It gives you 1+ [the average value of the rest of your treasures]. Roughly, I think this would be greater than 3 when (number silvers + 2*number of golds) > (number of coppers). So if you've trashed no coppers, it'll be after you have 3 or 4 silvers and 2 golds.
That's not right - you need number of golds > number of coppers. (Easy check: when you find a silver, you break even, so you can ignore them.)
So without copper trashing and without platinums, venture will basically never beat gold.
But this doesn't factor in the possibility of Venture hitting Venture.
If we factor this in, letting b be the number of basic treasures you have, g the number of golds you have, v the number of ventures you have (apart from the one you're playing), and c the number of coppers you have, the condition is g + vb/(b+1) > c.
(This is only looking at the value of Venture, not other benefits. Also, to be correct for a given play, g,v,b,c should be determined by only your draw deck, not your entire deck--I ignored that for simplicity.)
To derive, start with the condition
(3g + 2s + c)/b + v/(b+1) > 2