1. Ok, use a mirror gallery
2. So use gaea's cradle and orochi leafcaller instead
3. It's still effective because of the constantly growing number of mana reflections and creatures
4. So get rid of the infinite colorless loop, as it reduces the number of iterations by a constant factor only (ie instead of 4 mana, each costs 14 mana)
I don't get it. How does the Gaea's Cradle not get affected by Celestial Dawn?
How is your point 4 to have him fix your nombo?
I don't get it. How does the Gaea's Cradle not get affected by Celestial Dawn?
How is your point 4 to have him fix your nombo?
Orochi Leafcaller replaces celestial dawn, and cradle replaces sanctum.
Point 4 is to get rid of the tyrant and sol ring, as they are not necessary for the combo. They simply reduce the mana required by a constant factor. We could achieve the same effect with mana echoes on the leafcaller
What kinds of untapping cards are you looking at to fill the remaining deck slots? It seems unlikely that your setup would allow you to put anything after that, let alone enough things to create 210 nested loops.
I also assume you'll want to squeeze in a source of haste, or else Cathars' Crusade isn't doing anything.
What kinds of untapping cards are you looking at to fill the remaining deck slots? It seems unlikely that your setup would allow you to put anything after that, let alone enough things to create 210 nested loops.
I also assume you'll want to squeeze in a source of haste, or else Cathars' Crusade isn't doing anything.
A lot of my post is approximation. It wasn't really intended to be optimum in any way, simply another approach at creating a finitely bounded combo with a large amount of damage. As such, adding a haste source is a pretty trivial inclusion. Let's say it is an enchantment so that it will add to our damage total. Let's say it is a single copy of Italian legends Concordant Crossroads (since I have one :))
For a slightly better mana engine, you can play Mirrorworks one at a time, paying for each successive copy. After each you will have 1, 3, 7, 15 mirrorworks respectively.
After that, you can play Copy Artifact, Phyrexian Metamorph, and Sculpting Steel as copies 5-16 of mirrorworks. They keep growing so that you always have a total of 2^n-1, yielding a total of 65,535. Now you can play your 4 candelabras, making an additional 65,535, yielding a total of 262,148 candelabras. We can also use cards like Turnabout and Blinkmoth Infusion to untap them all.
Now you have 12 + (12 * 262,148)*8 = 2,097,196 activations of each of your lands, which each time produces an amount of mana equal to n*2^n, where n is the number of mana reflections you have. Of course since you will use the combo to near completion (minus enough to use one of your candelabras to untap all your lands again), the number of mana reflections you have will grow DRASTICALLY every time.
But we're getting ahead of ourselves. Let's start by defining an iteration of the combo. We know that casting Rite of Replication with Radiate each time will give us 6^n... or will it? Because we are using doubling season, the number we get will double for each doubling season we have.
So for each time we cast rite of replication, it will give us this many doubling seasons (and our other enchantments / creatures):
5*n*2^n + n
Of course, this is a vast simplification, since each copy of rite of replication resolves separately. This means that every copy will be doubled an additional number of times equal to the number of doubling seasons produced during the resolution of the previous rites of replication. So let's break this down and see how many a SINGLE copy of rite of replication will produce and define it as a recursive function (n is the number of doubling seasons we started this iteration of rite of replications with):
R(0) = 5*2^n
R(i) = 5*2^(n+R(i-1))
So the total number of each enchantment will be:
X(n) = Summation i=0 to n R(i)
Similarly, thanks to Cathar's Crusade, each of them will have gained a +1/+1 counter for each of these creatures/enchantments entering the battlefield, for each Cathar's Crusade you make, doubled for each doubling season you have. The function for determining this is an even more complicated recursive function, since you are increasing the number of Cathar's Crusades as well as doubling seasons as you go along.
So lets now figure out how many times we can do a rite of replication iteration with the tapping of a single land. Tapping the land gives us 4*X(n) green mana, which can be filtered by our Orochi Leafcaller's to be any color. Each iteration costs 14 mana, so we can do the combo n[i] = 4*X(n[i-1])/14 times before we must then tap another land.
And we can tap one of our lands 2,097,196 times before we run out. And with all that, I am still at 52 cards, leaving 8 to set up the whole thing.
As for the 210 nested loops... you're right, but this method derives its growth by nested recursion, rather than loops. Admittedly I'm a little rusty on my complexity analysis, but I think this engine could certainly give yours a run for its money.
Mirror Gallery lets you dodge the legend rule, but no card in existence lets you dodge the world rule. As soon as Radiate gives you a copy of Rite of Replication targeting Concordant Crossroads...not the greatest idea in the world (enchantment). Mass Hysteria would be a safer choice there.
Turning 16 "copies" of Mirrorworks into only 65535 is a criminal underperformance. Presumably you shouldn't be playing Mirrorworks or Candelabra until you actually need them, and there will be lots of Doubling Seasons racked up in the mean time. So the second playing of Mirrorworks, instead of resulting in 3 copies, will result in 1+2^N. The third playing will trigger that many times...
Right away, you cannot have Copy Artifact. That card's unusual copy effect says that it remains an enchantment, which means Opalescence turns it into a creature. So you can use that to copy Candelabra and get a makeshift version of Magus of the Candelabra, in that it's a creature who untaps lands. As soon as Rite of Replication starts making token copies of a creature whose purpose is to produce mana...that's bad news.
Phyrexian Metamorph is possibly troublesome for the same reason by using the "copy nothing" option so that Mirrorworks copies can all hit different things, but because no card allows it to stay alive for any length of time in that form, there's no way to have Rite of Replication hit a Metamorph that's copying nothing, and it looks safe from here. Just don't go trying to add any cards like Coat of Arms. or this will be a problem. Sculpting Steel that copies nothing can't overreach this way, so at least there's nothing to worry about on that front.
It's also extremely fortunate that both Turnabout and Blinkmoth Infusion are monoblue, so that All Suns' Dawn can't return either of them without forfeiting Rite of Replication, and that they're both instants, so you can't feed them to copies of Spellweaver Helix.
Now let's see what this thing is actually doing.
-Each playing of Rite of Replication turns N copies of Doubling Season into roughly 2^N copies. This is layer 1.
-Each playing of Radiate lets you repeat layer 1 for each Doubling Season, plus get some bonus copies of Mana Reflection and stuff to keep them level with the rest. Cathar's Crusade ultimately isn't doing much here, as a batch of Crusades will trigger but without a way to use +1/+1 counters as a resource, neither the number of Crusades nor the number of Doubling Seasons will be increasing in between those triggers. All this can do is a static mapping of N->2^N, which is an effect that is entirely invisible starting with 3 Knuth arrows. This is only the second arrow now, so there will be an increase in the second operand, but only by a constant multiplicative factor.
-For each 9 mana, the Radiate loop can be repeated. (It's more efficient not to kick the Rite--if you kick it, 28 mana gives 2^^(2^^5N), but unkicked allows 27 mana to give 2^^(2^^(2^^N)), which is far larger.) This is layer 3.
-For each tap of a Gaea's Cradle, you get lots of mana. In fact, Mana Reflection (whose numbers are on par with Doubling Season) is the sole asymptotically driving force, and the difference between Gaea's Cradle and a basic Forest is just N*2^N versus 2^N, and the factor of N is immediately invisible in the sparse representations available at this point. This is layer 4.
-For each tap of a Candelabra, you can untap the Gaea's Cradles once. The number of Cradles is fixed throughout at a constant 12, which obviously vanishes with respect to the large numbers of everything else. This is layer 5.
-Then you have two different things each trying to reuse the Candelabras: Mirrorworks attempts to create more copies, while Turnabout and friends untaps the copies you already have. What Turnabout cannot do is create more copies, so once you're done with Mirrorworks, that number becomes static, and the construction is ill-advised.
Instead, here's a better plan you can try:
-Mirrorworks grants copies for each of itself, and in turn for each Doubling Season (as it makes copies of Candelabra, they can immediately tap for at least enough mana to cover all the Mirrorworks triggers, no matter how many of those you have to deal with). This is layers 6 and 7.
-Now...don't play Turnabout for a mere untap. Instead, play Ghostly Flicker, cycling out a Mirrorworks and a Candelabra. They will come back untapped, and more importantly, produce more Mirrorworks triggers. This is layer 8.
-I would have liked to add a Pyromancer Ascension and probably also a Leyline of Anticipation to the board, which would give a lot more than four Ghostly Flickers, but this would unfortunately be infinite by giving copies each time All Suns' Dawn is cast from Spellweaver Helix, severing the narrow thread of "All Suns' Dawn can never return a blue instant without cutting off the ability to perpetuate the combo". So that won't be any good.
"For each Ghostly Flicker" is 4 times, or 8 times if you add a single Snapcaster Mage which will obviously get enough token copies to allow flashing them all back, or up to 22 times if you also add Holistic Wisdom and fill the rest of the deck with useless instants that serve only to be pitched to that and bring back Ghostly Flicker (but probably less, since this setup has to be put into place somehow). That still leaves the final damage output somewhere in the realm of 2^^^^^^^^25, or about 200 arrows short of what took 19,000 words to explain.
More improvement could be achieved by adding Rings of Brighthearth, which both allows Candelabra's untap ability to be copied several times, and does the same for Holistic Wisdom if you decide to use it. But other than that, this skeleton doesn't offer much room for extensibility. Orochi Leafcaller prevents any steps that might allow you to use a single mana of one color to produce a lot more mana of another, and you've seen how there are lots of innocuous cards like Copy Artifact or Pyromancer Ascension which go infinite due to circumstances that exist around it.
Ultimately, fast-growing combos take the form "for each X...for each Y where Y increases each time you do X...", and adding 4 or 12 copies of the same card doesn't do much to change that. Far better to add a single additional card that allows reusing the first one a lot more than 4 times, because that's worth a whole new "for each" repetition. The introduction to the 2009 attempt at a large combo might explain this more clearly.
A new tweak has incurred 2 extra cards in overhead (including Cephalid Shrine...in a singleton deck...yeah). It requires some pretty damning cuts to make space, but it pays back so well, with most of the ending bumped up to 8 layers per card, that it still gains 11 layers in the end, for a total of 221.
If deck size wasn't an issue, I now know of ways to add at least 43 layers on top of the cards that did make the cut (this would bring it up to 84 cards), and it remains to be seen if moving up to a 99-card limit for Commander still leaves room for any appreciable improvement on top of that.
My brains hurts just trying to understand all that combo with 60 cards (after all I still don't get it)
after all I always wondered if there were a way to do an high amount of dmg without going infinite, I think its all came to duplicating the more possible time a doubling season and try to get an high amount of mana and find some way to untap a Solarion
SadisticMystic, are you archiving the history of the whole combo? I remember something close to the old archived version, but then I've missed a few years of improvement.
At the very beginning of that page, there's a link to the predecessor. The forum topic linked at the end has a more thorough archive of the many ideas to come up.
Also, as far as Solarion, it just doesn't do enough. Combined with Sinking Feeling, it says "{1}: Get more damage." Pretty good especially with multiple Doubling Seasons around, but if 2 mana can simply produce a lot more Doubling Seasons, that will churn out an increase in power far beyond anything Solarian can hope to keep pace with.
It actually turns out that Mirror Gallery was a disposable card even before the new legend rule came into effect, but the new rule makes the necessary maneuvering a hell of a lot easier, so I might as well toss that card out of the deck. Besides, the lack of a Mirror Gallery--and only the lack thereof--means Empress Galina can come on board for some big gains. Yes, with Tsabo Tavoc still there.
Update available, link in the first post. There's a weirdly nice symmetry to seeing a damage figure of "2 -> 34 -> 234".
I don't get it. How does the Gaea's Cradle not get affected by Celestial Dawn?
How is your point 4 to have him fix your nombo?
Orochi Leafcaller replaces celestial dawn, and cradle replaces sanctum.
Point 4 is to get rid of the tyrant and sol ring, as they are not necessary for the combo. They simply reduce the mana required by a constant factor. We could achieve the same effect with mana echoes on the leafcaller
I also assume you'll want to squeeze in a source of haste, or else Cathars' Crusade isn't doing anything.
A lot of my post is approximation. It wasn't really intended to be optimum in any way, simply another approach at creating a finitely bounded combo with a large amount of damage. As such, adding a haste source is a pretty trivial inclusion. Let's say it is an enchantment so that it will add to our damage total. Let's say it is a single copy of Italian legends Concordant Crossroads (since I have one :))
For a slightly better mana engine, you can play Mirrorworks one at a time, paying for each successive copy. After each you will have 1, 3, 7, 15 mirrorworks respectively.
After that, you can play Copy Artifact, Phyrexian Metamorph, and Sculpting Steel as copies 5-16 of mirrorworks. They keep growing so that you always have a total of 2^n-1, yielding a total of 65,535. Now you can play your 4 candelabras, making an additional 65,535, yielding a total of 262,148 candelabras. We can also use cards like Turnabout and Blinkmoth Infusion to untap them all.
Now you have 12 + (12 * 262,148)*8 = 2,097,196 activations of each of your lands, which each time produces an amount of mana equal to n*2^n, where n is the number of mana reflections you have. Of course since you will use the combo to near completion (minus enough to use one of your candelabras to untap all your lands again), the number of mana reflections you have will grow DRASTICALLY every time.
But we're getting ahead of ourselves. Let's start by defining an iteration of the combo. We know that casting Rite of Replication with Radiate each time will give us 6^n... or will it? Because we are using doubling season, the number we get will double for each doubling season we have.
So for each time we cast rite of replication, it will give us this many doubling seasons (and our other enchantments / creatures):
5*n*2^n + n
Of course, this is a vast simplification, since each copy of rite of replication resolves separately. This means that every copy will be doubled an additional number of times equal to the number of doubling seasons produced during the resolution of the previous rites of replication. So let's break this down and see how many a SINGLE copy of rite of replication will produce and define it as a recursive function (n is the number of doubling seasons we started this iteration of rite of replications with):
R(0) = 5*2^n
R(i) = 5*2^(n+R(i-1))
So the total number of each enchantment will be:
X(n) = Summation i=0 to n R(i)
Similarly, thanks to Cathar's Crusade, each of them will have gained a +1/+1 counter for each of these creatures/enchantments entering the battlefield, for each Cathar's Crusade you make, doubled for each doubling season you have. The function for determining this is an even more complicated recursive function, since you are increasing the number of Cathar's Crusades as well as doubling seasons as you go along.
So lets now figure out how many times we can do a rite of replication iteration with the tapping of a single land. Tapping the land gives us 4*X(n) green mana, which can be filtered by our Orochi Leafcaller's to be any color. Each iteration costs 14 mana, so we can do the combo n[i] = 4*X(n[i-1])/14 times before we must then tap another land.
And we can tap one of our lands 2,097,196 times before we run out. And with all that, I am still at 52 cards, leaving 8 to set up the whole thing.
As for the 210 nested loops... you're right, but this method derives its growth by nested recursion, rather than loops. Admittedly I'm a little rusty on my complexity analysis, but I think this engine could certainly give yours a run for its money.
Turning 16 "copies" of Mirrorworks into only 65535 is a criminal underperformance. Presumably you shouldn't be playing Mirrorworks or Candelabra until you actually need them, and there will be lots of Doubling Seasons racked up in the mean time. So the second playing of Mirrorworks, instead of resulting in 3 copies, will result in 1+2^N. The third playing will trigger that many times...
Right away, you cannot have Copy Artifact. That card's unusual copy effect says that it remains an enchantment, which means Opalescence turns it into a creature. So you can use that to copy Candelabra and get a makeshift version of Magus of the Candelabra, in that it's a creature who untaps lands. As soon as Rite of Replication starts making token copies of a creature whose purpose is to produce mana...that's bad news.
Phyrexian Metamorph is possibly troublesome for the same reason by using the "copy nothing" option so that Mirrorworks copies can all hit different things, but because no card allows it to stay alive for any length of time in that form, there's no way to have Rite of Replication hit a Metamorph that's copying nothing, and it looks safe from here. Just don't go trying to add any cards like Coat of Arms. or this will be a problem. Sculpting Steel that copies nothing can't overreach this way, so at least there's nothing to worry about on that front.
It's also extremely fortunate that both Turnabout and Blinkmoth Infusion are monoblue, so that All Suns' Dawn can't return either of them without forfeiting Rite of Replication, and that they're both instants, so you can't feed them to copies of Spellweaver Helix.
Now let's see what this thing is actually doing.
-Each playing of Rite of Replication turns N copies of Doubling Season into roughly 2^N copies. This is layer 1.
-Each playing of Radiate lets you repeat layer 1 for each Doubling Season, plus get some bonus copies of Mana Reflection and stuff to keep them level with the rest. Cathar's Crusade ultimately isn't doing much here, as a batch of Crusades will trigger but without a way to use +1/+1 counters as a resource, neither the number of Crusades nor the number of Doubling Seasons will be increasing in between those triggers. All this can do is a static mapping of N->2^N, which is an effect that is entirely invisible starting with 3 Knuth arrows. This is only the second arrow now, so there will be an increase in the second operand, but only by a constant multiplicative factor.
-For each 9 mana, the Radiate loop can be repeated. (It's more efficient not to kick the Rite--if you kick it, 28 mana gives 2^^(2^^5N), but unkicked allows 27 mana to give 2^^(2^^(2^^N)), which is far larger.) This is layer 3.
-For each tap of a Gaea's Cradle, you get lots of mana. In fact, Mana Reflection (whose numbers are on par with Doubling Season) is the sole asymptotically driving force, and the difference between Gaea's Cradle and a basic Forest is just N*2^N versus 2^N, and the factor of N is immediately invisible in the sparse representations available at this point. This is layer 4.
-For each tap of a Candelabra, you can untap the Gaea's Cradles once. The number of Cradles is fixed throughout at a constant 12, which obviously vanishes with respect to the large numbers of everything else. This is layer 5.
-Then you have two different things each trying to reuse the Candelabras: Mirrorworks attempts to create more copies, while Turnabout and friends untaps the copies you already have. What Turnabout cannot do is create more copies, so once you're done with Mirrorworks, that number becomes static, and the construction is ill-advised.
Instead, here's a better plan you can try:
-Mirrorworks grants copies for each of itself, and in turn for each Doubling Season (as it makes copies of Candelabra, they can immediately tap for at least enough mana to cover all the Mirrorworks triggers, no matter how many of those you have to deal with). This is layers 6 and 7.
-Now...don't play Turnabout for a mere untap. Instead, play Ghostly Flicker, cycling out a Mirrorworks and a Candelabra. They will come back untapped, and more importantly, produce more Mirrorworks triggers. This is layer 8.
-I would have liked to add a Pyromancer Ascension and probably also a Leyline of Anticipation to the board, which would give a lot more than four Ghostly Flickers, but this would unfortunately be infinite by giving copies each time All Suns' Dawn is cast from Spellweaver Helix, severing the narrow thread of "All Suns' Dawn can never return a blue instant without cutting off the ability to perpetuate the combo". So that won't be any good.
"For each Ghostly Flicker" is 4 times, or 8 times if you add a single Snapcaster Mage which will obviously get enough token copies to allow flashing them all back, or up to 22 times if you also add Holistic Wisdom and fill the rest of the deck with useless instants that serve only to be pitched to that and bring back Ghostly Flicker (but probably less, since this setup has to be put into place somehow). That still leaves the final damage output somewhere in the realm of 2^^^^^^^^25, or about 200 arrows short of what took 19,000 words to explain.
More improvement could be achieved by adding Rings of Brighthearth, which both allows Candelabra's untap ability to be copied several times, and does the same for Holistic Wisdom if you decide to use it. But other than that, this skeleton doesn't offer much room for extensibility. Orochi Leafcaller prevents any steps that might allow you to use a single mana of one color to produce a lot more mana of another, and you've seen how there are lots of innocuous cards like Copy Artifact or Pyromancer Ascension which go infinite due to circumstances that exist around it.
Ultimately, fast-growing combos take the form "for each X...for each Y where Y increases each time you do X...", and adding 4 or 12 copies of the same card doesn't do much to change that. Far better to add a single additional card that allows reusing the first one a lot more than 4 times, because that's worth a whole new "for each" repetition. The introduction to the 2009 attempt at a large combo might explain this more clearly.
If deck size wasn't an issue, I now know of ways to add at least 43 layers on top of the cards that did make the cut (this would bring it up to 84 cards), and it remains to be seen if moving up to a 99-card limit for Commander still leaves room for any appreciable improvement on top of that.
after all I always wondered if there were a way to do an high amount of dmg without going infinite, I think its all came to duplicating the more possible time a doubling season and try to get an high amount of mana and find some way to untap a Solarion
Also, as far as Solarion, it just doesn't do enough. Combined with Sinking Feeling, it says "{1}: Get more damage." Pretty good especially with multiple Doubling Seasons around, but if 2 mana can simply produce a lot more Doubling Seasons, that will churn out an increase in power far beyond anything Solarian can hope to keep pace with.
Update available, link in the first post. There's a weirdly nice symmetry to seeing a damage figure of "2 -> 34 -> 234".