubling seasons up to 2^^^^(2^^^(2^^^12)). Each subsequent combat damage will allow you to take X Doubling Seasons to 2^^^^X, so after N combat damage steps you will be able to generate roughly 2^^^^^N Doubling Seasons, so this would be a "five-arrow deck".

Next, let's address Sakiko. Say you have X Boon Reflections and Y Children of Korlises, and have lost Z life after channeling all your life away. Sacrificing one Children of Korlis will add Z*2^X life to you life total, which you can then convert to mana. Then the second Children of Korlis will add (Z*2^X)*2^X = Z*2^(2X) life. So sacrificing Y Children of Korlis will result in Z*2^(XY) life. Note that, while this is ostensibly larger than X and Y, puny operations like exponentiation aren't going to make a dent in large Knuth arrow numbers. So for example, if you have roughly 2^^^(2^^^12) Boon Reflections and 2^^^(2^^^12) Children of Korlises, you're not going to get anywhere close to 2^^^(2^^^13) life, so the estimate remains at 2^^^(2^^^12). Similarly, having a large number of Doubling Seasons, Ageless Entitys, Sakiko, Mother of Summers, or Furnace of Raths will only multiply similarly sized numbers together, and won't get you anywhere close to 2^^^(2^^^13). So you'll wind up generating about 2^^^(2^^^12) green mana, which means the Sakiko combo isn't anywhere near as effective as the combo with Sword of Feast and Famine. Thus the final damage of the deck will remain at roughly 2^^^^^N where N is the number of combat damage steps that you can muster up.

Ok. Did not RTFC Paradox Haze. I can solve that with Karn Liberated by restarting the game with all the cards Hazes and Braids in play. I can actually just use the Illusionist's Bracers to get a large number of combat phases I did not realise. I think Karn is one of the few infinite loops that can actually go into this deck. I can restart the game with Karn as many times as I want because the challenge specifies the amount of damage I can deal on turn 1. Each different game is a different turn 1 and thus not cumulative. I am sure I can come up with an alternate way to do this say with Simian Spirit Guides and no Riftsweeper such that I activate the Aggravated Assault the first time with all of the Illusionist's Bracers on it and then do it a second time after all of those combat phases. At some point it probably becomes more efficient to cut the Elite Arcanist and just put Seething Songs or the like in so that I can get an amount of Red mana that let's me have more combat steps.

The 2^...^2 bit was obviously an oversight in simplification. So to pick up where that simplification started. (2^^14)^(2^^14) which will then be copied 2^^14 times or ...(((2^^14)^(2^^14)^(2^^14)^(2^^14)))... This gives us the function f^n(n) = n^n.

This simplifies to n^^(n(2^n)) or in our case (2^^14)^^((2^^14)*(2^^15)). Given that 2^^14 is 1/(2^210)th the size of 2^^15, we can simplify to (2^^14)^^(2^^15). We then follow these steps for each Rhys activation. The second one will become ((2^^14)^^(2^^15))^^(((2^^14)^^(2^^15))*(2^((2^^14)^^(2^^15))) which we will simplify to ((2^^14)^^(2^^15))^^(2^((2^^14)^^(2^^15)). When we activate Rhys n times we end up with a chain of activation greater than n^^^n where n is 2^^14. This is just 2 of each of the Serra's Sanctum taps that we are using.

Let's say we have m life. We channel down to zero and then activate a Children of Korlis copying the ability with the Illusionist's Bracers. I will then gain m(2^n) life where n is the number of Boon reflections I have. I can then channel it back down in between each use of each child. So we will be increasing it by 2^n n times over, for a total of m(2^n^n). I also have at least n Children of Korlis. m(2^(n^^3)). When each of my attacking Ageless Entities deal damage, that damage is multiplied by 2^n thanks to Furnace (call the total damage dealt d) and then I will gain d(2^n) life. where When I deal damage I will also gain n(2^n) that much life due to Exquisite Blood. So the power of one of my Ageless Entities is 4 + ((2^n^2 + n(2^n))(m(2^(n^^3)))). Even when we simplify that down to 2^n^^3 or 2^^43 for the first step. n*(2^n^^3)-1 is the number of times we get to activate our Rhys each damage step.

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"He who is skillful in winning against the enemy does not wrestle with him" - Lao Tzu

"All Warfare is deception" -Sun Tzu

"Magic is just another form of Warfare" - Anonymous

You might want to read Karn Liberated: it only puts back non-Aura cards from exile. There is absolutely no way to get a Paradox Haze trigger on the first turn of the game, restarted game or otherwise.

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Hmm, was Dual Nature really a problem in this deck? It looks okay at a glance, and if we add it and remove Splinter Twin, Crown of the Ages, and Gideon, Champion of Justice, we can save two card slots.

EDIT: And, we can use one of those slots right away - replace Overgrown Tomb and Lifetap with Thawing Glaciers, Island, and Thoughtleech. (Island/Thoughtleech is better than Forest/Lifetap, since we can use the Island in the opening hand.)

EDIT #2: We can save a card slot by replacing Llanowar Reborn, Hardened Scales, and Psychic Battle with Mighty Emergence and Grip of Chaos.

2 Dual Nature

3 Starfield of Nyx

4 Grip of Chaos

5 Cowardice

6 Dismiss Into Dream

7 Bloodbond March

8 Cephalid Shrine

9 Mana Crypt

10 Grinding Station

11 Mimic Vat

12 Omniscience

13 Leyline of Anticipation

14 Mirror of Fate

15 Chrome Mox

16 Mirror Gallery

17 Sharuum the Hegemon

18 Gelectrode

19 Mortiphobia

20 Spellweaver Helix

21 World at War

22 World at War

23 Urborg, Tomb of Yawgmoth

24 Consecrate Land

26 Spellshift

27 Kaho, Minamo Historian

28 Drownyard Temple

29 Enemy of the Guildpact

30 Crimson Acolyte

31 Harbinger of Spring

32 Downdraft

33 Elvish Guidance

34 Distorting Wake

35 Night Dealings

36 Alhammarret's Archive

37 Thoughtleech

38 Amulet of Vigor

39 Island

40 Thawing Glaciers

41 Farsight Mask

42 Spiritual Focus

43 Pain Magnification

44 Backfire

45 Spiteful Shadows

46 Guilty Conscience

47 Justice

48 Five-Alarm Fire

50 Cultural Exchange

51 Animate Artifact

52 Precursor Golem

53 Insurrection

54 Mighty Emergence

55 Show and Tell

56 Yawgmoth's Bargain

57 Thought Reflection

58 Finest Hour

59 ???

60 ???

EDIT #3: I thought I had an improvement by replacing Farsight Mask with Unfulfilled Desires, Telekinetic Bonds, and Betrayal (the troublesome Mortiphobia could be replaced by Screams of the Damned and Voidmage Husher), but unfortunately we could put Betrayal on a Gelectrode donated to the opponent, and the opponent could tap it for free. We could replace Betrayal by Sphinx's Disciple, but then we lose the Betrayal layer.

EDIT #4: Instead, we can replace Farsight Mask with Unfulfilled Desires into Waste Not into [/c]Consecrated Sphinx[/c], again replacing Mortiphobia with Screams of the Damned and Voidmage Husher. We need to add Stunted Growth or something similar to keep the opponent's library replenished, so we wind up using four extra cards. I'm not sure whether Insurrection or Thought Reflection is needed to get started; for the moment I will stick with Finest Hour.

2 Dual Nature

3 Starfield of Nyx

4 Grip of Chaos

5 Cowardice

6 Dismiss Into Dream

7 Bloodbond March

8 Cephalid Shrine

9 Mana Crypt

10 Grinding Station

11 Mimic Vat

12 Omniscience

13 Leyline of Anticipation

14 Mirror of Fate

15 Chrome Mox

16 Mirror Gallery

17 Sharuum the Hegemon

18 Gelectrode

19 Screams of the Damned

20 Spellweaver Helix

21 World at War

22 World at War

23 Urborg, Tomb of Yawgmoth

24 Consecrate Land

26 Spellshift

27 Kaho, Minamo Historian

28 Drownyard Temple

29 Enemy of the Guildpact

30 Crimson Acolyte

31 Harbinger of Spring

32 Downdraft

33 Elvish Guidance

34 Distorting Wake

35 Night Dealings

36 Alhammarret's Archive

37 Thoughtleech

38 Amulet of Vigor

39 Island

40 Thawing Glaciers

41 Consecrated Sphinx

42 Waste Not

43 Unfulfilled Desires

44 Spiritual Focus

45 Pain Magnification

46 Backfire

47 Spiteful Shadows

48 Guilty Conscience

49 Justice

50 Five-Alarm Fire

52 Cultural Exchange

53 Animate Artifact

54 Precursor Golem

55 Mighty Emergence

56 Show and Tell

57 Voidmage Husher

58 Stunted Growth

59 Yawgmoth's Bargain

60 Finest Hour

I think Dual Nature at least causes problems with Sharuum the Hegemon. The etb of free copies would go infinite. There might be other pitfalls with that card.

Consecrated Sphinx seems to lead to an infinite where we donate a sphinx, keep one for us and then just have them trigger each other. Usually that would be limited by one of the libraries, but here we are trying to have just our life as the limiting factor. Doesn't seem to work out.

EDIT: The original reason to get rid of Dual Nature:

Hmm, Consecrated Sphinx can be replaced with Psychic Possession, which can't be donated. So that part at least should work. Unfortunately, if we take the latest deck and go back to Splinter Twin / Crown of the Ages / Gideon, Champion of Justice, we would be at 61 cards even without Finest Hour / Thought Reflection / Insurrection. So we need to make a cut somewhere; I was hoping Dual Nature would fit the bill.

I don't think I agree with the quote that with Dual Nature, we can get the combo started after a board clear without using any resources below the Obliterate marker. We have no hasted Gelectrodes, and we can't use any of the Gelectrode triggers to create one. The quote says we can return the original Kaho back to our hand, but we have no way to bounce it. So unless I am missing something, we do need to use some the stack to reset the stage even with Dual Nature.

However, Dual Nature with Sharuum the Hegemon is certainly a problem. Since Dual Nature saves two cards, if we could replace Sharuum with no more than two cards we would make a profit. Perhaps Grinding Station could be replaced as well; but I'm not seeing a fix at the moment.

EDIT: Now that I think about it, the original reasoning for needing Kaho, Minamo Historian (to insure that we used resources from below the Obliterate marker) no longer seems to apply. So, we could theoretically replace the Spellweaver Helix / Spellshift / Kaho, Minamo Historian engine with something more efficient. Something that lets us fetch and cast an instant or sorcery from our library for reasonably cheap (or maybe for a colored mana, and we could make exiling a card in our graveyard cheap.).

EDIT #2: I think I have a sequence that gives 20 layers. We remove the Spiritual Focus section, leaving life gain for later. We do 3+ damage with Fire Covenant (aided by Precursor Golem) which transtions to Curse of the Forsaken. Angel's Grace is added to avoid dying from self-inflicted damage. Including Dual Nature and Sharuum the Hegemon for the moment.

2 Dual Nature

3 Opalescence

4 Grip of Chaos

5 Cowardice

6 Dismiss Into Dream

7 Bloodbond March

8 Cephalid Shrine

9 Mana Crypt

10 Grinding Station

11 Mimic Vat

12 Omniscience

13 Leyline of Anticipation

14 Mirror of Fate

15 Chrome Mox

16 Mirror Gallery

17 Sharuum the Hegemon

18 Gelectrode

19 Screams of the Damned

20 Spellweaver Helix

21 World at War

22 World at War

23 Urborg, Tomb of Yawgmoth

24 Consecrate Land

26 Spellshift

27 Kaho, Minamo Historian

28 Drownyard Temple

29 Enemy of the Guildpact

30 Crimson Acolyte

31 Harbinger of Spring

32 Downdraft

33 Elvish Guidance

34 Distorting Wake

35 Night Dealings

36 Alhammarret's Archive

37 Lifetap

38 Amulet of Vigor

39 Forest

40 Thawing Glaciers

41 Psychic Possession

42 Waste Not

43 Pain Magnification

44 Backfire

45 Spiteful Shadows

46 Guilty Conscience

47 Justice

48 Fire Covenant

49 Curse of the Forsaken

51 Cultural Exchange

52 Animate Artifact

53 Precursor Golem

54 Mighty Emergence

55 Show and Tell

56 Voidmage Husher

57 Stunted Growth

58 Angel's Grace

59 Yawgmoth's Bargain

60 Finest Hour

Does Angel's Grace work with Pain Magnification? It reads to me as if it replaces the 3 damage effect on us with no damage if we are already on 1, not triggering the donated Pain Magnifications.

Should that chain work somehow we can't take advantage of Mighty Emergence and the second Precursor Golem layer at the same time, since we are not able to change the target of a Fire Covenant copy to creature with a fresh toughness boost at the right time. I did not count the layers to see if you accounted for that, just thought I'd mention it

Angel's Grace does work with Pain Magnification; the damage is not prevented, Angel's Grace just resets our life total to 1.

EDIT: Whoops - Among the 19 layers for the latest sequence, I counted a layer for Alhammarret's Archive on Curse of the Forsaken, but it looks like we can't. Although Angel's Grace prevents the damage from Spiteful Shadows and Backfire from killing us, it doesn't prevent them from eating away at our damage, so we can't afford to pay for further castings of Fire Covenant. Of course, we could cast a bunch of Fire Covenants right after we gain the life, but that doesn't result in another layer. So, back to 18 layers, or less than the previous sequence.

EDIT: No, we can make multiple Starfield of Nyxes, and then donate at least one to the opponent. Oh well. The previous sequence is currently better anyway.

EDIT: I've been looking to replace Sharuum the Hegemon, but with no real success. We could replace it with say Arcbound Reclaimer and Neurok Familiar, but that uses up a card slot that we can't afford to spare. Saprazzan Bailiff unfortunately can return enchantment cards as well, including Elvish Guidance. Sanctum Gargoyle, Junk Diver, and Myr Retriever fill much the same role that Sharuum does. Treasure Hunter seems like it would fit the bill, but it's unfortunately white. Roo****er Diver seems to be too expensive to work. You'd think there would be something like Treasure Hunter in red or blue, but I can't find anything like that.

But, perhaps Sharuum isn't so bad. We can't use it to create lots of Sharuum tokens, because they get destroyed from Dual Nature when Sharuum leaves the battlefield. We could do shenanigans with Dual Nature and Sharuum to make more tokens, but that requires bouncing them, so it's not free. So the only thing we can do infinitely is shuffling artifacts back and forth from the graveyard to the battlefield and back, and the only thing that produces is colorless mana. The only thing that messes up with is Sylvan Offering (Distorting Wake doesn't benefit from overspending). We can replace it with say Hunted Phantasm, and then replace Elvish Guidance with Dawn's Reflection, for example. That could complicate the start, but hopefully we still have enough.

EDIT: It just occurred to me, that instead of using Gelectrode, we could get the untapping effect from the resolution of a spell instead, like Insurrection. So for example, we could have three World at Wars, and imprint a World at War and Obliterate on one Spellweaver Helix, and imprint a second World at War and Insurrection on a second Spellweaver Helix. Then when we cast a World at War, we put an Obliterate on the stack, and then an Insurrection on top of it; the Insurrection untaps the token copies of whatever we're using as the hyperstage creature, with the Obliterate lurking on the stack below. This change allows us to use a blue or artifact creature as the hyperstage creature, so we could conceivably get a third stage on top.

Should we consider going for more? This last idea allows us to get rid of Gelectrode, and I think the general notion of untapping as our stage transition benefit allows us to get rid of Kaho, Minamo Historian as well. So, is it possible perhaps that we could handle the hyperstage using something more limited like artifacts, allowing huge amounts of design space for further stages? Or possibly another hyperstage, or a hyperhyperstage? We could repace Obliterate with something that destroys lands and artifacts but not creatures, saving Obliterate for later. (The only thing I can find by a quick search is Wave of Vitriol, which unfortunately destroys enchantments as well, but it could be worked around - we could use colorless mana to build our enchantments back up.)

Before we get ahead of ourselves, the first step is to set up the hyperstage using something limited like artifacts. Of course we can use Rust Tick as the targeter, but we need some way to cast and recycle instants or sorceries at the cost of a resource. Colored mana is the obvious first thought, but now it could also be a nonartifact creature of some kind - there's got to be something out there that works.

What do you think?

EDIT: I think I have one way to make it work: Use Bosium Strip so that we can cast spells from our graveyard, and then have three of the same sorcery card using one mana of whatever color we desire. Insurrection can be replaced by Blinkmoth Infusion. We can replace Obliterate with Wave of Vitriol, but I think it would be allowable to keep Obliterate if we so desired; destroying all creatures doesn't help us since all the Mimic Vats get destroyed at the same time. And it doesn't necessarily hurt the higher stages, since we only go to a lower stage when all our hasted token copies are tapped and no longer used. But please verify that if you can.

EDIT: A tentative first attempt:

2 Psychic Battle

3 Cowardice

4 Horobi, Death's Wail

5 Bloodbond March

6 Cephalid Shrine

7 Mana Crypt

8 Mimic Vat

9 Omniscience

10 Leyline of Anticipation

11 Mirror of Fate

12 Chrome Mox

13 Splinter Twin

14 Crown of the Ages

15 Karn, Silver Golem

16 Gideon, Ally of Zendikar

17 Mirrorworks

18 Opalescence

19 Spellweaver Helix

20 Blinkmoth Insurrection

21 Obliterate

22 black sorcery

23 black sorcery

24 black sorcery

25 Urborg, Tomb of Yawgmoth

26 Consecrate Land

27 Drownyard Temple

28 Bosium Strip

30 Ink-Eyes, Servant of Oni

31 Walker of Secret Ways

32 Ambassador Laquatus

33 Merfolk Sovereign

34 Seahunter

35 Mercenary Informer

36 Boreal Griffin

37 Boreal Druid

38 Ohran Yeti

39 Everglove Courier

40 Nectar Faerie

41 Ghosthelm Courier

42 Possessed Aven

43 Grassland Crusader

44 Possessed Nomad

45 Shauku's Minion

46 Centaur Archer

47 Maze Glider

48 Paragon of Eternal Wilds

50 Royal Assassin

51 Goblin Tunneler

52 Flamestick Courier

53 Dralnu's Crusade

54 Frightshroud Courier

55 Paragon of Open Graves

56 Viashino Fangtail

57 Show and Tell

58 Spatial Binding

59 Yawgmoth's Bargain

60 Bargain

If everything works, this should get around F_{w^2 + w18}(340), give or take. I'm sure it can be improved. (and there are probably problems)

Doesn't Obliterate interfere with using the creature for the stages? Or do we convert them all into triggers on the stack anyway, whenever we are obliterating?

I think the following will work: Target the original creature with one of the Psychic Battle triggers; it dies, and triggers Mimic Vat. Go ahead and imprint it, and then activate the Mimic Vat. Respond to the activation by processing the next stage down. The Mimic Vat will get destroyed later, but the activated ability will still resolve, so long as the original creature remains exiled. I *think* that should work.

1x Boon Reflection

1x Brain Geyser

1x Channel

1x Concordant Crossroads

1x Cranial Plating

1x Craterhoof Behemoth

1x Despotic Sceptre

1x Elite Arcanist

1x Faithless Looting

1x Furnace of Rath

1x Gaea's Cradle

1x Harmless Offering

1x Karn, Silver Golem

1x Lion’s Eye Diamond

1x Lich's Mirror

1x Lifespark Spellbomb

1x Mimic Vat

1x Mirror Gallery

1x Mizzix Mastery

1x Omnath Locus of Mana

1x Opalescence

1x Orochi Hatchery

1x Platinum Angel

1x Sakiko, Mother of Summer

1x Shimmer Myr

1x Soulblast

1x True Conviction

1x Vedalken Orrery

2x Prototype Portal

2x Rite of Flame

3x Simian Spirit Guide

4x Doubling Season

4x Phantasmal Image

4x Second Harvest

4x Copperhorn Scout

4x Blinkmoth Infusion

4x World at War

Opening Hand: Mizzix's Mastery, 3x Simian Spirit Guide, Faithless Looting, Rite of Flame, Lich's Mirror.

Exile all 3 Simian Spirit Guides, Cast Faithless Looting, drawing and discarding, Channel, and Rite of Flame. Cast Rite of Flame from hand and cast Mizzix's Mastery targeting Channel. Cast Channel. Cast Lich's Mirror. Add 15 colourless mana to your mana pool and then use the Lich's Mirror replacement effect to shuffle in and draw 7 cards that will contain the Lich's Mirror and Lion’s Eye Diamond. This is not an infinite loop; it is an indeterminate loop that could happen in a real game, but is statistically unlikely. Given the rules for this challenge allow me the favour of fate, I am going to get Lich's Mirror and Lion’s Eye Diamond in every hand and net 15 colourless mana on each iteration and 3 mana of a colour of my choosing. This is how I will be casting all of the spells from here on out. I did start to count the number of iterations required but it became tedious when I realised how big the other numbers in this post are.

Penultimate hand of 7: Lich's Mirror, Prototype Portal, Prototype Portal, Brain Geyser, Rite of Flame, Rite of Flame, Lion’s Eye Diamond

Cast Prototype Portal Imprinting Prototype Portal. Cast Brain Geyser targeting you to draw your deck and then cast Lich’s Mirror, Lion’s Eye Diamond both Rite of Flames and all 4 World at War. Tap Prototype Portal to make a Prototype Portal then maintain priority and cast Blinkmoth Infusion. Repeat the activation of Prototype Portal and then Blinkmoth Loop 3 more times (activating Prototype Portal an additional time after the last Blinkmoth Infusion). Maintaining priority, crack Lion’s Eye Diamond and Channel down to zero again.

Ultimate hand of 7: Phantasmal Image, Vedalken Orrery, Shimmer Myr, Lion’s Eye Diamond, Prototype Portal, Brain Geyser, Mimic Vat.

Still maintaining Priority cast Brain Geyser drawing all but one card of your deck, the remaining cards are Harmless Offering and Soulblast in that order. Before letting the Prototype Portal abilities resolve cast the following: Concordant Crossroads, 4x Doubling Season, True Conviction, Mirror Gallery, Boon Reflection and Opalescence. Let the first Prototype Portal ability resolve, creating 16 Prototype Portals imprinting Mimic Vat, Llfespark Spellbomb, Lich’s Mirror, Lion’s Eye Diamond, Orochi Hatchery, Despotic Sceptre, and Cranial Plating. Before letting the other Prototype Portal abilities resolve, activate the Prototype Portals to make 16 Mimic Vats and 16 Despotic Sceptres and then cast 4x Copperhorn Scout, 4x Phantasmal Image, Karn, Silver Golem, Platinum Angel, 4x Copperhorn Scout, Sakiko, Mother of Summer, Ancient Ooze, Elite Arcanist, and Cratehoof Behemoth. Cast the Craterhoof Behemoth second last only to the 4 images that will come in as copies of the Craterhoof Behemoth before letting the triggers resolve.

Use the Despotic Sceptre to destroy the Boon Reflection putting it under a Mimic Vat and then sacrifice each of the Phantasmal Images imprinting them as well.

Activate a Mimic Vat with a Phantasmal Image under it copying Doubling Season 16 times. Repeat this Process for all of the Mimic Vats with Phantasmal Images under them. Creating 2^20 Doubling Seasons with the second one…

…We would like to take a break from our regular scheduled broadcast to invite you to check out

Approximately 2^^20 Doubling Seasons with the third, and 2^^^20 with the fourth. From about here onward we are just going to round to the nearest relevant figure/term.

Now tap a Mimic Vat making 2^(4)20 Boon Reflections and then destroy the other non-artifact creatures putting them under Mimic Vats. Also cast and destroy the Furnace of Rath putting it under Mimic Vats.

Now tap the Mimc Vat with Elite Arcanist under it creating 2^(4)20 Elite Arcanists Imprinting 4x Blinkmoth Infusion and 4x Second Harvest. Tap each of your remaining Mimic Vats and Prototype Portals making a great many things. Use Elite Arcanist with a Blinkmoth Infusion under it to untap all of my artifacts. Make 2^(7)20 Doubling Seasons. Rinse and repeat this process three more times ending with 2^(19)20 Doubling Seasons and (very loosely) somewhere in the vicinity of 2^(20)20 everything else. Now activate an Elite Arcanist with a Second Harvest under it. This is going to do something a bit different, see before we were trying to put one Doubling Season into play from the Mimic Vat but now we are trying to put one Doubling Season into play for each Doubling Season token we have. We now have 2^(2^(20)20)20 Doubling Seasons in play. Now with the additional Mimic Vats we are going to Despotic Sceptre our the rest of our non-token creatures including the original Doubling Seasons and make additional copies of those along the way. Let’s do that again three more times

We now take a(nother) break from our regularly scheduled broadcast to bring your attention to

We are now going to start using f n to describe the number we are at, where f 1 is 2^(20)20 and each consecutive f n will have a number of ^ equal to the previous term.

This brings us to f 5 Doubling Seasons. Now we are going to let those other Prototype Portal abilities resolve.

Unfortunately, I am now out of mana from my lucky loops of Channel & Mirror. Play Gaea's Cradle.

Tap Cradle to equip the Cranial Platings to Ancient Oozes, activate a spellbomb targeting the Cradle, and turn all of the relevant Prototype Portals and Mimic Vats into creatures.

Move to Combat.

Attack with my Legion putting 4(f 5) Copperhorn Scout triggers on the stack. Crack 2 LEDs and 1 Lifespark Spellbomb to draw and cast the Harmless Offering. Giving my opponent a now tapped Platinum Angel Token.

With each Copperhorn Scout Trigger I am going to turn as many of my non-Cranial Plating, non-Lion’s Eye Diamond, non-creature artifacts into creatures; activate all of my relevant Prototype Portals and Mimic Vats (with the Craterhoof Behemoths) entering last; and activate each of my Elite Arcanists in an order that won’t surprise you.

For each Copperhorn Scout Trigger I will be activating the Elite Arcanists thereby increasing the number of tokens of each type I have by f 4. How many times will I be doing that? Why 4(f 5) of course. So we are going to end up with f (1+16 (f 5)) tokens.

No blocks?

How much damage is my opponent going to take? Well my relatively small number of creatures are each getting +X/+X where X is the number of creatures I control. Each Ancient Ooze equipped with a Cranial Plating gets +1/+0 for each of artifact I have (remember those 3(f 6) Prototype Portals). Each of My Ancient Oozes are */* where * equals the total CMC of all creatures I have in play. But probably most importantly I have f 5 Furnace of Raths in play. Each of my f 5 Ancient Oozes with a multiple of f 6 base power, equipped with + f 6/+0 platings will be dealing damage that is doubled f 5 times.

This comes out at something like this ((cf 5)^3 + 3(f 6)) (where c is the number of different types of creatures I have is). This number is not particularly relevant because, in the grand scheme of these monstrous numbers we are reaching, this might as well be simplified to f 6. Even when you take in to account that each of the f 5 attacking Omnaths will each be gaining (f 5)^2 power thanks to the Sakikos, the doubling or even squaring of a number doesn’t actually increase the number by enough to warrant noting it at this point. The amount of damage they deal with Double Strike will then be multiplied by f 6 and finally we will gain f 7 life.

We do need to leave some mana in our pool for our next combat step when we hit our opponent again fortunately that mana is less than the amount our Gaea’s Cradle generates when it is tapped once.

We can Channel away our f 7 life to cast an Orochi Hatchery which will come into play with (f 7/2) x 2^f (1+ (16 (f 5)) counters on it and will make… such a silly number of creatures.

This number continues going up absurdly and the deck can obviously be built in a way to optimise the absurdity, I chose to include cool cards. The end result is a board state you couldn’t map if you used quarks as cards on a table the size of the known universe. There are currently no notations that can quantify the final number. This is the biggest number used for a practical application to date; bigger even than TREE(50). After attacking on the last combat step, I will Despotic Scepter my Opalescence, crack an LED and a spellbomb to draw and cast Soulblast which will deal an amount of damage equal to the amount of damage I have already dealt multiplied by 2 to the power of the amount of damage I have already dealt.

I think I win the challenge. My apologies Mr. Graham.

NOTE: My formatting may not have copied over very well. I will try to update any errors.

"All Warfare is deception" -Sun Tzu

"Magic is just another form of Warfare" - Anonymous

The math with Knuth up-arrows doesn't work out that way. the third mimic vat will put 2^(2^20) doubling seasons into play. The fourth will then put 2^(2^(2^20) into play. the n-th will put 2^(2^(...(2^20)...)) with n-1 ^s. Knuth up-arrow notation then writes that as 2^^n or thereabout (the 20 makes it not fit nicely, but we are rounding a lot here anyway).

Getting more arrows is somewhat harder. The function f you used later seems more likely to correspond to up-arrows but I didn't check if that works out correctly.

And while your Lichs Mirror+Channel combo can not be used for arbitrary amounts of mana in a game by declaring it as a loop we can still play it out as long as we want. By playing it out arbitrarily long we can later reach arbitrary amounts of damage. The non-repetitive parts of most combos here take longer than the lifespan of the universe to play out anyway, so we can't say we don't have the time. So for the purpose of the challenge here this counts as an infinite loop and disqualifies the deck. But that part seems to just be for the setup, so you can probably find replacements if you want to work on the deck some more

Iijil is right about the error with Knuth arrows, and also the Lich's Mirror + Channel combo. Although it may be statistically unlikely for you to draw and be able to play Lich's Mirror many times, you are already doing that in your combo, so you can't really draw a line and say "I can only repeat it THIS many times, and then it becomes unreasonable". In any case, the rules of the challenge state that the outcome of chance events always work out in your favor, so you can obtain arbitrary amounts of damage (by creating arbitrary amounts of colorless mana and casting Orochi Hatchery, say).

To illustrate the correct use of Knuth arrows:

After the second Mimic Vat activation adding a Phantasmal Image token, you wind up with 2^20 + 20 Doubling Seasons, or more than 2^^4. After the third, you get more than 2^2^20, or more than 2^^5. After the fourth, more than 2^^6. Then you cast Blinkmoth Infusion, which allows you to add a Phantasmal Image token four more times, which gets you to 2^^10. Repeat the process three more times for more than 2^^22. Then you cast Second Harvest. Now, the key point here is that all the new tokens come onto the battlefield at the same time. In particular, you don't add one of the Doubling Season tokens first, increasing to 2^^23, then add a second Doubling Season token, increasing to 2^^24, and so on; all the new tokens come onto the battlefield at the same time, so all are multiplied by the same number 2^^23. So we wind up with more than (2^^23)*(2^22) Doubling Seasons, which is essentially 2^^23. You then can get four Mimic Vats imprinted with Doubling Seasons, which increases your number of Doubling Seasons to 2^^27. Then you cast Second Harvest three more times, which brings you up to 2^^30.

So the number of Doubling Seasons you have at that point is between 2^^30 and 2^^31, not f 5.

Attacking with Copperhorn Scout allows you to exponentiate several times for each trigger, so that brings you to more than 2^^(2^^31).

EDIT: Going back to our deck, we can do a little better by switching from the Splinter Twin + Crown of the Ages structure to Dual Nature + Changeling Berserker. We can replace the lands with Island and Titania, Protector of Argoth to save a card, and use Show and Tell as our triple sorcery.

2 Psychic Battle

3 Cowardice

4 Horobi, Death's Wail

5 Bloodbond March

6 Cephalid Shrine

7 Mana Crypt

8 Mimic Vat

9 Omniscience

10 Leyline of Anticipation

11 Mirror of Fate

12 Chrome Mox

13 Dual Nature

14 Changeling Berserker

15 Assembly-Worker

16 March of the Machines

17 Gideon, Ally of Zendikar

18 Opalescence

19 Spellweaver Helix

20 Blinkmoth Insurrection

21 Obliterate

22 Show and Tell

23 Show and Tell

24 Show and Tell

25 Island

26 Titania, Protector of Argoth

27 Bosium Strip

29 Labyrinth Minotaur

30 Anaba Ancestor

31 Rend Spirit

32 Hollowsage

33 Merfolk Sovereign

34 Seahunter

35 Mercenary Informer

36 Boreal Griffin

37 Boreal Druid

38 Ohran Yeti

39 Everglove Courier

40 Nectar Faerie

41 Ghosthelm Courier

42 Possessed Aven

43 Grassland Crusader

44 Possessed Nomad

45 Shauku's Minion

46 Centaur Archer

47 Maze Glider

49 Devout Chaplain

50 Royal Assassin

51 Goblin Tunneler

52 Flamestick Courier

53 Dralnu's Crusade

54 Frightshroud Courier

55 Paragon of Open Graves

56 Viashino Fangtail

57 Drowner of Secrets

58 Spatial Binding

59 Yawgmoth's Bargain

60 Bargain

Should improve to around F_{w^2 + w19}(340).

Correct me if I went wrong somewhere.

Someone pointed out to me that if you Mirrorweave the Hatchery tokens after phasing each of the relevant Elite Arcanists out you make the number less difficult to round and also increase it faster.

"All Warfare is deception" -Sun Tzu

"Magic is just another form of Warfare" - Anonymous

2^^20 = 2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^(2^2)))))))))))))))))). That's 20 2's on the right hand side. I explicitly wrote the brackets here so the order of operation is clear.

In comparison 2^(2^20) is bigger than 2^(2^16) = 2^(2^(2^(2^2))) = 2^^5 but a lot smaller than 2^(2^65536) = 2^(2^(2^(2^(2^2)))) = 2^^6.

If you pile up multiple copies of that, it makes all the triggers go on the stack at once, which is unfortunate because it really inhibits its ability to affect the growth rate meaningfully. Furthermore, if the design is built around a series of "you can't be allowed to get this effect more than once per instance you recur a particular card", it's not even safe, same as a card like Rings of Brighthearth would be. But it is the most fascinating new engine part they've released in quite a while.

In the latest deck, if we replace Spatial Binding + Yawgmoth's Bargain + Bargain with Korozda Gorgon + Corpsejack Menace + Selvala's Enforcer, I believe the damage increases to F_{w^2 + w19 + 1}(X) where X is going to be roughly 40 or so.

1x Ageless Entity

1x Black Lotus

1x Boon Reflection

1x Channel

1x Children of Korlis

1x Concordant Crossroads

1x Craterhoof Behemoth

1x Despotic Sceptre

1x Donate

1x Elite Arcanist

1x Elvish Spirit Guide

1x Enter the Infinite

1x Exquisite Blood

1x Five-Alarm Fire

1x Furnace of Rath

1x Illusionist’s Bracers

1x Leonin Shikari

1x Leyline of Anticipation

1x Mimic Vat

1x Mirror Gallery

1x Necropolis Regent

1x Omniscience

1x Opalescence

1x Riftsweeper

1x Rhys, the Redeemed

1x Platinum Angel

1x Puresteel Paladin

1x Sakiko, Mother of Summer

1x Serra’s Sanctum

1x Show and Tell

1x Sword of Feast and Famine

1x True Conviction

1x Upwelling

1x Clone

2x Prototype Portal

4x Paradox Haze

4x Braids of Fire

4x Doubling Season

4x Phantasmal Image

4x Second Harvest

Following a similar process as before. This time we use Black Lotus to cast Show and Tell to put Omniscience in play to cast Enter the Infinite.

Channel provides the colourless mana to activate the Prototype Portal to make 2^9 copies of Mimic Vat and Despotic Sceptre.

Each time I try and put a Doubling Season in play I will be adding 2^n where n is the current number of Doubling Seasons I have. I can afford to destroy and vat three Doubling Seasons before I channel myself to 0. The first one will create 2^8 Doubling Seasons and the second will attempt to add a further 2^(2^8) or 2^256 or 2^^5. Each additional Doubling Season that I try and put in play will add 2^n thus increasing the number by 1 after the ^^ such that 2^^5 becomes 2^^6 and so on.

I destroy my Boon Reflection and then make 2^^7 copies putting it under a vat and then sac my Children of Korlis which will gain me 20(2^^7) life. I now have enough colourless mana to continue operating Vats, Portals, and Elite Arcanists.

The first step here is to create as many Braids of Fire and Paradox Hazes as I can before I move to my second upkeep. Using one Elite Arcanist with a Second Harvest under it and equipped with 2^^14 Illusionist's Bracers I can attempt to put 2^^14 Doubling Seasons in play. Whenever I try and put 1 Doubling Season in to play I instead put 2^n where n is the current number so when I try and put a number of Doubling Seasons in to play equal to n I instead put 2n^n or (2(2^^14))^(2^^14). Let's simplify this down and say that it is 2^^2^(2^^2) because each Illusionist's Bracers trigger is separate we repeat this process for each Bracers. So 2^^2^(2^^2)... which ends at 2^^(2^^2) or 2^^^2. Each iteration will then grow by 1 ^ such that we end with a number bigger than 2^(6)2. If we have been exiling our Elvish Spirit Guide along the way, Shuffling it back in with Riftsweeper, and drawing it with Puresteel Paladin we also have GGGGGG floating which we can use to activate one of our many Rhys, the Redeemed to increase by 3 more arrows but that will also net GGG and so on such that we end with G in our pool and 2^(11)2. If we then create Paradox Hazes and Braids of Fire' we will have 4(2^(2^(11)2)) Paradox Hazes and four time that many Braids of Fire which will give us 2(sum of the numbers 1 to (2^(2^(11)2))) combat steps. We'll call this number

C.In our main phase we need to play a Serra's Sanctum.

In order for our opponent to not die we have to Donate one of our tapped Platinum Angels before the first damage step.

The 2^(11)2 Sword of Feast and Famine Triggers will allow us to all of our current Rhys, the Redeemed for each trigger, which can each be equipped with an equal number of Illusionary Masks that will continue our pattern. Each Rhys, the Redeemed activation will attempt to put n^n tokens into play but we have n triggers. So our first will raise n^n the second will raise (n^n)^(n^n) and so on. Resulting in an n step process whereby we raise n to the power of itself and then raise that number to the power of itself. We can also write this as n^^^n each step of this process will then be repeating this thereby raising the number of arrows in our solution by ^ for each step. Given that we are activating n Rhys this will result in n^(n)n. When our creatures deal damage for the second time thanks to Double Strike we will get to repeat this process starting with n^(n)n there by getting to a stage of n^(n^(n)n)n. Here is where we introduce

f. For each combat phase we will be increasing our term number offby 2, with termf (1)being n^(n)n andf (2)being n^(n^(n)n)n. If this were all that were happening we would end up atf (c), but we also have Sakikos to contend with.To work out how much green mana we get from Sakiko, we need to work out how much combat damage we are dealing each combat damage step. Let's start with how much life we have. Let's assume we have spent all of our life as colourless mana so far. After dealing damage we are going to have

f (1)Boon Reflections and an equal number of Children of Korlis. If we sac one Child we will gain the life we have lost so far multiplied by 2 to the power of the number of doubling seasons we have, let's round that to 2^f (1). We can then repeat this process by Channeling down to zero whereby we will then attempt to gain 2^f (1)life, again after multiplying it by 2^f (1). Repeating this Processf (1)times will give us ((2^f (1))^f (1)). To measure the sum of our total life gain we will be adding the sum of the set 2^f (1)^1... ((2^f (1))^f (1)). This is the power of each of our Ageless Entities. Because each of these will then deal damage and add mana to our mana pool equal to the damage they deal (which is increased by the Furnace of Rath's but not by a relevant amount in terms of the rounding we are doing). It means that the number of times we can activate our Rhys each combat step is actually going to be equal to thefof our previous combat step. So when we arrive in our second main phase we havef (f (1))rather than justf (2). At the end of all our combat steps we will havef (f (f (f ( ...where there arecfunction of functions in our chain. Our total damage is somewhere beyond that.Correct me if I went wrong somewhere.

EDIT: Oops I forgot the Necropolis Regent.

"All Warfare is deception" -Sun Tzu

"Magic is just another form of Warfare" - Anonymous

Because Braid of Fire ends up being useless, Aggravated Assault is also useless, but it's an extremely dangerous card to look out for in any case: even a simple Tormod's Crypt would give you the freedom to imprint Black Lotus on Prototype Portal before copying the tokens, and that's way too good.

2^^(2^^2) is 2^^^3 (because there are three instances of 2), not 2^^^2. You really don't want to get stuck on 2^^^^(...anything...)^^^2, because that number reduces to simply 4.

One iteration of something like Elite Arcanist doesn't "add an arrow", it adds one to the number at the end of the arrows. Building off the previous example, 2^^(2^^(2^^2)) is 2^^^4, not 2^^^^2. Any expression you build using iterated ^^ operators will be simplified in terms of ^^^, exactly one arrow beyond the iterated one. To get to ^^^^, you have to be able to iterate an even larger process, one on the power of ^^^ to begin with. And so on: in order to add more arrows, you have to keep finding larger loops which can be dynamically repeated a number of times commensurate with the output value of your sub-loops, with each loop you can manage to wrap around the rest being worth just

oneextra arrow.GodAmongEquals: I'd like to go over your math, so for the moment I'm going to assume that your deck can do everything you say it does without checking it particularly carefully (Although, as SadisticMystic points out you can't actually generate any mana from Paradox Haze / Braid of Fire to pay for Aggravated Assault.). I'm not sure how you get up to 2^^14 Illusionist's Bracers, but let's assume you have that many Bracers and 2^^13 Doubling Seasons. The first time you resolve a Second Harvest spell, attempt to add 2^^13 Doubling Seasons, and each one gets replaced with 2^(2^^13) = 2^^14 Doubling Seasons, so you get (2^^13)(2^^14) ~ 2^^14 Doubling Seasons. Then the next Second Harvest will increase it to 2^^15, then to 2^^16, and so on. So after 2^^14 Second Harvest spells, you will get to 2^^(2^^14) Doubling Seasons total. If you then generate 2^^(2^^14) Illusionist's Bracers, and attach them to a second Elite Arcanist imprinted with Second Harvest, you will then pump the number of Doubling Seasons up to 2^^(2^^(2^^14)). After four Elite Arcanists you will therefore have about 2^^(2^^(2^^(2^^(2^^14)))) Doubling Seasons, or between 2^^^7 and 2^^^8 Doubling Seasons. Each Rhys the Redeemed activation (while equipped with an updated number of Illusionst's Bracers of course) will do the same thing, so after five Rhys activations you will get more than 2^^^12 Doubling Seasons. Then, Serra's Sanctum will allow for about 2^^^12 more Rhys activations, bringing the number of Doubling Seasons up to 2^^^(2^^^12). Ignoring Sakiko for the moment, each Sword of Feast and Famine will allow you to untap Serra's Sanctum and therefore take X Doubling Seasons to 2^^^X, so if you equip a creature with 2^^^(2^^^12) Swords of Feast and Famine and deal combat damage with it, that will allow you to pump the number of Doubling seasons up to 2^^^^(2^^^(2^^^12)). Each subsequent combat damage will allow you to take X Doubling Seasons to 2^^^^X, so after N combat damage steps you will be able to generate roughly 2^^^^^N Doubling Seasons, so this would be a "five-arrow deck".

Next, let's address Sakiko. Say you have X Boon Reflections and Y Children of Korlises, and have lost Z life after channeling all your life away. Sacrificing one Children of Korlis will add Z*2^X life to you life total, which you can then convert to mana. Then the second Children of Korlis will add (Z*2^X)*2^X = Z*2^(2X) life. So sacrificing Y Children of Korlis will result in Z*2^(XY) life. Note that, while this is ostensibly larger than X and Y, puny operations like exponentiation aren't going to make a dent in large Knuth arrow numbers. So for example, if you have roughly 2^^^(2^^^12) Boon Reflections and 2^^^(2^^^12) Children of Korlises, you're not going to get anywhere close to 2^^^(2^^^13) life, so the estimate remains at 2^^^(2^^^12). Similarly, having a large number of Doubling Seasons, Ageless Entitys, Sakiko, Mother of Summers, or Furnace of Raths will only multiply similarly sized numbers together, and won't get you anywhere close to 2^^^(2^^^13). So you'll wind up generating about 2^^^(2^^^12) green mana, which means the Sakiko combo isn't anywhere near as effective as the combo with Sword of Feast and Famine. Thus the final damage of the deck will remain at roughly 2^^^^^N where N is the number of combat damage steps that you can muster up.

The 2^...^2 bit was obviously an oversight in simplification. So to pick up where that simplification started. (2^^14)^(2^^14) which will then be copied 2^^14 times or ...(((2^^14)^(2^^14)^(2^^14)^(2^^14)))... This gives us the function f^n(n) = n^n.

This simplifies to n^^(n(2^n)) or in our case (2^^14)^^((2^^14)*(2^^15)). Given that 2^^14 is 1/(2^210)th the size of 2^^15, we can simplify to (2^^14)^^(2^^15). We then follow these steps for each Rhys activation. The second one will become ((2^^14)^^(2^^15))^^(((2^^14)^^(2^^15))*(2^((2^^14)^^(2^^15))) which we will simplify to ((2^^14)^^(2^^15))^^(2^((2^^14)^^(2^^15)). When we activate Rhys n times we end up with a chain of activation greater than n^^^n where n is 2^^14. This is just 2 of each of the Serra's Sanctum taps that we are using.

Let's say we have m life. We channel down to zero and then activate a Children of Korlis copying the ability with the Illusionist's Bracers. I will then gain m(2^n) life where n is the number of Boon reflections I have. I can then channel it back down in between each use of each child. So we will be increasing it by 2^n n times over, for a total of m(2^n^n). I also have at least n Children of Korlis. m(2^(n^^3)). When each of my attacking Ageless Entities deal damage, that damage is multiplied by 2^n thanks to Furnace (call the total damage dealt d) and then I will gain d(2^n) life. where When I deal damage I will also gain n(2^n) that much life due to Exquisite Blood. So the power of one of my Ageless Entities is 4 + ((2^n^2 + n(2^n))(m(2^(n^^3)))). Even when we simplify that down to 2^n^^3 or 2^^43 for the first step. n*(2^n^^3)-1 is the number of times we get to activate our Rhys each damage step.

"All Warfare is deception" -Sun Tzu

"Magic is just another form of Warfare" - Anonymous

non-Auracards from exile. There is absolutely no way to get a Paradox Haze trigger on the first turn of the game, restarted game or otherwise.