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[Markov Chain]

If there are two viable strategies in a multi-player game, one involving Goons, then I believe whichever strategy has more players has the advantage.  The reason is that Goons players don't work towards ending the game, as they buy a variety of actions and won't empty any pile other than Goons.   A lone VP-card player has to buy so many VP cards that he slows down his deck, while the Goons keep going; two VP-card players can end the game much faster, either taking the Provinces or running out VP kingdom piles.

I played a 3-player game with the following kingdom:

Remake, Island, Mining Village, Caravan, Mint, Tactician, Jester, Contraband, Goons, Fairgrounds

This is a very good Goons deck, because there are Tactician and Mining Village to allow you to play multiple Goons, and Remake, Island, and Mint to get rid of unwanted copper.

But with all the cards good, it's also a reasonable Jester/Fairgrounds deck, particularly with three players so that you have two chances to gain cards (both good cards, and cards that will count towards the magic 15) with the Jester.  Remake also helps because it makes it possible to get rid of most of your copper and all but one Estate, and possibly to get a missing card later.

I went for Jester/Fairgrounds against two Tactician/Goons players.  I got all of the kingdom cards except Mint either in the normal course of events or as Jester prizes; I didn't have a deck that benefited as much from Tactician, but I Jestered one, and also Jestered a Goons (and bought one later).  My 15th card was a Duchy.

The problem is that I was the only player buying lots of greens, and thus I couldn't bring the game toward an end as I greened my deck.  I was ahead in VP, but I could only end the game by buying Fairgrounds (and getting all 12 would take forever), or by giving up lots of VPs to buy out another pile.  If there had been two Fairgrounds players, we would have had six each and then run out the Duchies or Islands if necessary.

The Tactician/Goons players were taking Tactician turns and playing several Goons with the help of Mining Village; a typical turn for the winner was Tactician, MVx2, Goonsx3, buy Caravan, Mint to trash a bunch of money, and three coppers for 15 VP.  This was an ideal setup for mega-Goons turns.

Meanwhile, a typical turn for me late in the game was to discard two cards to a Goons and then use the remaining three to buy a Fairgrounds for 6 VP, or to play my own Goons and buy Duchy/Copper for 5 VP.

I was actually ahead in VP on my last turn, 71-66, with two Provinces and six Fairgrounds for 48 of my points, but the next player ended the game with a 17-point turn, buying the last three Caravans and two Estates.  The other Tactician player had only 48. 

[mischiefmaker]

While I agree that the majority strategy might have more power to end the game, I don't think that it necessarily follows that the majority strategy necessarily has the advantage. In your example, if one of the other players had also played Jester/Fairgrounds, it's likely the game would have ended more quickly, but due to Jester rather than to buying out Fairgrounds.

If there had been no Jester in the kingdom, I think it's very likely the Goons player still wins, since as you say, he bought out two piles to end the game. If there were only one Goons player and two Fairgrounds players, Fairgrounds gets emptied, but there will be fewer players contesting Caravans and Estates, and the Goons player can continue to pile up mega-turns.

On the other hand, if Jester is replaced by Black Market, a single Fairgrounds player might have the advantage, even if he can't end the game, since a longer game gives him more opportunity to pump up the Fairgrounds that only he has.

As another counterexample, I played a 4p game not too long ago with these key cards:

Hamlet, Pirate Ship, Goons, Tactician, Colony

2 players, including me, intended to go Tactician/Hamlet/Pirate Ship, while the other two went Pirate Ship. After several rounds of having no treasure, I chickened out and bought a couple of Pirate Ships. By the middle of the game, the three pirate ship players had ships worth $8, $9, and $11, or something like that, but the Goons player had nearly 50 points of VP chips, and was consistently playing Tactician/4xHamlet/4xGoons to get 10-20 points a turn. At that point, even if one of the pirate ship players managed to get 6 colonies, which seems pretty unlikely, he's still going to lose to the Goons player (who, remember, can also buy Provinces instead of Copper when the PS players stop helping him out).

Had three of us gone for Goons and only one for Pirate Ship, there would have been more pressure on the Goons pile, which might have split 4/3/3 instead of 5/5. And there would have been enormous pressure on the Hamlet pile, which might have gone 4/3/2/1 or 3/3/2/2. That means the Goons players likely only get to play 2 Goons per Tactician turn, and they don't get nearly as much Copper trashing. I think the lone Pirate Ship player has a good shot to win this.

[DG]

You were just seeing two advantage of goons; collecting vp without degrading the deck and ending the game with multiple buys. Having fairgrounds in the kingdom was no great advantage since you needed even more green cards and other supporting cards to win the game.

[theory]

Race for the Galaxy has the same 3p problem.  Most strategies can be devolved down into a build or produce/consume strategy, and whichever strategy gets 2 players has a big advantage.  Build needs to end the game quickly, and so two builders can combo off of each other's dev/settles and end the game twice as fast, shutting down the P/C engine before it can get enough cranks.  But two P/C players could play off of each other's produces/consumes and force the builder to call every single dev/settle to end the game very slowly, one build phase at a time.

So it's very similar to the Goons problem: when you can choose between short term and long term victories, 3p games get decided by whichever faction draws more players.