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Perilous Research has a comma and "then" in the text description. I am unclear whether this allows triggered abilities to be considered in the middle of the spell resolution. Specifically, if I control Improbable Alliance, when I cast Perilous Research and draw two cards, can I sacrifice the token that has just been created by the triggered ability of Improbable alliance??

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No, whatever permanent you want to sacrifice to Perilous Research already has to be on the battlefield before it starts resolving.

Improbable Alliance does trigger in the middle of Perilous Research's resolution, as soon as you draw the two cards and before you sacrifice a permanent. However, triggered abilities only enter the stack, let alone resolve, the next time a player would get priority. That only happens after Perilous Research has finished resolving, so you can't sacrifice the token that would be created on that specific Improbable Alliance trigger.

603.2. Whenever a game event or game state matches a triggered ability’s trigger event, that ability automatically triggers. The ability doesn’t do anything at this point.

603.3. Once an ability has triggered, its controller puts it on the stack as an object that’s not a card the next time a player would receive priority.

117.3b The active player receives priority after a spell or ability (other than a mana ability) resolves.

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    Don't know if it's even worth mentioning, but the bold summary sentence is correct for this question but not true as a general rule/principle. If in theory you had a replacement effect such as "whenever you would draw a card, instead create a food token", or something along those lines, then you would be able to sacrifice your new food token that didn't exist when Perilous Research started to resolve. – GendoIkari Jun 10 at 2:25

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