After the filler games broke up, we brought out Attika and gave it a shot as a four-player game. Three of us had played before, one many times (Yellow), while Blue and Red had played a handful of times as noted in this Green was a first-time player.
The initial placements saw Green and Red build near the top-left and top-right temple space. Green would then spend almost the whole game building around that area, slowly expanding the space with tiles, with only a brief second settlement built around a the lower-right temple to block red's possible connection victory late in the game.
Blue and Yellow staked out the middle lower part of the board, the only remaining resource rich area, but Blue ended up getting cut off from the any connections by Yellow building around. To claim more space for buildings, Blue ended up building around the lower left and top right temples to both block easy connection victories by yellow and red, and to get new space in which to build, and safe places to lay new tiles.
Yellow alternated between large building and attempts to get easy connection victories between the two bottom temples, blocked by Blue's defensive building and placement of new tiles. This included a second settlement in the far right to steal the resources red would have needed for his own building victory.
The final game state looked like this, Yellow managed a building victory having been also someone narrowly kept from several dashes at connection wins between the lower two temples. Each of the other players were a couple of turns from winning with Red next closest to a building victory.
The resource distribution in the early part of the game led to two early corner builds by Green and Red while Blue and Yellow ended up a little more central. Most of the early blocking was Yellow and Blue trying to circle around each other and eventually stop red while Green was left to expand largely unmolested.
It was interesting that Red, being in a really strong resource + building positions actually had to be blocked from all four corner temples during the course of the game. It seemed far easier in a 3-player game to make several of the temples almost completely, or at least have players comprehensively block each other in the centre of the board. The four-player game's shorter and more numerous connection opportunities can make them a constant threat through much of the game.
The four-player game is certainly dynamic, and the requirement to block a player from the more frequent winning connection opportunities can be shared out more, but it may also be left up to a particular player to sacrifice resource/carrots/tiles to make the attempt and stop someone else winning. This could conceivably become degenerate, but didn't in this case. A fun game, but a longer slog than the 3-player game.
Yeah, the 4-player game has some...issues. Don't get me wrong, I enjoy it, but everyone needs to understand the Kill Dr. Lucky vibe floating around.
"It's a magical world, Hobbes, ol' buddy..."
"For the listener, who listens in the snow, and, nothing himself, beholds nothing that is not there and the nothing that is." -- Wallace Stevens
The connection threats in the four player game keep things interesting. I'm not sure that there are more threats in the four player vs. the three player version (but there are certainly more variables at work).
I do understand where you're coming from with regard to one player bearing the responsibility of blocking. It's possible that when one player is threatening a connection, two of the other players will leave the blocking responsibility to the player immediately preceding the potential winner. This is a dangerous strategy, though, if it's not obviously apparent that the chosen player has enough resources to complete the block.
This sort of issue comes up in any number of multi-player games where connecting certain territories is a victory condition (Condottiere for example). It can make the game exciting, but also a bit frustrating if you're the one getting stuck all the time.