Number of Players: 2
Board: A go board is perfect, but graph paper or any sufficiently large square grid will do.
Play: Each player secretly chooses one of the 12 twelve pentominos as eir goal pattern. (Unless you and your opponent really trust each other, it is a good idea to write these down.) They then alternate placing stones on the points on the board as in go, with the first player using black stones and the second player using white. If a player can form eir goal pentomino on the next turn-- (this includes any combination of reflections and rotations of the original--) on the next turn, e must mark a position which would allow it to be achieved. Eir opponent is then forced to place eir stone on the marked point on eir next turn. Note that only one such point must be marked, even if several threats for forming the goal pentomino are made.
Exactly once during the game each player may, before placing a stone, attempt to guess the goal pentomino of eir opponent. If the player guesses correctly, then e wins.
Strategy:
Whenever a player is missing only one point from achieving a pentomino which is not eir goal, the fact that the point is not marked will allow eir opponent to narrow down eir possible goal pentominoes. It is therefore good strategy to play in unconnected groups of two or three stones and not connect them until you have multiple attacks towards your goal pentomino while simultaneously having multiple attacks on a couple of other pentominoes. This may seem very difficult, but remember, your opponent has no idea what you are trying to do! Defensively, it is a good idea to move between your opponents groups. Even if you have no idea about your opponents goal, you stand a good chance of thwarting eir plans. Do not waste your guess until your opponent marks a threat.
[TO DO: graphic of bluffing threat]
It can work to bluff and create a threat that could belong to a large number of pentominoes, without actually having an alternate threat to win. Once your opponent has lost eir guess, e will be at a real disadvantage. However, if your opponent calls your bluff and does not use eir guess, you will have seriously narrowed down the possibilities for your own goal pentomino It is also sometimes a good idea to create a threat in a position that where your opponent will create a group of four or five by filling it, giving you information about eir goal.
As much as Pentomination is a game of pure strategy, there is a very real psychological element to it. If you've chosen different pentominoes each of the last five games, you might trick your opponent by using the same pentomino twice in a row. If you haven't made bluffing threats lately, you might get away with it in the next game.
It may be that some pentominoes are easier to win with than others. In theory, the ease of achieving a certain pentomino would be somewhat balanced by the fact that the opponent would know that it is played more often and would therefore be more likely to guess it. However, nobody knows right now which pentominoes are easiest. Harary's research shows that certain pentominoes are a guaranteed win for the first player in the simple go-moku like game, but these results might not be particularly relevent to Pentomination. I think the easiest pentominoes in Pentomination are probably the ones that fit in a 3 x 3 box, since many of them will be achievable from the same positions, offering more choices to a player forced to guess.
An additional rule for multiple game matches:
After you've played this game a few times, you'll notice a serious flaw: it is pretty rare to get a winnable position without narrowing down your possible goals to two or three pentominoes. There is therefore not sufficient reason to make any sort of offensive attack. To work around this, in a match of several games, a win by pentomino achievement should be worth two points, and a win by guessing should be worth one. Pentomination is a short enough game that you were probably going to be playing it more than once anyway, right?