Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[Catalytic]

When to Venture

(I would like to thank the commentators in this thread for there invaluable input; you have forced me to be clearer and correct some of my errors and I thank you.)

I tend to play decks with a lot of money (I know; I'm boring).  As such, I have an interest in alternative treasures and how they interact with your deck.  I wanted to provide my thoughts on Venture.

Venture is quickly becoming one of my favorite additions to a low action / heavy money deck.  Part of the problem for a money-centric deck is what you should do with $5 hands.  Do you go with another silver?  Buy another terminal that might conflict with your other terminals?  Venture provides an answer: if you have a couple of enablers in your deck and it is not yet time to pick up Duchies, Venture is a good solution.

Big Money / Enabler / Venture

A single Venture is strictly better than Silver in a pure money deck (ignoring  edge cases like Horn of Plenty, Potion and Philosopher's Stone) since you are guaranteed to hit $2 with every play (the $1 from Venture and Venture will find at least a Copper) and can be worth as much as $4 (assuming no Platinum of course).  So, if you hit $5, a single Venture is a better purchase than Silver in a pure money deck (you would hope so for $5).  Stacking Ventures provides potentially an even larger return on your investment which Silver cannot.  So, multiple Ventures provide an even larger benefit than simple Silvers.

But, of course, playing a pure money deck is both boring and inefficient.  So, you want to add in a couple of Big Money enablers (e.g. Envoy, Smithy, Monument, etc.) to speed up your deck and make it competitve.  But then your Venture is always in danger of bypassing your action cards looking for that next Treasure card.

How bad is it to skip a terminal action in a money deck?  Not a hinderance at all. Using Geronimoo's Simulator (http://dominionsimulator.wordpress.com/), I edited the optimized Smithy, Envoy, Monument and Courtyard bots to simply purchase Venture whenever the deck hit $5 assuming that it was not yet time to purchase Duchies.  The results:

Venture greatly improves Smithy / Big Money:
Smithy / Venture beats Smithy 55% to 37%.
Smithy / Venture beats Big Money Ultimate 80% to 15% (Smithy beats BMU 72% - 22%).

Venture does not improve Envoy much if at all:
Envoy / Venture ties Envoy 46% to 46%.
Envoy / Venture beats Big Money Ultimate 81% to 15% (Envoy beats BMU 80% to 15%)

Venture greatly improves Monument / Big Money:
Monument / Venture beats Monument 60% to 37%
Monument / Venture beats Big Money Ultimate 87% to 11% (Monument beats BMU 80% - 17%)

Courtyard / Venture is only a slight improvement on straight Courtyard:
Courtyard / Venture beats Courtyard 46% to 44%
Courtyard / Venture beats Big Money Ultimate 84% to 12% (Courtyard beats BMU 82% to 13%)

So, there is no reason to worry about Venture bypassing your Big Money terminal enablers; Venture empowers the Big Money deck by keeping the $ rolling and helping you hit the crucial $5 and $8 price points and missing your terminal action is no drawback to your deck.

Big Money / Copper Trashing / Venture

But, where Venture really shines is in decks with light copper trashing.  Adding Venture to decks with Moneylender or Spice Merchant increases the expected value of Venture.  As your money density increases, so does the value of Venture.  Moneylender and Spice Merchant allow you to purchase quality Treasure, trash low quality treasure and Venture will go and find the high quality treasure and become increasingly less likely to find Copper.  (I recommend looking over WanderingWinder's excellent article on Money based decks: http://dominionstrategy.com/2012/02/27/the-keys-to-big-money-money-density-and-opportunity-cost/).

Moneylender / Venture improves greatly over a single Moneylender:
Moneylender / Venture beats Moneylender 64% to 28%
Moneylender / Venture beats Big Money Ultimate 68% to 25% (Moneylender beats BMU 49% to 42%)

Spice Merchant / Venture improves greatly over a single Spice Merchant:
Spice Merchant / Venture beats Spice Merchant 67% to 26%
Spice Merchant / Venture beats Big Money Ultimate 59% to 33% (BMU beats Spice Merchant 54% to 38%)

As you can see, Venture drastically improves as Coppers are trashed out.  I am not a fan of Loan / Venture but that is more due to my dislike of Loan (which might be a future write-up).  Obviously, Venture would be nice in Chapel decks as well and provides a solid 5/2 opening if other strong 5s are lacking or minus strong Engine possibilities.

Venture In the Face of Attacks

How does Venture fair in the face of attacks?  Venture is a nice soft counter in the face of handsize reduction attacks like Militia and Goons since it will search for another card, effectively giving you a four card hand thus cutting the power of the Goons/Militia/Torturer style attack in half.  Venture thus provides a nice soft counter to handsize attacks.

Of particular note, Venture can be a good soft counter to Ghost Ship.  Ghost Ship's attack can be particularly vicious since it effects both this turn (via handsize reduction) and future turns (forcing you to redraw the previous cards and thus slowing cycling time; a Ghost Ship attack actually slows down your entire game unless your deck has serious and consistent drawing power). But, Venture can both reduce the this turn effect and the slow down effect.  By putting non-Treasure cards on top of your deck, Venture can cycle through them, gaining a fourth card (another Treasure) and skipping over Curses, extraneous Actions and Green.  In the face of Ghost Ship, Venture lets you effectively discard Green Cards, conflicting terminal actions and Curses.

In a similar vein, Venture can counter deck inspection attacks that put Green on top of your deck and has synergy with deck inspection plays.  Cards like Bureaucrat, Rabble, Fortune Teller, etc. try to slow down your deck by forcing you to draw Green on your following turn (and thus reducing your hand quality), but Venture can cut through the Green and search for the next treasure.

For similar reasons, cards that help you reorder the top of your deck (e.g. Navigator) can help cut through the Green by placing any Green at the top of the deck and playing Venture to bypass it for the next treasure.  If it is worth the trouble of setting this up is questionable  but there is some benefit to be found in the combination.

Venture can help against cursers as well.  Swindler's power to turn Coppers into Curses can be brutal to some decks, but Venture can turn that negative into a small positive since Swindler's propensity in the early game to turn Coppers into Curses thins the Copper in the deck which means Venture is more likely to hit the better treasures (as in the Spice Merchant / Moneylender case).  If Swindler is used to load your deck up on terminals, Venture can help you bypass the terminals in search of other Treasure cards effectively reducing the clutter that Swindler can cause.

In a Witch, Young Witch or Sea Hag battle, Venture can smooth your deck once the curses are dealt out since it can search past the curses to look for Treasure.

On the flip side, Venture will be hurt by attacks like Ambassador, Mountebank and Jester since those attacks can also add Copper to your deck which reduces the value of Venture considerably.

Venture in Green Decks

Venture can be a valuable asset in a heavy green deck; it can make the difference between hitting that crucial $ point and missing it.  In any deck where you have far more Green than usual, Venture can help you search past the green.

That said, Venture clashes directly at the $5 price point in a Duke / Duchy deck and needs to be bought either before or after it is time to make the Duke / Duchy run if it should be at all.

Venture is ideal in money-based Silk Road decks since you are green heavy and your primary buying power will come from finding enough Treasure fast enough.  This is not typically an ideal Silk Road strategy, but Venture does provide a boost in money heavy Green deck.

Venture will not work in a Vineyards deck though since Vineyards decks are action heavy and bypassing a number of actions is a stiff drawback.  For the same reason, Venture is non-ideal in a Fairgrounds deck.

Finally, Venture helps in the greening phase of standard Province games.  As you green and load up on Provinces and Duchies, Venture can help push through the Green and help you keep hitting $5 and $8 and help prevent your deck stalling at less than $5 hands.

Further, Venture can help you cycle your deck faster.  This is both a cost and a benefit.  Reshuffles while greening make you more likely to draw the Green cards you just added (thus reducing your money density).  On the benefit side, your key treasures have already likely been used to buy the Green cards and faster cycling means that you can get the key cards back into your deck faster and thus keep buying Victory cards.

Bypassing Gold for Venture

When can I bypass Gold for Venture, if ever?

In a straight Big Money deck, the simulator shows no benefit in choosing Venture over Gold.  Modifying Gerinomoo's simulator to begin purchasing Ventures over Gold at intervals of the number of Gold in your deck (6, 5, 4, 3, 2)  yields no statistically relevant difference between Venture and Gold.  Venture neither hurts nor harms a straight money deck in choosing Venture over Gold.  Note, that I set the bot to buy Venture once a certain number of Golds are reached and does not apply to earlier $5 buys, so, what I said earlier about Venture still applies (it is a solid $5 addition to a money deck), but it is of no benefit to your deck to choose Venture over Gold if you hit $6.

What about the light copper trashing of Spice Merchant and Moneylender?  I set the bot to buy Venture at $5 and then Venture over Gold once a certain number of Golds were reached in the deck against a straight money deck.  Here are the results:

Buy Venture Once:   Spice Merchant + Money Win Rate   Moneylender + Money Win Rate
6 Golds in deck            68%            59%
5 Golds in deck            68%            59%
4 Golds in deck            67%            58%
3 Golds in deck            68%            58%
2 Golds in deck            66%            57%
1 Gold in deck            64%            54%

Purchasing Venture over Gold is a very slight benefit in both decks once you have three Golds in your deck.  I would not expect it to make a large difference (and it doesn't) but it certainly does not hurt your deck to do so.  If other factors are present (e.g. a moderate amount of curses, extra green, etc.), Venture might become a better purchase than Gold once a small number of Golds are already in your deck.

Comparing Venture to Adventurer

Venture draws a natural comparison to Adventurer given that both search for Treasure.  Adventurer is generally considered very weak (see http://forum.dominionstrategy.com/index.php?topic=1668.0).  But, there are important differences between Venture and Adventurer.

First, Adventurer is an action whereas Venture is a Treasure.  So, Venture does not compete with good action cards in a non-+Action deck whereas Adventurer does.  Second, the price points are importantly different.  Adventurer competes directly with Gold at $6 and thus you must justify bypassing the Gold which Adventurer has a difficult time doing (I think there are cases where it might be a better purchase than Gold, but this is merely an intuition).  Venture is only $5 and thus need not exclude a Gold purchase.  As I mentioned above, there might be cases where Venture is better than Gold, but you never need to bypass Gold for Venture which makes it a more convenient buy than Adventurer.  Finally, Adventurer is twice as likely to bypass critical action cards in a light action deck compared to Venture.  To be fair, Adventurer will also hit twice as many treasures, but how beneficial hitting one Treasure over two will depend greatly on the Treasure composition of your deck.

Venture can shine in the same types of cases that Adventurer does, but is far more convenient since it is not an action, is at a better price point and reduces the chances of hitting your terminal actions.

In Conclusion

I hope that this sheds some light on the cases where Venture can be a powerful addition to your deck.  Thank you for reading and, of course, any and all thoughts are welcome.

Works With

High Quality Money Decks (stacking Ventures, Bank)
Light Copper Trashing (Moneylender / Spice Merchant)
As a soft counter to curse battles
As a soft counter to hand size attacks (especially Ghost Ship)
As a soft counter to deck attacks (Bureaucrat, Rabble, Sea Hag, Spy, Fortune Teller)
Heavy Green Decks
Mint

Conflicts With

Action Heavy Decks
Attacks that add copper to your deck (e.g. Ambassador, Mountebank, Jester)

[blueblimp]

I like Venture too, but a nitpick...

Venture can be a valuable asset in a heavy green deck; it can make the difference between hitting that crucial $ point and missing it.  In any deck where you have far more Green then usual, Venture can help you cycle through it by searching past the green.

This doesn't make sense to me. If you're greening, cycling is a bad thing, not a good thing. Skipping over green is (on average) a wash, since it doesn't improve the cards you draw after the treasure venture plays. Additionally, Venture is at its best in decks that have a lot of treasures that are better than Silvers, and I expect this to be less the case in typical alternative green decks.

[Catalytic]

blueblimp:

Isn't it better to not draw the green on your next turn than to draw the green on your next turn?  If you play a Venture and it skips past a Victory Card, this is possibly good for your next hand (and can't hurt it) since it guarantees that you won't draw a (likely) useless green.  Venture thus improves two hands simultaneously (this hand for the extra $) unless I am missing something here.

I add the rider (which needs to be clearer) to most of the alternative green decks that the decks must be treasure-centric which, I agree, is not usually the case.  But, if it is, Venture can be a valuable addition assuming that the claim above is correct.

I hope that it is clear that if Venture is going to be truly effective, it must be a quality treasure deck (as I hope the Moneylender / Spice Merchant examples show).  I don't think that means that most of your treasure needs to be better than Silver since a lot Silver will make your Venture worth $3 and thus equal to Gold at a better price point and the possibility of $4 (assuming that your deck can deal with the downsides and realize the benefits of Venture).  So, a silver-centric alternative green deck (e.g. say with Trader) should benefit from a Venture as well I would think.

I hope that is clear and thank you for your thoughts.

Note: I changed the wording that you quoted from "cycle" to "search past".  Cycle has a specific meaning that I should have avoided.  I rather meant that we can sift past the green rather than cycle the deck.  I hope that is clearer and addresses your point blueblimp.  If not, please let me know.

[ecq]

I think blueblimp is right about the cycling thing.  Venture doesn't do much of anything to your next hand on average.  Assuming Venture doesn't trigger a reshuffle, your next hand will contain 5 random cards from your draw pile one way or the other.  Yes, Venture might skip some green.  It also might not skip them, or it might skip your Smithy.  It all evens out and is pretty much a wash.

The one thing it does do is move you closer to the next shuffle.  If you're actively buying green, that's a bad thing.

Venture is only as good as the card it draws, plus $1.  Where Venture really shines and green-proofs your deck is when it's likely to hit another Venture or a high-value treasure (Gold, Bank, Platinum).  If Venture hits a Gold, it's worth $4, which is really nice.  If it hits a few Ventures before the Gold, $$$.  If you can get it to do that consistently, you don't need to draw much treasure to consistently buy Provinces.  Obviously the card loves Mint.

[DG]

You mentioned ventures as a defence to ghost ships but they also defend against bureaucrats, fortune teller, rabbles, and sea hags as well. As well as managing the top of the draw, the venture responds well if the top of the deck is managed for it by a navigator type card. For example you can set the top cards as estate, estate, silver, copper, gold  if you've six to spend plus a treasure drawn by the venture.

There is more than one way to evaluate the venture. The value a venture adds to your hand is 1 + the next treasure you draw. The value a venture adds to your deck is still 1 but you can also discount the non-treasure cards discarded when playing the venture. All the treasure in the deck will be played before you reshuffle but the non-treasure cards might not. Another way to consider a venture is that it's a pretty much like a peddler except that it draws the next treasure instead of the next card. Another way to consider ventures is to describe every other treasure in the deck as a terminal and each venture as part of a chain to a terminal treasure, so if you have a potion in your deck as the only terminal treasure then the ventures will always make a chain to draw that potion (or draw all the ventures and empty the draw deck if the potion is in hand already).

Venture/loan is a beneficial combination since the loan gets played very frequently. Venture/bank is likely to score highly. You can do fancy things with other special treasures too.

The venture really fails when you can draw all your treasures before you play the venture. This isn't as ridiculous as it sounds. It also often causes a reshuffle and this can either just be poor value or really bad deck management.

[Catalytic]

ecq:

First, thank for the note on Mint; completely forgot that.

Second, triggering a reshuffle with Venture in play is certainly bad since it will not be available until the next reshuffle.  I did not mean to assert this and I hope I made it clearer with a slight rewording.

But, I fail to see how missing green cannot be a benefit unless I am just missing something.  Suppose that my Venture discards two greens and does not trigger a reshuffle.  Now, my possible draws are five random cards from my remaining deck but now the possible draws include two less useless green cards.  The probability that my next hand is better than it would have been without the Venture must be better than it would have been had the green still been in my deck.

As far as missing my actions, if I have less action cards than green then the probability that I miss greens is larger than the probability that I miss an action so, on average, Venture will benefit my next hand rather than hurt it.  An assumption of my piece is that Venture is being played in a low action deck, so generally, there will be more or equal green to action cards.  In this type of deck, I am more likely to miss Green than actions, so it is on average a benefit to bypass non-treasure cards I think.

Moving towards a reshuffle while greening is not a bad in itself; if I am avoiding cards that will not help me and playing the cards that will then moving towards the reshuffle is good.  Uselessly moving towards a reshuffle is bad.  For instance, if I cannot take the remaining Province because I am behind and $5 in my hand and a Smithy, I don't want to play the Smithy (generally) since any cards I draw will not benefit me since I am forced to buy the Duchy and can already do so.  So, if I can usefully move towards the reshuffle this is a benefit; blindly moving towards the reshuffle is not.  Further, if I have not hit my high quality treasure yet, then moving towards the reshuffle is again good; I'm getting to the cards that I need to move towards a win.

So, the moving through the deck (assuming a reshuffle is not triggered) is a benefit if I am passing cards that will not help me and using the cards that will.  On average, I will play the cards that will help me and miss the cards that won't, so even if I occasionally miss an action card, I am better off on average since I will more likely miss cards I don't want rather than miss cards that I do.

I hope that is clear and thank you for your thoughts. 

[blueblimp]

blueblimp:

Isn't it better to not draw the green on your next turn than to draw the green on your next turn?  If you play a Venture and it skips past a Victory Card, this is possibly good for your next hand (and can't hurt it) since it guarantees that you won't draw a (likely) useless green.  Venture thus improves two hands simultaneously (this hand for the extra $) unless I am missing something here.

I add the rider (which needs to be clearer) to most of the alternative green decks that the decks must be treasure-centric which, I agree, is not usually the case.  But, if it is, Venture can be a valuable addition assuming that the claim above is correct.

I hope that it is clear that if Venture is going to be truly effective, it must be a quality treasure deck (as I hope the Moneylender / Spice Merchant examples show).  I don't think that means that most of your treasure needs to be better than Silver since a lot Silver will make your Venture worth $3 and thus equal to Gold at a better price point and the possibility of $4 (assuming that your deck can deal with the downsides and realize the benefits of Venture).  So, a silver-centric alternative green deck (e.g. say with Trader) should benefit from a Venture as well I would think.

I hope that is clear and thank you for your thoughts.

Note: I changed the wording that you quoted from "cycle" to "search past".  Cycle has a specific meaning that I should have avoided.  I rather meant that we can sift past the green rather than cycle the deck.  I hope that is clearer and addresses your point blueblimp.  If not, please let me know.

Here's how I analyze it. If you don't play the Venture, you draw 5 average cards from your draw deck. If you do play the Venture, you skip over some non-treasures, play a treasure, and then draw 5 average cards from your draw deck. Either way, you're drawing average cards from your draw deck.

This is different when the top of your deck is getting messed with, such as by Rabble. If you know the top 3 cards of your draw deck are green, then without playing Venture, you're drawing 3 green and 2 average cards, whereas with playing Venture, you're drawing 5 average cards, a huge improvement.

Edit: The analysis trick I'm using here is to pretend that, when you don't have information about a particular card in your draw deck, then it's a random card. This is a valid viewpoint if you're careful (because it can be pretty subtle what it means to have information about a card).

[Catalytic]

DG:

Thank you for your thoughts as well.

I thought about Rabble (but didn't mention it), but I missed Bureaucrat and Fortune Teller so I will add those to the list.  Thank you.

You mention Venture / Loan.  I have my doubts about Loan, but there are certainly some situations where it can beneficial.  My main concern here was with Big Money style decks with enablers and if you are adding quality treasure I think that Loan can often do more harm than good.

A couple of you have mentioned some crazy chains that you can make with Venture (especially to find Bank).  This can be impressive, but I wonder how viable those decks are in Province games.  There will be cases (as with any card or combo) where it will work, but the costs to set it up are so high my guess is that it will be generally better to simplify your strategy and play for the Provinces.  In a Colony game, all bets are off and there are some crazy things to be done with the non-traditional treasures that you have mentioned.

DG, I am glad you mentioned the importance of deck management and that has been a theme in this thread.  I think that it is generally an undervalued skill and how well we can really use Venture (as well as most draw cards, especially something like Hunting Party) will depend greatly on our knowledge of what is left near the end of our deck.  The more meticulous we are in our deck management, the more gains we can expect from a card like Venture.

[Catalytic]

blueblimp:

Don't the probabilities of what my next hand look like change when I play Venture whether I discard a card or not?

If I play Venture and immediately hit a Treasure then the chances that I draw a dead card on my next turn increase since there is one less non-dead card available to be drawn.  Therefore, I should not play the Venture unless the card I hit will be useful to me this turn and/or the chances that I discard useless cards are greater than the chances that I discard or waste useful cards.  If I knew, for instance, my remaining deck contained six green and four treasures, I should play the Venture since chances are that I will improve my odds of a better next hand since there will be likely be less green cards to draw from.

If I play Venture and am allowed to discard a green, then the chances that I don't draw a dead card in my next hand increase since there is one less dead card and one less good card.  If I have more good cards than bad, then discarding one good card for one bad card is a net probability gain of drawing good cards.

So, it cannot be bad to discard a green since even though I will draw 5 random cards the cards available to be drawn contain a higher percentage of more useful cards than it would have had I not played the Venture and been able to discard a green.

But, whether Venture helps or hurts depends on the composition of my remaining deck, whether the Treasure that I hit helps me this turn or not and some luck.  But there are probabilistic decisions that I can make even if completely unaware of the actual remaining cards in my deck.

If I have a very light green deck and another Treasure will not help me this turn then it would be a bad idea to play Venture since probability says that I will not hit green and merely play a card that could be useful next turn (whether it be a Treasure or Action) and increase my odds that I draw green cards since I now have less good cards to draw from.

If I have a very heavy green deck and another Treasure will not help me this turn then it still might be a good idea to play Venture in order to discard some Green.  Just like we know that we should play Venture after being hit with Rabble or Bureaucrat just to get by the Green (likely no matter what), if probability says that I will hit Green then I should try to discard it.  Drawing Green is bad and should be avoided if it can be done and there are no considerations that weigh against it (like triggering an unnecessary reshuffle).

So, I guess my point is that if Venture will help me this turn I probably want to play it since the changes in probability on my next hand are less important than what I can do this turn.

If Venture will not help me this turn, it makes sense to play Venture if I will probably discard at least one green (i.e. the amount of useless cards in my deck are greater than the amount of useful cards or I know that the top of my deck is green).

If Venture will not help me this turn, then I should not play it this turn if I will likely discard or play a card that could be useful on my next turn.

I hope that is clear and thanks again for your helpful thoughts.

[tlloyd]

When to Venture

Comparing Venture to Adventurer

Venture draws a natural comparison to Adventurer given that both search for Treasure.  Adventurer is generally considered very weak (see http://forum.dominionstrategy.com/index.php?topic=1668.0).  But, there are important differences between Venture and Adventurer.

First, Adventurer is an action whereas Venture is a Treasure.  So, Venture does not compete with good action cards in a non-+Action deck whereas Adventurer does.  Second, the price points are importantly different.  Adventurer competes directly with Gold at $6 and thus you must justify bypassing the Gold which Adventurer has a difficult time doing (I think there are cases where it might be a better purchase than Gold, but this is merely an intuition).  Venture is only $5 and thus need not exclude a Gold purchase.  As I mentioned above, there might be cases where Venture is better than Gold, but you never need to bypass Gold for Venture which makes it a more convenient buy than Adventurer.  Finally, Adventurer is twice as likely to bypass critical action cards in a light action deck compared to Venture.

Venture can shine in the same types of cases that Adventurer does, but is far more convenient since it is not an action, is at a better price point and reduces the chances of hitting your terminal actions.

So I think we forgot the most significant difference between Venture and Adventurer: Adventurer draws twice as many treasures! Somehow we remember that "Adventurer is twice as likely to bypass critical action cards" but forget that Adventurer, for only $1 more, is worth twice as much (-$1) when you play it. This is not a critique specific to this article, but to the community in general. I would say anytime you would prefer Venture to Gold, you should also prefer Adventurer to Venture. Being an action gives it some disadvantages (it can be dead in your hand; you can't put it back with Herbalist) and some advantages (you can Throne Room or King's Court it, you can put it back on your deck with Scheme). Finally, in a game with Bank, you should probably prefer Adventurer to Venture, as it allows you to play your treasures in the optimal order.

[blueblimp]

blueblimp:

Don't the probabilities of what my next hand look like change when I play Venture whether I discard a card or not?

If I play Venture and immediately hit a Treasure then the chances that I draw a dead card on my next turn increase since there is one less non-dead card available to be drawn.  Therefore, I should not play the Venture unless the card I hit will be useful to me this turn and/or the chances that I discard useless cards are greater than the chances that I discard or waste useful cards.  If I knew, for instance, my remaining deck contained six green and four treasures, I should play the Venture since chances are that I will improve my odds of a better next hand since there will be likely be less green cards to draw from.

Well, this is an interesting probability question. The argument I was giving before was a rough intuitive argument only, so I've sketched out the details carefully and it turns out that, if we ignore the effects of reshuffles, the expected number of treasures in your next hand does not change at all. The argument follows.

(EDIT: I've placed a more general and simpler argument in its own thread to avoid cluttering this one more.)

By linearity of expectation, the expected number of treasures in your hand when you draw from draw deck only (i.e. you don't trigger a reshuffle) is given by
  5 * (treasure density of draw deck)
where
  treasure density of draw deck = (# treasures in draw deck) / (# cards in draw deck).
So, the only question is what is the effect of playing Venture on the treasure density of your draw deck--again, if we ignore the effect of reshuffles, which I will discuss later. From now on, I'll only work in the simple situation where your draw deck contains treasures and green only, because that is the situation you proposed and it's simpler to deal with than the general situation.

The first thing to do is to figure out the probability of discarding any number g of green cards with your Venture. Let G denote the number of green cards in your draw deck and let T denote the number of treasures in your draw deck. In the example you gave, G=6 and T=4. At first we'll only assume T>=1, but since treasure density only makes sense when there is at least card in your draw deck, we'll assume T>=2 for the final calculation (since otherwise Venture might leave you with an empty draw deck).

Let's do the first few terms by example: the chance of Venture drawing a treasure immediately is T/(G+T), since there are T treasure cards and G+T total cards. The chance of Venture drawing exactly one green and then a treasure card is G/(G+T) * T/(G+T-1), since you first need to draw the green and then there is 1 fewer card in your deck. The chance of Venture drawing exactly two greens and then a treasure card is G/(G+T) * (G-1)/(G+T-1) * T/(G+T-2) since when you draw the second green, there is one less green in your deck that might be drawn.

In general, the probability of Venture drawing exactly g greens (where 0 <= g <= G) is equal to
  G/(G+T) * (G-1)/(G+T-1) * (G-2)/(G+T-2) * ... * (G-(g-1))/(G+T+(g-1)) * T/(G+T-g)
  = (product_{j=0,1,...,g-1} (G-j)/(G+T-j)) * (T / (G+T-g)).
Hopefully this formula makes sense based on the examples in the previous paragraph.

We observe now that g takes on exactly one value in the range 0,1,...,G, so these probabilities must sum to 1. That is:
  1 = sum_{g=0,1,...,G} (product_{j=0,1,...,g-1} (G-j)/(G+T-j)) * (T / (G+T-g)).
Notice that this holds for every T>=1. This will be important later.

Okay, so now we can figure out the expected treasure density of your draw deck after playing Venture. This is where we need to assume T>=2. If you draw exactly g green cards and then a treasure, then it will be (T-1)/(G+T-g-1), since there is one fewer treasure card and (g+1) fewer cards total. So, we just sum over all cases to get the value:
  sum_{g=0,1,...,G} (product_{j=0,1,...,g-1} (G-j)/(G+T-j)) * (T / (G+T-g)) * ((T-1) / (G+T-g-1))
  = T/(G+T) * sum_{g=0,1,...,G} (product_{j=0,1,...,g-1} (G-j)/(G+(T-1)-j)) * ((T-1) / (G+(T-1)-g)).
Notice that some of the denominators got moved around. This is really the key step so it probably helps to write it out on paper and make sure you see where everything is going. Observe that the sum here is the same as the sum that was 1 before, except with T replaced by T-1. So we see that the expected treasure density after playing Venture is just T/(G+T).

Of course, the expected treasure density if you don't play Venture is the same as what it was to start, which was T/(G+T). We conclude that if no reshuffle is triggered, then playing Venture, in expectation, has no effect on the number of treasures in your next hand.

What about the effect of reshuffles? Unfortunately, this doesn't help Venture. The case where you reshuffle is where you drew and discarded a lot green, so you had fewer than 5 cards in your draw deck when drawing your next hand. What this means is that although the treasure density in your draw deck is extremely high (since you discarded almost all its green), you run out your draw deck too quickly, and then you start drawing from your reshuffled discard pile, which almost certainly has a lower treasure density. Also, the treasures you had in your draw deck will miss the reshuffle. Ouch! On the other hand, they might have missed the reshuffle even if you hadn't played Venture and drew them later. How this effect balances out I don't know, and might depend on exactly how many cards are left in your draw deck.

This analysis is limited in that it only considers the expected value. Arguably the most important probability in Dominion is the probably of getting at least $8 in your hand, which is much more difficult to calculate. Maybe this probability is improved by the choice of whether to play Venture, but I'd need some convincing that it's significant.

[Catalytic]

blueblimp:

You are smarter than me :-)  There is a reason that I am a philosopher rather than a mathematician.  I am thinking my way through this, but I have a couple of brief thoughts.

First, we should never be completely oblivious to what remains in our deck if we are playing carefully.  So, the chances that we can play Venture effectively increase the better that we are at deck management.

Second, I wonder if we are talking past each other to some degree.  Let's see if we agree with some claims:

(1) If I know that Green is on top of my deck it is never bad to discard it.  Even if it does not increase the money density of my deck (and could even decrease it in the case of Venture since I will also play the next treasure) it is better to get it out of the way than to have it in my hand on my next draw.

(2) There is a further question of whether the playing of the Treasure card is a benefit or not.  If it is no benefit to my current hand then Venture might be a waste since it might just decrease the money density in my deck and not provide me any benefit this turn.

(3)  If I can benefit from the Treasure that I will play this turn from Venture then I should play it since my money density will not likely change given your argument below.

So, given your argument, Venture is a benefit to my deck if (a) we can discard Green with it (or are more likely to discard dead cards then good cards) and (b) it is likely to benefit my turn when I draw it.

This does not mean that Venture is a good buy yet since we have to compare it to other available options, etc. but it does establish the baseline questions that determine Venture's effectiveness

Do we agree on that much?  And, again, thank you so much for your thoughts and the work you put into to considering my article.  It is truly appreciated.

[DG]

Consider a draw deck of three estates and two coppers. When you play a venture you will discard the estates before the first copper, and leave behind the estates after the first copper and after the second copper. The distribution of the draw deck will be changed to have (on average) twice as many estates remaining as coppers. Extending this method to look at larger decks shows that a venture/loan/adventurer/golem/scrying pool will nearly always make a small change to the distribution of the remaining draw deck.

[ecq]

Consider a draw deck of three estates and two coppers. When you play a venture you will discard the estates before the first copper, and leave behind the estates after the first copper and after the second copper. The distribution of the draw deck will be changed to have (on average) twice as many estates remaining as coppers. Extending this method to look at larger decks shows that a venture/loan/adventurer/golem/scrying pool will nearly always make a small change to the distribution of the remaining draw deck.

The remaining draw deck, yes.  It's clear that Venture must make a small change, since you can't make a 3/5 ratio from fewer than 5 cards.  It's not obvious to me that Venture, on average, makes any appreciable changes to the next hand, though (discounting the effects of cycling, because Venture does make you reshuffle faster which can be good or bad depending).

Let's say Venture discarded an Estate and drew/played a Copper in your example, leaving behind 2 Estates and a Copper.  The Estate and Copper Venture drew go into the discard pile at the end of your turn.  When you draw your next hand, you draw 2 Estates, a Copper, then you reshuffle and draw 2 average cards from a pile that's missing 2 Estates and a Copper.  So, you're not necessarily drawing Estates 2:1 with Coppers.

If you assume that your discard, hand, and draw pile have roughly the same composition (again, I know that in practice they don't), would Venture mess with the distribution of the next hand?  Intuitively, it doesn't seem like it would or at least not in any perceptible way, but I haven't sat down to do the math.

[Captain_Frisk]

When to Venture

Venture is strictly better than Silver in a pure money deck since you are guaranteed to hit $2 with every play (the $1 from Venture and Venture will find at least a Copper) and can be worth as much as $4 (assuming no Platinum of course).  So, if you hit $5, Venture is a better purchase than Silver in a pure money deck (you would hope so for $5).

Minor nit - venture can be worth as much as (# ventures in deck + 3).  A single venture could be worth 4, but if you had all 10 ventures in your deck, and somehow only had 1 in your hand, that venture could be worth 13 (1 for itself, 9 for the other ventures, and 3 for the gold all the way at the end).  Also possibly increasing the value of ventures: Bank.

[Catalytic]

Thank you for you thoughts Captain Frisk.  I should add something about the stackability of Venture.  I have edited the piece slightly in the opening paragraphs to mention the potential benefits of stacking but a longer treatment might be necessary.  Again, thank you for your reading and your helpful comment.

[jomini]

A few points:
1. In the strictest sense Venture is not always better than silver. The simplest case is a deck with no other treasures. Chaining 7 ventures leaves you short a province, chaining 6 ventures and a silver gets you the province. This is mostly an issue with chapel decks where you can lose tempo if you aren't careful about having one or two terminal treasures (like gold, bank, royal seal, silver, plat, etc). Additionally, you can run into the problem where you have so many ventures in hand that they become effective coppers with chancellor power.

E.g. you have a deck where your most likely hand is 3 ventures & 2 other cards. You have only a gold in the deck. Another venture doesn't do much for you, you already are going to chain through all the treasures in the deck so you a really only adding 1 buying power. Silver is better at the moment in this case, though I suspect duchy is much likely to be the correct buy.

2. I'm suspecting that your simulators could be tweaked for a few percentage points because venture allows you to go into duchies sooner. Venture decks are more green tolerant. Suppose I have a 15 card deck with 5 ventures, 5 silvers, and 5 duchies. If I play a venture on the first hand I have a 5/14 chance of skipping a duchy on the first card and I have a 20/169 chance of skipping duchies before hitting a treasure. Due to the potential for training ventures odds of any one venture skipping a duchy are slightly higher. Overall this means this means that around 1/3 of my green cards won't ever get in my hand this shuffle. So when you calculate your money density it is appropriate to put in a discount factor. Say rather than saying that I have a money density of 1 coin per card (each card only at face value) or 1.7 (each venture counting as 3 coin) I'd say you should calculate these as 1.125 (discounting the size of a duchy by .33 cards) or 1.87.

Long story short, in a large enough deck ventures reduce the effective space that VP cards take up. This gives you a higher money density and allows you to green out sooner as you will simply play fewer greens each shuffle.

4. Another big place that venture decks shine are with plats. Like banks, plats come with a high cost and a high opportunity cost (often you face the choice between getting another VP card or getting the big shiny treasure). Ventures let you more quickly play the big treasures and reliably draw key break points. It takes an awful lot less to build a reliable BM engine with ventures & plats than it does to just bootstrap up to plats in a colony game.

5. Another huge enabler I would throw in would be Forge. Forge is very strong for venture decks because it: can destroy those pesky coppers, convert early 3 coin buys into ventures with estates, and can allow you to better control end game timing (e.g. forge province -> province or venture + silver -> province or venture -> duchy). This particularly applies for games where attacks are very useful early on (e.g. cutpurse, witch, hag, etc.) but lost their bite late game (swindler + estate -> gold, witch -> venture, etc.); venture both helps you get the forge (it has better odds than silver) in the face of attacks and makes use of the forge's ability rid your deck of early game dross for better treasure density or for VP.

[ecq]

Long story short, in a large enough deck ventures reduce the effective space that VP cards take up. This gives you a higher money density and allows you to green out sooner as you will simply play fewer greens each shuffle.

I don't think this is right.  You'll draw fewer greens each shuffle, but you'll also shuffle more.  If you're greening, shuffling more means you're seeing more greens per hand on average, not fewer.

Venture's power has little to do with skipping cards.  It's powerful because it adds $1 to the current hand while doing as little as possible to sacrifice the quality of the hand.  It can't be drawn dead.  It doesn't make you wish you bought a Silver, because it draws you a treasure card to replace itself.

[Catalytic]

jomini: Thank you for your thoughts.  They are greatly appreciated and I will think about them further.

ecq:  This is my worry with your and blumeblimp's position.  It is true that every time I skip or discard a card then I will reshuffle sooner.  And, yes, if I reshuffle sooner I will see Green cards more often.  But, neither of these claims means that it is not a benefit to skip over green cards.

Suppose we played a fancard that said: "If you play this card remove all Victory cards from your deck and place them in the discard pile.  You may only play this once per game."  The same conditions are satisfied: every time I skip or discard a card I reshuffle sooner (removing the green will make my deck thinner and thus trigger a reshuffle sooner).  And if I reshuffle sooner I will see the Green cards more often.  But, this card is obviously a benefit; my deck is efficient and each turn is maximally effective with no intrinsically dead cards (but obviously the distribution of the hands is random).

Similarly, if Venture manages to bypass a green, it must be better since the chances that my next hand is maximally effective (that is, no dead cards) increases.  Venture's primary value certainly does not come from skipping green, but we can derive a benefit from its search capacity by moving through it and helping this hand with more $ and next hand by even slightly increasing the chance that I draw a hand without green.

Further, your position seems to entail that a card like Cartographer derives no benefit from being able to discard Green.  Discarding Green makes the reshuffle come sooner and means I will eventually see more green, but this does not mean that it is no benefit from using Cartographer's ability to discard does it?  I hope I am being fair to your claims and I think I am.

Thank you for your continued discussion; I think that this is an interesting dicussion and is very fruitful as we consider other search cards like Hunting Party, Golem, etc. that DG mentioned.

[chogg]

When to Venture
A single Venture is strictly better than Silver in a pure money deck since you are guaranteed to hit $2 with every play (the $1 from Venture and Venture will find at least a Copper) and can be worth as much as $4 (assuming no Platinum of course).

Apart from a few marginal cases, anyway. Horn of Plenty is a Treasure card worth $0, so Venture could in principle only be worth $1.  Also, it could find Philosopher's Stone with less than 5 cards between Deck and Discard Pile.  Or heck, it could find a Potion.

[Catalytic]

Thanks for reading and your helpful comment, chogg ... I added a parenthetical to hopefully clear this up.

[Catalytic]

jomini:  Thank you for your time and very helpful comments.  I want to take a moment to consider them in turn.

1.  Venture is not always better than Silver; this is true.  I have edited the opening paragraph slightly to exclude some edge cases as chogg mentioned.  But I also added the rider that I was considering money based decks.  A Venture chain, while attractive, requires some serious help to set up and part of me doubts that such a chain is an efficient plan.  If I have the time to grab 8 copies of Venture, the pieces that allow me to do this are likely put to better use with some other Engine or combo.  I am sure there are boards where this might not be the case, but the time needed to set it up and still only grab one Province at a time is likely highly inefficient.

2.  The simulator could likely have been tweaked for better results; I agree based on the discussion in this thread concerning the benefits of Venture missing Green (I might be wrong about this as ecq and blueblimp are suggesting).  But the point was rather to compare Venture + Big Money + Enabler to straight Big Money + Enabler.  Given that Venture helped most of these decks out significantly was hopefully sufficient to motivate the claim that Venture can be a good addition to such decks.  The results in the light copper trashing decks (Moneylender / Spice Merchant) were incredibly significant which should show that Venture gets better as treasure quality increases.  So, I was not really worried about the winning percentages as such, but merely using them as a comparison point for Venture vs. non-Venture decks with similar parts.  The missing Green issue I address in the section on Venture and Green Decks; Venture I think can smooth out a deck once it starts greening and if this is right, we might be able to go Duchy earlier.  But, that also means bypassing another Venture and we would need to figure out if the Duchy now or the Venture to help smooth the deck later and hopefully hit $8 is a bigger benefit.  As it stands, I am not sure.

4.  The Platinum comment is certainly correct; the $5 is usually monstrous and Venture lets you play it more often.  The same could be said of Bank.  I avoided discussion of both Colony games and Bank, I hope, for good reason. 

I was mainly focused on Venture's performance in BM+Enabler contexts and   in Colony games simple money strategies tend to be inefficient and flounder.  You certainly can't play money with a couple of Enablers without some powerful trashing since you are constantly going to be hitting those annoying coppers and silvers you needed to ramp up to Platinum.  So, I was avoiding consideration of Colony games but if we have a deck built for it, Venture to find your Platinums can be a powerful combo if we don't mind missing what Venture might be skipping over to get to the Platinum.

I also avoided discussion of Bank for two reasons.  One, I think that there is some anti-synergy between Bank and Venture.  Since I am mainly worried about Province games, Bank's effectiveness is somewhat muted.  At the price point and given the speed of the Province games, the likely benefit of Bank is fairly small since it will likely only be played a couple of times.  Venture makes a Bank purchase better since it will help find it and even one extra play can be very important, but Bank was somewhat anathema to the focus of the article.  Second, Bank can really shine in large draw contexts with +Buy and, again, my focus on money-centric decks with non-chained draw power (Smithy, Courtyard, etc.), Bank will be less of a boon for this type of deck.  Now, if you hit $7 I wouldn't call it a bad buy in these kinds of decks, but the potential value of it is muted somewhat by the limited draw potential of these types of decks.

5.  For some of the same reason I avoided discussion of Bank I avoided discussion of Forge.  The price point is almost prohibitively high and I seriously wonder if it would just not be better to buy Gold in a money-centric deck.  Forge can be great, but I don't see that the type of deck I am thinking about can really take advantage of it.  First, Forge as copper trasher will be poor in the type of deck I am worried about since I am assuming the deck is light on actions and obviously little or no +Action.  Forge works best with increased hand sizes and the decks I am focused on just aren't going to do that for you.

Further, the point of Venture is that it will smooth out $ and help you hit the critical $5 and $8 price points in the late game.  So, there might be some anti-synergy here since Venture is supposed to help you buy the critical cards and Forge just wants to trash towards them.  Since I need to wreck my hand with Forge to get the Province, I likely won't be able to buy one as well.  Maybe I will mess with the simulator somewhat, but my guess is that Forge will create more problems here than it solves.  But I could be wrong.

Thank you again for taking the time to write such detailed comments; it is truly and greatly appreciated.

[blueblimp]

(1) If I know that Green is on top of my deck it is never bad to discard it.  Even if it does not increase the money density of my deck (and could even decrease it in the case of Venture since I will also play the next treasure) it is better to get it out of the way than to have it in my hand on my next draw.

If you know green is on top of your deck, then playing Venture will improve the money density of your next hand and of your draw deck, so yes, I agree. My post was only addressing the case where you don't know what's on top of your deck (since originally the discussion was about the alternative green case, where this assumption seems reasonable). Venture is absolutely great to play if e.g. you've just been Rabble'd or if you just played an Apothecary and rearranged your green to top of deck.

All I was trying to show in my post is that if you don't have any particular knowledge about what's on top of your deck, then playing Venture does not (on average) increase the treasure density of your next hand. For what it's worth, it's probably still a good idea to play it, since you're getting at least $2 more THIS hand.

(2) There is a further question of whether the playing of the Treasure card is a benefit or not.  If it is no benefit to my current hand then Venture might be a waste since it might just decrease the money density in my deck and not provide me any benefit this turn.

Well, it might be a waste or it might discard a bunch of green that was going to be in your next hand. On average, it doesn't matter, _except_ if you are choosing to whether to play Venture by considering the effects of reshuffles or by considering a number more refined than average treasure density.

(3)  If I can benefit from the Treasure that I will play this turn from Venture then I should play it since my money density will not likely change given your argument below.

I agree. Except if reshuffles cause complications.

Consider a draw deck of three estates and two coppers. When you play a venture you will discard the estates before the first copper, and leave behind the estates after the first copper and after the second copper. The distribution of the draw deck will be changed to have (on average) twice as many estates remaining as coppers. Extending this method to look at larger decks shows that a venture/loan/adventurer/golem/scrying pool will nearly always make a small change to the distribution of the remaining draw deck.

(EDIT: Possibly the confusion is that I'm looking at the _expected_ treasure density after playing Venture. In other words, the average treasure density over all possible orderings of your draw deck. It's true that for most orderings of your draw deck, Venture will change the treasure density. But on average it won't.)

I don't know if you're proposing this as a counterexample to my post, but anyway it isn't, so might as well check the cases by hand. (After all, I ran a simulation to increase my confidence before I wrote the proof, so this is a good check.) I'll write the order of the draw deck, then what's left remaining after the venture, then the treasure density of what's left.

EEECC -> C -> 1
EECEC -> EC -> 1/2
ECEEC -> EEC -> 1/3
CEEEC -> EEEC -> 1/4
EECCE -> CE -> 1/2
ECECE -> ECE -> 1/3
CEECE -> EECE -> 1/4
ECCEE -> CEE -> 1/3
CECEE -> ECEE -> 1/4
CCEEE -> CEEE -> 1/4

The average is
  (1 + 1/2 + 1/3 + 1/4 + 1/2 + 1/3 + 1/4 + 1/3 + 1/4 + 1/4)/10
  = (1 + 2 * 1/2 + 3 * 1/3 + 4 * 1/4)/10
  = (1 + 1 + 1 + 1)/10
  = 4/10
  = 2/5,
exactly what we started with.

Anyway, if this isn't convincing, please let me know and I will try to come up with some other argument! I've spent enough time thinking about this problem already that I would rather spend more time on it than convince nobody.

[jomini]

1. I'm not sure how you arrive at your conclusion that a venture chain needs big help setting up. A large number of simple cards - spice merchants, council room, etc. can do quite well. While I wouldn't adivse it in most circumstances, countinghouse can set them up nicely. Also something like chapel/highway/iw can add a venture each turn & play it the same turn ... without ever leaving a BM deck.

2. Well, what I think would be most helpful is a discussion of how venture is more green tolerant. Yes you have to weigh another venture against a duchy, but at some point, and with light trashing it comes fairly early, you want the duchy instead of a venture in a BM deck.

4. Both Bank and Plat can come with zero opportunity cost in venture decks under some circumstances. E.g Suppose I go light trashing, venture, mine. If bank is in the deck, I may well come to a point where I can mine a venture into a bank. This increases my pay out that hand and makes it much more likely that I will get a province or even province + duchy if I have +buy. BM generally isn't as good at colony games, but venture is actually one where it is. Because plat is such a high variance card, venture/trashing (strong or weak), and plats can actually make BM work on colony boards. Hitting your plats every hand, or your banks, after several ventures can get you to reliable colony decks with only one or two plat buys and you can green like mad after that (buy duchy over plat in a lot of cases).

5. Forge is very much worth it in slow province games. For instance in a hag game you are almost invariably going to hit 7 coin and you will have maybe one province at that point. Forge allows you to trash curses - forcing your opponent to win the province split 5 - 3 - this more than makes up for down buying the forge. Likewise, near game end forging provinces is very strong you can either win a 4-3 split (depriving your opponent of a chance to get his big hand and reach parity) or forge otherwise crappy hands (like gold/estate) into VP. In a fast BM game, yeah forge is too slow. In a long one with plenty of attacks, it will tend to be worth it because you will get enough play out of it to make it huge.


ECQ: So what if I shuffle more? That allows me to use the value in my deck more. Take some other cards that skip VP cards - why would you buy Farming Village over a regular Village if they have the same overall effect? We say Farming village is normally strictly better than regular village (excepting the corner cases like a baron deck) ... why would that be the case if skipping green doesn't help you?

Likewise cartographer, golem, and hunting party all work by skipping a bunch of dross and reshuffling more. Yet they are all GREAT cards.

The real thing I'm trying maximize is value of each hand. Shuffling impacts that in two ways:
A. It brings your new (normally higher-than-average value) cards into the draw deck.
B. It brings your previously played higher-than-average value cards back into the draw deck.

For instance suppose I have a deck with ventures, one plat, one gold and some mostly useless stuff (like a spent moneylender and horse traders and a province or two). Once I've played the Plat and the gold, I want to shuffle as soon as possible. There just isn't anything in the deck that is going to get me back to province buying power as fast as reshuffling. Each useless card I skip before I reshuffle makes it that much sooner that I can get back to paydirt and buy more VP.

Or try thinking about this way. Say I have 16 coin my deck total. At most I can get 2 provinces per shuffle. The faster I shuffer, generally speaking, the more times use that 16 coin again to buy VP.


I get that venture doesn't help my next hand - it can both give (zoom past a bunch of green) and take away (pull on out my gold or plat when I'm already at 8 or 11). What I do know is that if I just bought a province, that says that the means to buy a province are now going to be sitting in the discard. Generally, I want that cash back into my deck pretty quickly. Now if I'm playing a high memory game and can work out the odds of hitting a province next time, or the danger of skipping a useful action, etc. then yes I may not play the superfluous venture so as to not get a badly timed shuffle ... but those dangers are more an issue with non-BM decks. Venture is a golem for treasures, yeah you might skip some useful stuff, but it never misses big coin cards and you want to play those as often as possible (just like golem/witch).

Yes I know, the green I just bought decreases my treasure denisty when I shuffle it in, however, most decks don't haven consistent buying power and the one thing we know is that the means to buy a province is going to be in the discard until we reshuffle. This explains why envoy/venture is so little improvement over baseline. Envoy decks have low variance and benefit less from heavy reshuffling.

[blueblimp]

ecq:  This is my worry with your and blumeblimp's position.  It is true that every time I skip or discard a card then I will reshuffle sooner.  And, yes, if I reshuffle sooner I will see Green cards more often.  But, neither of these claims means that it is not a benefit to skip over green cards.

Suppose we played a fancard that said: "If you play this card remove all Victory cards from your deck and place them in the discard pile.  You may only play this once per game."  The same conditions are satisfied: every time I skip or discard a card I reshuffle sooner (removing the green will make my deck thinner and thus trigger a reshuffle sooner).  And if I reshuffle sooner I will see the Green cards more often.  But, this card is obviously a benefit; my deck is efficient and each turn is maximally effective with no intrinsically dead cards (but obviously the distribution of the hands is random).

Similarly, if Venture manages to bypass a green, it must be better since the chances that my next hand is maximally effective (that is, no dead cards) increases.  Venture's primary value certainly does not come from skipping green, but we can derive a benefit from its search capacity by moving through it and helping this hand with more $ and next hand by even slightly increasing the chance that I draw a hand without green.

Further, your position seems to entail that a card like Cartographer derives no benefit from being able to discard Green.  Discarding Green makes the reshuffle come sooner and means I will eventually see more green, but this does not mean that it is no benefit from using Cartographer's ability to discard does it?  I hope I am being fair to your claims and I think I am.

Thank you for your continued discussion; I think that this is an interesting dicussion and is very fruitful as we consider other search cards like Hunting Party, Golem, etc. that DG mentioned.

The key difference between Venture and the examples you bring up is that Venture does not put cards back on the deck. Cartographer is great not because it reveals 4 cards, but because it lets you put the good ones back on the deck. If Cartographer were "reveal 4 cards, discard them", then it wouldn't be any good for sifting. And this is essentially what Venture does: it reveals a bunch of cards, plays 1, and discards the rest. It has NO sifting effect on the rest of your deck, on average.

It's a similar situation with the fancard that removes all green from your draw deck. It's great because, after revealing your whole deck, it puts the non-green cards back in your draw deck. If its effect were "reveal your whole deck, then discard the revealed cards" then it wouldn't be so great except for triggering reshuffles (hey Chancellor).