I saw a 3913 in what I consider ok condition with 1 mag sell on gunbroker for $590. It did have the original box but does that make such a difference?

Internet pricing.

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'Merica!

$590 is too much. I see a 3913 on Armslist for $315 with no box. A plain Jane 3913 would have to be immaculate with box, docs and mags to get anywhere near that price. A LadySmith would be worth more, a 3953 more still, a 3913/14 or 3953/4 Tactical would be worth more still. If you're a collector, you want immaculate, original condition. If you plan on shooting it, then top end for me is about $525-$550 for a 3913TSW or 3953TSW with two mags and original box. Your mileage may vary. For plain Jane 3913 , think $400 with two mags, VG-EXC condition.

So what could the value difference be between having box and papers or not?

The box is only important if you actually have "collector" grade, I think. I'd give $25 more for an original box on any of my Smiths, but it's mostly the gun and mags that I'm interested in. IF the gun were in unfired, or nearly unfired immaculate condition, THEN I think a collector would up the ante for the original box, papers, and cartridge case. I store my pistols in generic boxes ( if I don't have the originals) and the generics ( Plano ) cost about $8 each in quantity.
Brent

I got lucky & snaged My 3913 in 95% condition shortly after it was listed on GB with a $349 buy it now No box but I don't care you can't shoot or CCW the box.