This matchup is a race against their colorless Eldrazi threats and land-based engine (Urza's Saga, Eldrazi Temple, Ugin's Labyrinth). Unholy Heat is excellent removal for Basking Broodscale, and once we hit delirium it deals 6 damage, which is enough to kill Sowing Mycospawn too. Meltdown answers their Urza's Saga Construct tokens and Talisman, while Tormod's Crypt disrupts Malevolent Rumble's graveyard value and can strip fuel before Emrakul, the Promised End gets cheaper. Cut low-impact pump/burn that doesn't trade well with their big bodies: Mutagenic Growth, Lava Dart, and Violent Urge are the weakest cards against 2/2s and bigger that don't die to 1 damage.
Mono-Green Eldrazi ramps into huge colorless threats like Emrakul, the Promised End and Ulamog, the Ceaseless Hunger, so your best plan is racing them before their ramp lands like Eldrazi Temple and Ugin's Labyrinth come online. Consign to Memory can counter triggered abilities like Sowing Mycospawn's land search before it accelerates them further, and Unholy Heat handles creatures like Fanatic of Rhonas or Slumbering Trudge with delirium. Mutagenic Growth and Violent Urge don't meaningfully help you race or interact with their giant threats, so they come out. Prioritize aggression and try to end the game before turn 5-6, since you have very little that can answer a resolved Emrakul or Ulamog.
Mono Green Eldrazi is a slower ramp deck relying on Urza's Saga, Eldrazi Temple, and Sowing Mycospawn for mana advantage. Meltdown can't touch Urza's Saga itself, since it is an Enchantment Land rather than an artifact, but it is still good at sweeping the Construct tokens the Saga makes, along with Blade of the Bloodchief and other cheap artifacts like Talisman of Resilience, Springleaf Drum, and Vexing Bauble, before they matter. Tormod's Crypt shrinks Emrakul's cost reduction, which scales with the card types in their graveyard, and turns off graveyard-based plays like Shifting Woodland's delirium after Malevolent Rumble fills their yard. Unholy Heat answers Basking Broodscale before it adapts and other small creatures, and with delirium its 6 damage can kill bigger threats like Devourer of Destiny. It can't target Emrakul, though, since Emrakul has protection from instants. Mutagenic Growth and Violent Urge are cut since this matchup rewards proactive disruption and racing over combat tricks against a deck that wants to go over the top with Emrakul or Devourer of Destiny.
Suggested new sideboard cards to pick up for the current metagame.
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