Flash is definitely the reason you can do this. When the Mulldrifter ETBs, it puts 2 triggers on the stack (if cast with Evoke). The draw and sac triggers. Normally, you cannot cast a creature at this time due to the triggers, but since the Fiend has Flash, you can cast it with the sac me trigger on the stack, and sac the Drifter for Emerge
W may only be paid with white mana. U may only be paid with blue mana. B may only be paid with black mana. R may only be paid with red mana. G may only be paid with green mana. C may only be paid with colorless mana. 1 may be paid with white, blue, black, red, green, or clolorless mana.
Effects that reduce the cost to cast a creature spell (such as Heartless Summoning) don't affect its converted mana cost (according to C.R. 202.3, converted mana cost is generally based only on mana cost). In this case, Mulldrifter's converted mana cost remains 5. Moreover, Mulldrifter on the battlefield isn't a spell anymore, so it won't be affected by Heartless Summoning's cost reduction anyway.
There are no official Rules about Emerge yet. But according to the reminder text explain this ability , Emerge cost should be Alternative cost.
However , in Daily MTG , Emerge is an ability which consist of additional cost/cost reduction too.
To determine Elder deep-fiend's total cost you actually pay , start with spell's Mana cost or Alternative cost ([5][U][U]) in this case. Then plus additional cost (sacrifice Mulldrifter) and cost increases (no in this case). Then minus all cost reduction (CMC of Mulldrifter is 5 - no matter you have cast it with Evoke cost or not) and Heartless summoning.
So , [5][U][U] + sacrifice Mulldrifter - [5] - [2] = [U][U] + sacrifice Mulldrifter. The effect from HS can't reduce [U][U] anyway.
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Yes , I was Rules Advisor.
Obviously , English is not my first Language (sorry about that ).
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I believe flash is the essential part, without it you cannot do this.
If you're sacrificing Mulldrifter, not at all, beyond reducing Mulldrifter's cost by 2. If you're sacrificing Offalsnout, then it will reduce Elder Deep-Fiend's Emerge cost in addition to the cost reduction from Offalsnout.
So Evoke and Emerge are reduced by HS then. Cool.
However , in Daily MTG , Emerge is an ability which consist of additional cost/cost reduction too.
To determine Elder deep-fiend's total cost you actually pay , start with spell's Mana cost or Alternative cost ([5][U][U]) in this case. Then plus additional cost (sacrifice Mulldrifter) and cost increases (no in this case). Then minus all cost reduction (CMC of Mulldrifter is 5 - no matter you have cast it with Evoke cost or not) and Heartless summoning.
So , [5][U][U] + sacrifice Mulldrifter - [5] - [2] = [U][U] + sacrifice Mulldrifter. The effect from HS can't reduce [U][U] anyway.
Obviously , English is not my first Language (sorry about that ).