Get to Dakmor in hand, Gitrog on table, discard outlet
Draw deck with Dakmor Salvage (or, for cleanup phase kill, craft a hand of Necromancy, Dark Ritual, Skirge Familiar, Elvish Spirit Guide, Crop Rotation; requires land on battlefield; thanks to razzliox for this one)
Infinite black mana. You can do this at instant or sorcery speed. At instant speed, razzliox mentions exile of Elvish Spirit Guide, Crop Rotation on land for land that produces black mana, tap for B, Dark Ritual to BBB, Necromancy as an instant on Skirge Familiar. Discard land and Kozilek, shuffle library. Dakmor for infinite black mana and infinite draw triggers.
Infinite green mana with Riftsweeper. Let's create a cycle in the state graph. Current state: zero green mana, Riftsweeper in hand, Necromancy in hand, Culling the Weak in hand, ESG in exile, infinite black mana, infinite draw triggers. Discard Riftsweeper, Necromancy (as an instant) on Riftsweeper, Riftsweeper ETB, Elvish Spirit Guide to library, draw ESG, exile ESG, one green, Culling the Weak sacrificing Riftsweeper, Riftsweeper and Necromancy to graveyard, discard Kozilek, draw library with draw triggers. New state: one green mana, Riftsweeper in hand, Necromancy in hand, Culling the Weak in hand, ESG in exile, infinite black mana, infinite draw triggers. Cycle complete, infinite green mana.
razzliox, I'd love to hear your updates on the following from a competitive game play perspective, i.e. the following may work, and be very clear to explain in a goldfishing scenario, but may be more vulnerable to disruption:
1 - Dakmor Salvage to generate draw triggers with every flipped land
2 - When you hit Gaea's Blessing or Kozilek, immediately shuffle (there may be edges cases covered by the algorithm, but this works in practice)
3 - Repeat (there may be some edge cases that are covered more fully in your algorithm and proof, mazeTemporal) until draw trigger > number of cards in deck. I find in practice this takes about 5-6 loops to a shuffle trigger.
4 - Draw deck
5 - Discard Kozilek, shuffle into library, and draw so all remaining draw triggers are removed from stack (so we can play non-instants)
5 - Lotus petal, crack for one mana
6 - Discard four lands generating four draw triggers, discard Kozilek shuffling library. mazeTemporal, do you consider this the simplest base case for which you can show every possibility leads, in a finite number of steps, to drawing the entire library to repeat step 5? Of course you can do it with less discarded lands, but it seems in those cases you can only say that you can draw your library with arbitrarily close to 1 probability. For example, say you crack Lotus Petal, discard land (draw trigger), Kozilek shuffle, but the order of the library is not with the petal in the third slot, then you have to shuffle with the first dredge and repeat until petal is in third slot, which will get arbitrarily close to one, but in an infinite number of steps.
So, in the above, crack Petal, 4x land/draw triggers, Kozilek. If at least one land in top 2, then we increase our draw triggers and repeat. If Petal and Kozilek in top two, then bottom four are lands. Dredge, hitting two lands, draw the last two lands, shuffle, and then draw 4-card library with 4+ draw triggers on stack.
Now, it seems it is easier to just use free rocks to land Skirge Familiar, after drawing the deck, but I want to better understand this particular interaction, as it is closely related to the general process of drawing the deck. The above process with Petal is how we win, it seems, with Praetor's Grasp (i.e. discarding four lands after casting Praetor's Grasp), exiling everybody's library (if necessary).
It seems the above allows you create more draw triggers than library size in about five minutes. After that, all the infinite interactions, like creating infinite mana, or casting Praetor's Grasp repeatedly, it seems, can be shortcut with fairly straightforward explanations.
mazeTemporal, I recognize you as having created the algorithm which shows, deterministically, how to draw the deck with Dakmor Salvage, discard outlet, and Gitrog: https://www.reddit.com/r/CompetitiveEDH/comments/4fbhk1/proof_of_determinacy_for_the_gitrog_monster_combo/
razzliox, I'd love to hear your updates on the following from a competitive game play perspective, i.e. the following may work, and be very clear to explain in a goldfishing scenario, but may be more vulnerable to disruption:
1 - Dakmor Salvage to generate draw triggers with every flipped land
2 - When you hit Gaea's Blessing or Kozilek, immediately shuffle (there may be edges cases covered by the algorithm, but this works in practice)
3 - Repeat (there may be some edge cases that are covered more fully in your algorithm and proof, mazeTemporal) until draw trigger > number of cards in deck. I find in practice this takes about 5-6 loops to a shuffle trigger.
4 - Draw deck
5 - Discard Kozilek, shuffle into library, and draw so all remaining draw triggers are removed from stack (so we can play non-instants)
5 - Lotus petal, crack for one mana
6 - Discard four lands generating four draw triggers, discard Kozilek shuffling library. mazeTemporal, do you consider this the simplest base case for which you can show every possibility leads, in a finite number of steps, to drawing the entire library to repeat step 5? Of course you can do it with less discarded lands, but it seems in those cases you can only say that you can draw your library with arbitrarily close to 1 probability. For example, say you crack Lotus Petal, discard land (draw trigger), Kozilek shuffle, but the order of the library is not with the petal in the third slot, then you have to shuffle with the first dredge and repeat until petal is in third slot, which will get arbitrarily close to one, but in an infinite number of steps.
So, in the above, crack Petal, 4x land/draw triggers, Kozilek. If at least one land in top 2, then we increase our draw triggers and repeat. If Petal and Kozilek in top two, then bottom four are lands. Dredge, hitting two lands, draw the last two lands, shuffle, and then draw 4-card library with 4+ draw triggers on stack.
Now, it seems it is easier to just use free rocks to land Skirge Familiar, after drawing the deck, but I want to better understand this particular interaction, as it is closely related to the general process of drawing the deck. The above process with Petal is how we win, it seems, with Praetor's Grasp (i.e. discarding four lands after casting Praetor's Grasp), exiling everybody's library (if necessary).
It seems the above allows you create more draw triggers than library size in about five minutes. After that, all the infinite interactions, like creating infinite mana, or casting Praetor's Grasp repeatedly, it seems, can be shortcut with fairly straightforward explanations.