Best case, I would up it to CR 1, or drop it to CR 1/4.
But, I tend to not up CRs that often, even with slightly superior equipment since I expect each encounter to be different and the CRs to be an overall average.
Having no equipment as opposed to just inferior equipment, though, probably should lower the CR.
And, one area in which I raise or lower CR is that of ambush. If the PCs ambush their opponents, I lower the CR. If the opponents ambush the PCs, I raise the CR.
And, by ambush I mean that they prepared ahead of time with things like spells and/or traps, not just that they happened to get to go on a surprise round.
Surprise rounds tend to average out over time anyway, just like slightly superior or inferior equipment will.
But, if either side prepares significantly, that is a major combat advantage. IMO.