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So, question that comes up because of some Inquisition choices:
If something says "You can re-roll (whatever) for units with the (whatever)", does that mean you can re-roll 'succesful' results?

I ask, because - For example - Inquisitors with the right Ordo do get those rerolls, but they also bring weapons like Thunder Hammers that give them a -1 to hit. Normally this would mean they roll, hit on '3s', re-roll 1s and 2s, and then remove 1 to the rolls so that those 3s they rolled don't get to hit anymore. However, since they can apparently reroll anything that they want to, they should theoretically be able to re-roll the 'succesful' 3 result, right?

When all else fails, read the rule exactly as it is written.

A rule will say either:

"Re-roll failed Fight rolls..."

or

"Re-roll Fight rolls..."

Unless otherwise instructed (per FAQ etc.) always take the rules at face value initially.

From what I've seen there are three types of re-rolls:

Re-roll failed rolls, which happens before modifiers and so fits the example you provided.

Re-roll the result, which forces you to re-roll all dice inculding the successful rolls (the Dark Eldar's re-roll failed charges would be an example of this, and the FAQ has clarified that you do not get a choice on which dice you re-roll, it has to be all of them).

Re-roll X, which let you re-roll either a specific number of dice (like the Strategem's re-roll a single dice), a specific natural roll (like the mass of re-roll 1's rules out there) and the much rarer re-roll any dice which gives you complete freedom on which dive to re-roll (can't think of any examples of the top of my head for this).

So which of the above does the wording on the the inquisition rules best match?

It's funny because the way that the Inquisitorial rules are worded (You can re-roll hit rolls and wound rolls for) when compared to something like Logan Grimnar's rule (You can re-roll failed hit rolls) means that yes, you can re-roll successful rolls just fine for Inquisitors. Nice catch!

The core rules for re-rolls don't restrict them to failed rolls, and there are lots of situations where you might want to re-roll successful results in the first place.

I would forge the narrative of Inquisitors being so single minded and have OPPlzNerfHax that they can do whatever they want, including ignoring the re-rolls before modifiers rule.

Imateria,
There is nothing categorizing re-rolls, you are seeing a pattern that simply does not exist.

Opening Poster,
It will always be determined by the body of the Rule in question and, in this case, those instructions grant permission to re-roll ANY result by not limiting us to just the 'failed' ones.

In my honest opinion, I would like to see the word 'failed' or 'success' removed from these Rules entirely. The amount of feared shenanigans that might occur from such a change are not only minor, but those could occur fall more under 'Tactical Decisions' instead of 'Exploits.' Due to the fact the players are going to want to get the maximum amount of damage possible, they are unlikely to ever use the ability to re-roll 'successful' results and thus said Rule only ever gets used on failed results anyway. For those abilities that force 'successful' re-rolls to occur, simply grant the opponents permission to choose the dice to be re-rolled and they will ensure it is used on every 'success,' every time, to limit the amount of damage they take.

Though adding a "Natural 1/6 Rule" would have worked better for the 'Get Hots' situation!
Only Game Workshop would, through a Frequently Asked Question answer, try to define 'Natural 1' so poorly that it breaks other situations
Then keep the poor-definition version of the concept, and the oddities it causes, instead of using a very common gaming term....