I encountered this situation today in the Pauper League and in examining the game, this decision had a huge impact on how the game played out.
It is game three and you’re on the play. You are on BG Aristocrats and your opponent is on Flicker Tron. You won game one where your opponent went to four cards and you easily ran them over. In game two Tron did its thing and assembled a lock.
It’s now game three. Here is your deck:

You have sided out the two Plagued Rusalka and two Nest Invader for three Mesmeric Fiend and a Falkenrath Noble. You assume your opponent is on this deck or a very similar list:

Your starting hand isn’t amazing but it includes Carrion Feeder and Loam Dryad – key cards to explosive starts. Your opponent has taken a mulligan to six.
You lead on Carrion Feeder and they lead on Urza’s Tower. On your turn you draw Mesmeric Fiend – one of the best cards in this situation. You cast it and stack the triggers with Carrion Feeder so that you can nab the card forever. This is what you see:

The cards you can take are Ephemerate, Impulse, Prophetic Prism, Stonehorn Dignitary, and Mulldrifter. The other card in their hand is Cave of Temptation.
What card do you take and why? You’ll find my answer below.
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There are merits to every card you can take. Let’s start with Ephemerate. This card is key to their endgame engine and with either Mulldrifter or Stonehorn it can bury you, either under cards or blanked combat steps. Exiling it is a good call since Mnemonic Wall can easily get it back. However, the deck runs anywhere from two to three other copies of this effect and given the other cards in their hand, taking Ephemerate doesn’t seem wise.
What about Prophetic Prism? This is the only card they can currently cast next turn and it sets up their Impulse on turn three which digs them deeper and potentially helps to set up Tron. Prism also replaces itself and while they already have fixing in the form of Cave, taking Prism does buy you time which is what you need right now. Of course, so much of this is undone by them drawing a land, but Prism, to me, remains a viable option.
Next up is Impulse. As good as this card is I don’t think you can justify taking it here. Impulse digs them four deep and can find other hammers like Moment’s Peace or another Urza Land, but it costs them time. Time is something you want them to be taking so leaving them that option doesn’t seem too terrible.
Next up is Stonehorn Dignitary. This card is a nightmare. While you have reach in the form of Falkenrath Noble and Lampad of Death’s Vigil, you need to attack to get them low enough where your reach can close the game through a Pulse of Murasa. They are, at best, two turns away from Stonehorn Dignitary which, given the cards in your hand and composition of your deck, you cannot win by. Taking Stonehorn means they need to find another other fast – something Impulse and Mulldrifter can do. Still, if you’re looking for time taking Stonehorn buys you the most.
Mulldrifter might be the most flexible card in this hand, coming down on turn three, four, or five. However if they are able to cast Mulldrifter for five there’s a good chance you’ve already lost the game. If they cast it for three, you are likely able to pull ahead. Given the variance here, I don’t think you can reasonably take the flying fish.
That leaves the cards to take as Prophetic Prism and Stonehorn Dignitary. I believe I made the wrong decision and I took Prism, thinking that the draw I was denying them would be good enough. Their next two draws were lands – Tranquil Cove and Urza’s Mine – meaning I lost my combat steps in short order. Taking Dignitary forces them to spend resources to find another (or a Moment’s Peace) while you’re able to build out your army and deploy threats, getting them low enough to where Lampad or Noble can finish the job.