[vitus]

> Actually no they won't due to parity reasons!

Can you elaborate? I think I can construct some boards that effectively have complete rotational symmetry.

For the purposes of the game, black can be thought of as another white card (since you will never reveal it in the middle of a round), and the double agent can be placed in the center. Then, you just need to place the remaining categories with rotational symmetry (e.g. red on the two main diagonals, and blue on the squares directly clockwise from those). So, for instance:

  RBwwR
  wRBRB
  wBdBw
  BRBRw
  RwwBR

(w)hite and (d)ouble-agent are in lowercase; feel free to replace any single white square with blAck (Assassin).

[anonymoushn]

Double agent isn't a color that appears on the card. A card has 7 white spaces, 1 black space, 9 spaces of one color, and 8 spaces of the other color. If you think that white and black are separate colors, you can't make a rotationally symmetric 5x5 board.

From the perspective of a player who is memorizing boards, it's beneficial to know which square is black, so as the memorizer's adversary it's probably best to put the black square in all 8 non-blue non-red squares for a given layout of blue and red squares.

[vitus]

The reason why I claim that black is uninteresting for the purposes of board memorization is that if you are explicitly stalling until there is enough information to uniquely identify the game board, then either the black square is never uncovered, or the opposing team uncovers the black square, in which case you win automatically.

It's not difficult to be adversarial against the proposed naive strategy (just generate boards with enough overlap such that you can't uniquely identify them from such a small number of revealed squares), but it's easiest to generate fully random boards (without any concerns for "weird" boards) and be done with it.

[anonymoushn]

You could eliminate a board from consideration because a square was revealed to be white rather than black.