You're definitely correct mathematically. However, Venture can augment the value of another Venture by $1, and each Venture only adds $1 by itself. I think, though, that my original point wasn't supposed to be concerned with the average "value" of Venture at all (but of course it sounds a little ambiguous).
Well, venture vs gold is a pretty significant one - basically take the gold for a long time.
Wait, really? I mean, it depends on whether there is Copper trashing and several other factors, but I usually go by taking only 1 Gold over Ventures.
I feel like this is not necessarily true. Already having Ventures in your deck increases the average value of further Ventures, plus you have an effectively smaller deck. If you simulate BMU with Colonies, a bot that buys only Ventures at $6 absolutely crushes a bot that doesn't buy any Ventures (~73-21), even though according to you, one would pretty much never want a Venture at all in such a deck. I can't claim that the bots were optimized, but it shouldn't matter for the purpose of this argument.
Venture is relatively worthless in Province games, though, where hitting $8 is easy enough, unless you can couple it with +buy. The problem is that it also skips the vast majority of cards that give +buy.
EDIT: Scratch that last part. BMU Venture-only beats normal BMU by a fair margin as well (~51-40). Clearly average value isn't the metric that you want to optimize when buying your first Venture.
See, this is the sort of thing that the math helps you address concretely. The idea of Venture adding $1 to the average Treasure is extremely useful, but what exactly is the value of the Venture chain? Your intuition breaks down, and then your experience tells you the wrong thing.
This is why the math is helpful: you should *definitely* prefer Gold to Venture.
The value of the venture is
$1 + $d + $v/(1+N)
Let's say you go with your proposed 1 gold, then ventures, strategy. Let's say, generously, that you have 7 silvers in your deck. Then d = 1.4.
Now you start buying ventures because even though short-term it's bad, you believe that long-term you'll get nice pretty chains. How many ventures do you have to get before your venture (chain) does better than the gold? In order to get the total value above $3, you need v/(1+N) > 0.6, and with (7 coppers + 7 silvers + 1 gold) = 15 cards, you need to get 9 Ventures. You could get fewer silvers, but then d goes down. You could get more silvers to improve d, but then N goes up.
Yes, reshuffling and cycling helps a bit, but the more important effect is that, as WW points out, the Gold provides more value now. The Venture provides more value later ... but the math says, does it really? The Venture provides more value when you get 9 Ventures; are you really going to get 9 Ventures in the game?
Certainly you can drown in equations and there is no substitute to real, in-game experience. But the real experience is misleading because *your* experience mainly tells you, Venture is good, buy Venture, remember those awesome Venture chains; you don't realize that without trashing, the Venture chains you remembered fondly will just fizzle compared to gold until you get, like, all 10 Ventures, at which point the game is long over.
A corollary to these results is that in a Colony game without trashing, the reason why Ventures do better than Gold is not because of Venture chains. In order to get an extra $1 out of Venture chains, you need to buy more Ventures than are available in the stack. The reason why Ventures do better than Gold is primarily because of the chance that they'll run into a lucky platinum. (plus, as pointed out, one bot can buy venture at $5, and the other can't)
