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When invoking an aspect in Fate Core for a reroll, and the second roll is worse than the first, can you go with the first roll? Do rerolls in Fate work like rolling with advantage in D&D, or are you stuck with the second roll without spending another Fate point?

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Once you reroll you're stuck with the new result. You don't get to pick the highest of the two; the previous roll's gone.

It's for this reason the authors recommend only rerolling on a –3 or –4 in a sidebar on Fate Core page 68:

The reroll vs the +2

Rerolling the dice is a little riskier than just getting the +2 bonus, but has the potential for greater benefit. We recommend you reserve this option for when you’ve rolled a –3 or a –4 on the dice, to maximize the chance that you’ll get a beneficial result from rerolling. The odds are better that way.

The simple version of the odds at that point is that your chance of rolling –3 or –4 (again) is so vanishing small (~6%) you're nearly guaranteed to at least upgrade to –2, and the odds of getting at least a +0 aren't bad (~61%).

Being able to choose between the two sounds like a viable stunt though, or at least a half-stunt effect. Here's how I might handle it:

Quantum re-entanglement goggles. You get a +1 to Create Advantage with Lore when discerning scientific facts. In addition when you spend a fate point to reroll any science-themed Lore roll, you may keep your choice of the new or old result.

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