The deck is entirely built around a powerful interaction between Gitrog and Dakmor Salvage, or dredge overall. Dredge is an absurd keyword, and even WotC realised this after they released some cards with it. It's arguably the best graveyard filling mechanics and combo enablers, which Gitrog uses the best of all existing Legendaries in the Format. So, for those of you who don't know what dredge is, or don't understand it very well, here's a simple definition:
If a card with 'dredge X' is in your graveyard, whenever you would draw a card, you may put EXACTLY X cards from the top of your library into your graveyard instead. If you do, return the dredge card to your hand.
Note, that dredge is a so-called replacement effect, which effectively means that you decide whether to use it or not upon resolution of the draw trigger. For example, if you have a draw trigger on the stack and your opponent wants to respond to it by casting a spell, after their spell resolves you are THEN allowed to choose if you want to draw or 'dredge the draw'. This allows you to make decisions based on more information, and makes it impossible for your opponent to deprive you of your card by grave exile effects in response to the draw trigger.
Now, once we've covered dredge let's take a look at our commander herself. The Gitrog Monster is a (3BG) 6/6 legendary Frog Horror with deathtouch. She doesn't die to Lightning Bolt, she doesn't die to fatal Push or Dismember, overall she's not that easy to kill for some decks.
What makes Gitrog particularly interesting though, are her last 3 abilities. The first one states:
At the beginning of your upkeep, sacrifice The Gitrog Monster unless you sacrifice a land.
When you first read it you might think 'Okay, it's fair. She's an undercosted 6/6 with deathtouch, she has to have some downsides.' Well, when you read the second ability, you realise it's actually okay, because Gitrog has a built-in Exploration effect. Seems unfair already? Well, the best about the Froggo though is the last ability, which is precisely the one which, paired with Dakmor Salvage's dredge, enables our combo. The ability states:
Whenever a land is put into your graveyard from ANYWHERE, draw a card.
In case you didn't realise, this is absurd. With this beast on the battlefield, your fetch lands become cantrips as well, Lake of the Dead isn't as painful to play as before, and cycling lands become almost Ancestral Recalls, drawing 2 cards for 1 mana on instant speed.
The last component of our combo is a discard outlet, in other words an effect that allows us to discard cards from our hand for free at instant speed. There are numerous effects like this in the game, and the list currently uses 4 of the best (though I originally started with 5, with an addition of Oona's Prowler).
Some of you might already see where this is going, but I'll go through it step by step. Once you've assembled the pieces (Gitrog + Discard outlet on the battlefield and Dakmor Salvage in your hand) you're ready to go off.
A good way to start any combo is drawing your entire deck.
As it turns out, you don't need Enter the Infinite to do that.
All you have to do is repeatedly discard Dakmor Salvage using your discard outlet, and dredge the draw you get from Gitrog's last ability.
The pattern is:
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Discard Dakmor Salvage, putting a draw trigger on the stack.
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Dredge the very same draw, milling 2 cards into your graveyard.
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If you milled 2 nonland, non-reshuffling cards, discard Dakmor Salvage again
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If you milled one land and one nonland, non-reshuffling card, or two land cards, (which puts a draw trigger on the stack), respond to the draw trigger by discarding Dakmor Salvage again.
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If you milled into a reshuffling card, with a land or nonland, resolve the reshuffle trigger before the possible draw trigger, and then respond to it by discarding Dakmor Salvage again.
Following this pattern will slowly accumulate draw triggers on the stack, eventually reaching the number of cards in your library (+graveyard) or exceeding it. As this happens, after the next reshuffler you mill into, reshuffle and then resolve a number of draw triggers equal to the number of cards in your library. If you have any additional X draw triggers on the stack, just respond to them by discarding (X-1) nonland cards and Kozilek, thus reshuffling that many cards and draw them. This way you end up drawing your entire library for no mana at all. From now on we can proceed to actually shortcuttable loops that lead to winning the game.
Note: The pattern above is NOT shortcuttable, even despite the fact that every possible order of cards in your deck will eventually lead to you drawing your entire library. It will happen at a different pace though, which effectively means that you have to manually go through the process. It should take between 3 to 10 minutes if you get really unlucky.
Once you have your entire deck in your hand, proceed to this shortcuttable loop:
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Discard Kozilek, and allow it to reshuffle itself
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Discard any land, drawing Kozilek back
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Discard Kozilek, and allow it to reshuffle itself and the land back
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Play Lotus Petal
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Discard and dredge Dakmor Salvage, putting a draw trigger on the stack and a reshuffle trigger on top of it
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Resolve the reshuffle
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With the draw trigger on the stack, discard and dredge Dakmor Salvage again, ordering the triggers the same way
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Resolve the reshuffle, then dredge Dakmor for the final time, but this time before the reshuffle trigger resolves, sacrifice Lotus Petal for mana (usually black, but for safety add green as well so that you have Veil of Summer and Autumn's Veil backup if necessary for whatever reason).
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Resolve the reshuffle trigger
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Resolve 3 draw triggers
You're back where you started but with one mana more in the pool. Repeat the loop for 'infinite' mana.
Now it's time for the final killing loop:
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Cast Collective Brutality, draining your opponent for 2 life
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Cycle any 2 of your cycling lands
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In response to 4 draw triggers, discard Kozilek
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Resolve the reshuffle trigger
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Resolve 4 draw triggers
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Repeat previous steps
Congratulations! You've just killed your opponent! But it's just the beginning of Gitrog's capabilities.