In Monasterium, you run a cathedral school and want to place your novices in the handful of monasteries on the game board to increase the standing of your school above all others. At the end of three game years, with each year lasting 2-4 rounds depending on the number of players, you score points for having a plurality of your novices in a monastery (with ties being friendly), for having your novices in chapels (and the more chapels, the better), and (oddly) for having novices in both the chapel and the cloister at a monastery. Maybe they work in tandem to take down all of the other novices, which is why you need them in both places? I don't know.
Each round plays out in two phases: First, players take turns rolling their dice, choosing all dice of one number rolled, then placing those dice in the appropriate place on the game board. You keep taking turns until all dice have been placed, with one re-roll being possible.
Second, you take turns choosing dice from the board to take actions. You can choose only one 6 (as it's a joker that allows any available action) or up to three dice of the numbers 1-5. If dice of your color are on a space, you must take those dice before you can take neutral dice, and you can never take dice of another player's color.
To start, the actions available to all players are the same, but as you place novices on the game board, you open up other possible actions, so over the course of the game, each player develops their own action menu — which means that a 4 might be great for me while you still have only the basic "claim a rosary" action available to you.
If you clear out all of the novices in a row on your action board, you immediately place the "bonus" novice at the end of that row. Otherwise they have no chance of being freed, which seems somewhat cruel.
During the game, you score points for placing novices in buildings, for taking actions with certain die numbers (once you place a novice in a cloister to upgrade that number), and for completing rows and columns in your personal stained glass window. You also receive a bonus item for each pane you place, choosing the bonus from either the row or column of that pane.
Beyond that, you are given direction as to what you might want to do thanks to six objectives that are somewhat randomized. (I say somewhat as four of the objectives will always be about placing three novices in particular places in particular monasteries, but the other two will vary a bit more.) Direction is good since that gives you some idea of what you'll need to do first, which means you won't just be doing things for no reason. Well, you might, but you might not realize that initially...
Monasterium, as you might have gathered, is an efficiency game, with you trying to do as much as possible in the time allowed. With more players, you'll generally take fewer turns each round since more people are drafting the available dice, but each year will have more rounds, so things somewhat balance out.
Beyond that, you need a game or two to figure out how to do things better, which is true of nearly all games of this type. In our first game, the winning score was in the high 70s; for our second game, the winning score was 100; and for our third and fourth games, the winner was in the low 130s. It's easy to complain that a game is dumb and you barely did anything and this stained glass mechanism seems somewhat useless, but you might inadvertently be complaining that you are a bad player and just haven't yet understood that.
I've played Monasterium four times so far on a review copy from dlp games, twice with two players and once each with three and four, and I talk about the game in far more detail in the video below. As a bonus, here's a second video demonstrating how you can clean up after playing this game in less than a minute!
As for the availability of Monasterium outside of Germany, Reiner Stockhausen at dlp games tells me that he's consulting with U.S. publishers about licensing, and if that falls through, then possibly he can find retailers in the U.S. that can make the game available.