Ok, as promised...
I started simulating what happens at the reshuffle. Since we're interested in testing the filtering effect of Venture, I only shuffled in cards that were in the original draw pile. I didn't shuffle in Venture itself, whatever was in the Venture hand, or any buys or previous hands. All of that stuff would be there in reality, but it seems irrelevant when looking for a filtering effect.
Let T be the number of treasures, and D be the number of non-treasure draws (dead cards). The expected number of cards that Venture draws is (T + D + 1) / (T + 1).
I construct a deck with 3 treasures and 8 dead cards. We expect Venture will draw 3 cards in this case. Because of this, we'll compare it to a Smithy when running the numbers.
That math has been eating at me for a while. Let's say all the treasures are Copper. We expect that Venture's draw has a value of $1/3 per card, but the deck's average card value is $3/11.
On to the experiments:
First, we take a deck containing a Platinum, a Gold, a Copper, and 8 dead cards. We look at the next two hands in if we draw them normally, if we play a Smithy this turn, and if we play a Venture this turn.
Deck: 1x Platinum, 1x Gold, 1x Copper, 8x dead
Percentage of hands by coin value (500000 trials):
Coin value | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10
Next hand, normal | 12.17% | 15.09% | 0.00% | 15.14% | 12.16% | 15.06% | 12.23% | 0.00% | 12.11% | 6.03% | 0.00%
Second hand, normal | 12.14% | 15.11% | 0.00% | 15.23% | 12.09% | 15.11% | 12.14% | 0.00% | 12.11% | 6.07% | 0.00%
Next hand, Venture | 12.07% | 15.25% | 0.00% | 15.09% | 13.79% | 15.12% | 13.76% | 0.00% | 13.74% | 1.18% | 0.00%
Second hand, Venture | 16.91% | 16.95% | 0.00% | 17.12% | 9.59% | 17.05% | 9.68% | 0.00% | 9.64% | 3.07% | 0.00%
Next hand, Smithy | 12.16% | 15.17% | 0.00% | 15.21% | 12.07% | 15.13% | 12.15% | 0.00% | 12.09% | 6.02% | 0.00%
Second hand, Smithy | 12.00% | 15.11% | 0.00% | 15.17% | 12.13% | 15.19% | 12.22% | 0.00% | 12.11% | 6.07% | 0.00%
The normal hands and Smithy hands all have comparable coin values. The next Venture hands are significantly worse. I strongly suspect that it's only the reshuffle hand that's worse on average. Note that the hand after Venture is almost as good, and that hand is also the least likely to trigger a reshuffle.
In a normal game, though, having a crappy hand at the reshuffle is a good thing. Let's try a different experiment. This time, we'll construct two decks. The first deck contains 6 Coppers, 14 dead cards, and 1 Silver. The second is the same, but it contains a Venture instead of the Silver. Note that the Venture will always be worth as much as the Silver. We'll run through those decks a bunch of times and check the distribution of hand values drawn.
Deck 1: 14x dead, 6x Copper, 1x Silver
Deck 2: 14x dead, 6x Copper, 1x Venture
Percentage of hands by coin value (5000000 turns):
Coin value | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7
Deck 1 | 9.84% | 29.51% | 31.74% | 19.68% | 7.75% | 1.41% | 0.07% | 0.00%
Deck 2 | 9.87% | 29.35% | 31.49% | 19.82% | 7.93% | 1.46% | 0.08% | 0.00%
Those numbers are interesting. With that many trials, I think the percentages indicate a legitimate difference that can be chalked up to Venture's filtering; however, it's imperceptibly small. Venture gets ever so slightly better hands.
Let's try it again, this time with a 20-card deck so that nothing misses the shuffle in the Silver deck:
Deck 1: 6x Copper, 13x dead, 1x Silver
Deck 2: 6x Copper, 13x dead, 1x Venture
Percentage of hands by coin value (5000000 turns):
Coin value | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7
Deck 1 | 8.28% | 27.69% | 32.29% | 21.13% | 8.79% | 1.72% | 0.10% | 0.00%
Deck 2 | 8.37% | 27.55% | 31.91% | 21.16% | 9.10% | 1.81% | 0.10% | 0.00%
Similar results. Venture gets ever-so-slightly better hands.
Finally, let's look at a more realistic deck, where Venture has an average value of $3 and replaces a Gold.
Deck: 3x Copper, 5x dead, 4x Gold, 3x Silver
Deck: 5x dead, 3x Copper, 3x Gold, 3x Silver, 1x Venture
Percentage of hands by coin value (5000000 turns):
Coin value | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15
Deck 1 | 0.03% | 0.50% | 1.51% | 4.01% | 8.00% | 11.46% | 16.47% | 16.57% | 15.49% | 12.41% | 7.19% | 4.20% | 1.57% | 0.50% | 0.10% | 0.00%
Deck 2 | 0.04% | 0.51% | 1.56% | 4.13% | 7.88% | 11.69% | 15.86% | 16.59% | 15.38% | 12.06% | 7.78% | 4.10% | 1.80% | 0.52% | 0.11% | 0.00%
That one is more complex. Venture is beneficial depending on your target treasure value.
Before anyone says it, I've run these trials multiple times with a few different parameters, and the results are consistent with one another to the point that I'm convinced we're not looking at statistical noise.
Conclusion:
Because of the expected value formula, we expect Venture to draw cards that are worth more than the average value from the draw pile. Simulations show this to be the case. Venture is sending better-than-average cards to the discard, filtering in the wrong direction. You don't notice the effect until you reach the end of the draw pile, though. At the reshuffle, you tend to draw a slightly worse hand.
There's another side of this. Venture, being a card that draws, is more likely to miss the reshuffle. It's also a better than average treasure by definition.
In Dominion, it's a good thing to have bad hands miss the reshuffle. It's a bad thing to have better than average treasures miss the reshuffle. These effects nearly cancel each other out if you always play Venture. There is an slight difference in hand values that you'd never notice in practice.
I'd be really interested in someone explaining the math of what happens near the reshuffle point. It's been way too long since I've done any statistics work.