What should we do with Moats/Witches, Smithies and Council Rooms when one does not have any action forks played (+2 Actions such as Villages or Festivals)? My general rule of thumb is to actually discard the +Cards, though there are some clear exceptions. (There are always exceptions!) For this discussion, I will default to talking about the Smithy as there are clear reasons why one may want Moats (Defense), Witches (Attack), and Council Rooms (Buys).

Let's go into the reason I believe drawing cards as one's last action is typically a bad play.
There is a risk of drawing and discarding actions that will not be able to be used until the next shuffle. When one plays a draw card as their last action, the only cards that can help them are treasure cards (henceforth will be noted as gold or money). If that player draws gold, no damage has been done short of potentially damaging a future turn (with the trade-off of making the current turn "successful"). If that player draws victory points, the outcome is likely not ideal, but a positive nonetheless. However if action cards are drawn, they are completely wasted. The deck has been stripped of useful cards and the player must wait until at least the next shuffle to be able to play those actions.

So why is having to discard an action bad? Let's suppose on the initial shuffle you and your opponent both buy a Moneylender, but you were unfortunate and had to wait until after the second shuffle to use the Moneylender while your opponent used it after their first shuffle. Who has the advantage? The quantified power of one's deck can be somewhat simplified to the gold spent on its cards plus the number of real actions that have been played (think Chapel, Moneylender, Remodel, Feast, Workshop). By playing a Smithy to draw a Moneylender, that player will have lost tempo by having to wait another shuffle into the game to be able to utilize the Moneylender.

Now there are also some obvious examples when a player would definitely want to bend/break this rule. The first one that comes to mind is if a player buys a Smithy and Silver on their first shuffle. Then (provided playing Smithy won't require to shuffle in a recently bought action card), there's no fear of drawing a useless card. The more general application of this is when one counts their action cards remaining in their deck and knows that the probability is slim to none of drawing an action card. The other somewhat obvious rule is if the end of the game is near and you're close to purchasing that last Province for the win. It's certainly worth potentially sacrificing a useful card if it closes the game in your favor, or if it's highly unlikely you'll get another turn due to someone else being able to finish the game.

So before you just play that Smithy as your last action, think about it for a second and ask yourself if it is really necessary!

Villages are delicious. Essentially a cantrip that gives you an extra action, which inherently combos well with any other action, even other villages! What's not to love?

Silvers are boring. Drawing it enables you to buy more. That is it.

Now let's get into it. Your initial draw: 3-4 (equivalent to 4-3). We'll ignore 2-5/5-2's for now, and analyze the first few turns.

You have two choices for your first two turns - buy a village and a 4, or silver and a 4.

Now you have 12 cards - 7 copper, 3 vp, a 4, and either a silver or a village.

We will further simplify the 3rd turn by saying you drew the silver or the village - to allow for direct comparison. In other cases, it doesn't matter which one you have in your deck - you didn't draw it yet.

There are 792 total combinations, 330 of which contain the silver or the village. (5/12 of the time, in case you're wondering.)

Let's look at the scenarios:

4 copper. This will happen 35 times, or about 10% of the time. With the silver, that's a 6, which nets you gold. With the village, it will net you a card - 3/7 chance of getting you a copper, 1/7 chance of getting the 4, which you can use. It depends on what you get with the 4, and it depends on what you can get with the 5, but this means, by itself, that with the silver, this will get you the gold 10% of the time, while for the village, it's ~1.4%, and only if the action is a +2 coin action or if it's a draw action which drew (at least) 2 copper. Since you do not have another action, the extra action is wasted.

3 copper, 1 vp. This will happen 105 times, or slightly less than a third of the time. With the silver, you can purchase a 5. With the village, you have 4/7 chance of getting the copper, which gives you the 5, 1/7 chance of getting the 4, which you can use. Since you do not have another action, the extra action is wasted again. This follows the 4 copper scenario, except for about obtaining 5's instead of 6's. Though it's worth noting that if your 4 is a smithy (draw 3 cards), there is a chance you might draw 3 copper - a ~10% chance. There is a ~3% chance of getting a 6 with the smithy purchased. This does not exist for the silver. Unfortunately, that means you'll have 1 or 2 coins next turn, which might or might not be desirable.

3 copper, 4. This will happen 35 times as well, which is about 10% of the time. For the village, this is probably a better proposition than the last, but only barely - your cantrip draw won't be as good, but otherwise most of the same analysis follows. With a +2 coin action, there is a 4/7 chance you'll get the 6 needed for a gold. With a smithy, there's a ~10% chance that you'll get to 6, sacrificing the future (a little bit). With the 2, you can pick up a 5, and still use your action. No lack of support there.

Those are about half the possibilities. The other half is about the same - the general concept is that while village offers greater volatility in some circumstances while the silver offers more stability. The math seems to be very close overall in yielding the most out of the 2nd cycle turns - the silver is the safer move, but the village offers (in the right set) longer term viability, with higher volatility overall.

An interesting observation is that beginners tend to favor villages while veteran tend to favor silver is actually optimal - with the assumption that players tend to get better, beginners might need that extra volatility to yield a better overall win probability. It might be part of what feels like "beginner's luck" in these games.

Of course, that only applies given the right conditions. Villages need love too, and in the right set, it can be celebrated. What is Larry's advice?

Stay tuned and find out!