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[NoMoreFun]

What's the overall probability of there being a Masquerade pin in the kingdom, and which combination of sets allows for the highest probability?

Requirements for a pin:
A pin must eventually be able to reliably leave the opponent empty handed every turn regardless of the composition of his deck.
Pins will typically have Masquerade, and also require a way to play Masquerade with an empty hand and deck enough times to reduce the hand size of your opponent to 0. King's Court, Throne Room, Golem and Outpost are the cards to consider for this aspect.

If you can find a way to guarantee your opponent has a hand of all coppers every turn, Cutpurse pins are ok.
Bureaucrat pins only count if there's a way of ensuring your opponent has 5 victory cards.

Counters:
*Reactions and durations are not counters, since they can only hold off the pin and can't prevent masquerade stealing and trashing cards. Eventually the pin will be able to take those cards, so their presence does not prevent a pin from existing in a kingdom.
*Fortress may prevent some pins, but being a cantrip means that pin decks can usually function with too many fortresses. Eventually the fortress pile will run out, so if the pin deck can handle having all 10 fortresses, then it's ok to have fortress in the kingdom.
*When trash gainers are an interesting issue, but I don't think any of them can prevent the pin indefinitely.

[jomini]

This depends on how expansive your are in your definition of "pin"

In addition to Kc, Tr, Outpost, and Golem; I would also put out Cutpurse and Procession. The first I've looked at in good detail, it isn't perfectly reliable, but it is utterly brutal:

http://forum.dominionstrategy.com/index.php?topic=4676.0

You need a huge source of +action, copper gainers help (a lot), extra draw also helps (a lot), and a slightly slow board (which Cutpurse tends to give regardless) but you end up stealing (not trashing) the opponents deck and leaving him with nothing but copper. I have yet to lose a game when I've tried going for this combo. As you don't have to trash cards nor play dead masqs (those where you don't pass a card because you have none in hand/deck), all of the Dark Ages counters are pretty much meaningless (though Feodum may be a problem if the opponent has enough of them).

The second requires a way to recover trashed cards - Rogue and Grave Robber can both accomplish that.

Native village can also increase your dead Masq count using Golem -> Tr -> Masq -> Nv (draw Tr/Masq), but those tend to be complicated (needs +cards and a discard/top deck option).


Reactions and durations can counter the pin. You only need to 3 pile out and curses are a freebie. That leaves 2 other piles and it isn't that hard to play a moat, hand over your moat & 2 garbage cards, keep 1 VP card (e.g. province), play a card gainer (gain a moat), and buy a curse/copper. Plenty of cards (like Library, Menega, Outpost or Minion) can let me play my entire deck and do all sorts of nasty stuff. With action multipliers in play, forget it. Kc/Wharf/Iw or Tac/Kc/Remodel you can pile down before the other guy can destroy your deck. Of course, the kicker for countering a pin is ... masq. You are talking about an idiotically lean deck with lots of high value cards. If I can keep two cards (say Masq & a village) you have to part with something that takes you a full turn to get it back (in most pins).

Fortress can allow me to have that magical two card hand where I can steal a card back with masq (either Fortress or something better) and limit your destructive potential to 1 card per turn until the Fortress pile is depleted.

Feodum will completely nerf the classic pin. I pass a Feodum over, you can trash it (congrats you have 3 silver to pass me back) - I lose on net 1 card, but can exchange my worst card for a silver (pass your 2nd to worst card over first, get a silver, get your 2nd to worst card back for your worst card or get 2 silvers for your worst 2 cards). You end the turn with +1 treasure so next turn you have only 2 dead masqs (and if I pass another Feodum, you can't kill any of my cards at all). If you pass back the Feodum, well I just keep giving it back.

Pins are very fragile decks, with Masq out, you can keep giving pin decks junk (e.g. copper) and keep forcing them to give you not-copper stuff.  You are vulnerable to Discard -> Masq when you run a pin deck and with Kc our (to a lesser extent Tr or Prssn) megaturn strategies can get awfully quick.